{"id":32214,"date":"2022-03-29T17:00:42","date_gmt":"2022-03-29T11:30:42","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=32214"},"modified":"2022-03-29T17:12:05","modified_gmt":"2022-03-29T11:42:05","slug":"ncert-solutions-for-class-12-maths-chapter-9-ex-9-2","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2"},"content":{"rendered":"

These NCERT Solutions for Class 12 Maths<\/a> Chapter 9 Differential Equations Ex 9.2 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.2<\/h2>\n

\"NCERT<\/p>\n

Ex 9.2 Class 12 NCERT Solutions Question 1.<\/strong>
\ny = ex<\/sup> + 1 : y”- y’ = 0
\nSolution:
\ny = ex<\/sup> + 1
\nDifferentiating w.r.t. x, we get
\ny’ = ex<\/sup>
\ni.e., y” = y’
\n\u21d2 y” – y’ = 0
\nHence y = ex<\/sup> is a solution of y” – y’ = 0.<\/p>\n

Ex 9.2 Class 12 Maths Ncert Solutions Question 2.<\/strong>
\ny = x\u00b2 + 2x + C : y’ – 2x – 2 = 0
\nSolution:
\ny = x\u00b2 + 2x + C
\nDifferentiating w.r.t. x, we get y’ = 2x + 2
\ni.e., y\u2019 – 2x – 2 = 0
\nHence y = x\u00b2 + 2x + C is a solution of y’ – 2x – 2 = 0<\/p>\n

\"NCERT<\/p>\n

Question 3.
\ny = cos x + C : y’ + sin x = 0
\nSolution:
\ny = cos x + C
\nDifferentiating w.r.t., x, we get y’ = – sin x
\ni.e., y’ + sin x = 0
\nHence y = cos x + C is a solution of y’ + sin x = 0<\/p>\n

Question 4.
\ny = \\(\\sqrt{1+x^{2}} \\quad: \\quad y^{\\prime}=\\frac{x y}{1+x^{2}}\\)
\nSolution:
\n\\(\\sqrt{1+x^{2}}\\)
\nDifferentiating w.r.t. x, we get
\n\"NCERT<\/p>\n

Question 5.
\ny – Ax : xy’ = y (x \u2260 0)
\nSolution:
\ny = Ax … (1)
\nDifferentiating w.r.t., x, we get y’ = A
\ni.e., y’ = \\(\\frac { y }{ x }\\) [From(1), A = \\(\\frac { y }{ x }\\)]
\ni.e., xy’ = y (x \u2260 0)
\n\u2234 y = Ax is a solution of xy’ = y.<\/p>\n

\"NCERT<\/p>\n

Question 6.
\ny = x sin x : xy’= y + x \\(\\sqrt{x^{2}-y^{2}}\\)
\n(x \u2260 0 and x > y or x < – y)
\nSolution:
\ny = x sinx … (1)
\nDifferentiating (1) w.r.t. x, we get
\ny’ = x cos x + sin x … (2)
\nFrom (1) sin x = \\(\\frac { y }{ x }\\)
\n\"NCERT
\n\u2234 y = x sinx is a solution of xy’ = x\\(\\sqrt{x^{2}-y^{2}}\\) + y<\/p>\n

Question 7.
\nAy = logy + C : y’ = \\(\\frac{y^{2}}{1-x y}(x y \\neq 1)\\)
\nSolution:
\nxy = logy + C
\nDifferentiating w.r.t. x, we get
\nxy’ + y = \\(\\frac { 1 }{ y }\\) y’
\ni.e., xyy’ + y\u00b2 = y’
\ny’ – xyy = y\u00b2
\ny'(1 – xy) = y\u00b2
\ni.e., y’ = \\(\\frac{y^{2}}{1-x y}\\)
\nHence xy = logy + C is a solution of y’ = \\(\\frac{y^{2}}{1-x y}\\)<\/p>\n

Question 8.
\ny – cos y = x : (ysiny + cosy + x)y’ = y.
\nSolution:
\ny – cosy = x … (1)
\nDifferentiating (1) w.r.t. x, we get
\ny’ + sin y . y’ = 1
\ni. e., yy’ + yy’sin y = y
\n(x + cos y)y’ + yy’sin y = y
\n[since from (1) y = x + cosy]
\nxy’ + y’cosy+ yy’siny = y
\n(y sin y + cos y+ x)y’ = y
\nHence y – cosy = x is a solution of
\n(y sin y + cos y + x)y’ = y<\/p>\n

\"NCERT<\/p>\n

Question 9.
\nx + y = tan-1<\/sup> y : y\u00b2y’ + y\u00b2 + 1 = 0
\nSolution:
\nx + y = tan-1<\/sup>
\nDifferentiating w.r.t. x, we get,
\n1 + y’ = \\(\\frac{1}{1+y^{2}}\\)
\ni.e., (1 + y\u00b2)(1 + y’) = y ‘
\n1 + y’ + y\u00b2 + y\u00b2y’ = y’
\ni.e., y\u00b2y’ + y\u00b2 + 1 = 0
\nHence x + y = tan-1<\/sup> is a solution of y\u00b2y’ + y\u00b2 + 1 = 0<\/p>\n

Question 10.
\n\\(y=\\sqrt { { a }^{ 2 }-{ x }^{ 2 } } x\\in (-a,a);x+y\\frac { dy }{ dx } =0,(y\\neq 0)\\)
\nSolution:
\ny = \\(\\sqrt{a^{2}-x^{2}}\\) , x \u2208 (- a, a)
\nDifferentiating w.r.t. x, we get
\n\"NCERT
\nHence y = \\(\\sqrt{a^{2}-x^{2}}\\) is a solution of x + y\\(\\frac { dy }{ dx }\\) = 0<\/p>\n

Question 11.
\nThe number of arbitrary constants in the general solution of a differential equation of fourth order are
\na. 0
\nb. 2
\nc. 3
\nd. 4
\nSolution:
\nd. 4
\nThe general solution of a differential equation contains as many arbitrary constants as the order of the differential equation. Since the differential equation is of order 4, its solution contains 4 arbitrary constants.<\/p>\n

\"NCERT<\/p>\n

Question 12.
\nThe number of arbitrary constants in the particular solution of a differential equation of third order are
\na. 3
\nb. 2
\nc. 1
\nd. 0
\nSolution:
\nd. 0
\nThe particular solution is free from the arbitrary constants.<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/ NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.2 Ex 9.2 Class 12 NCERT Solutions Question 1. y = ex + 1 : y”- y’ = 0 …<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[3],"tags":[],"yoast_head":"\nNCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2 - MCQ Questions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/ NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.2 Ex 9.2 Class 12 NCERT Solutions Question 1. y = ex + 1 : y”- y’ = 0 … NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2 Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ Questions\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/\" \/>\n<meta property=\"article:published_time\" content=\"2022-03-29T11:30:42+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-03-29T11:42:05+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@ncertsolguru\" \/>\n<meta name=\"twitter:site\" content=\"@ncertsolguru\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Prasanna\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mcq-questions.com\/#website\",\"url\":\"https:\/\/mcq-questions.com\/\",\"name\":\"MCQ Questions\",\"description\":\"MCQ Questions for Class 1 to 12\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mcq-questions.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1\",\"contentUrl\":\"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1\",\"width\":170,\"height\":17,\"caption\":\"NCERT Solutions\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/#webpage\",\"url\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/\",\"name\":\"NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2 - MCQ Questions\",\"isPartOf\":{\"@id\":\"https:\/\/mcq-questions.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/#primaryimage\"},\"datePublished\":\"2022-03-29T11:30:42+00:00\",\"dateModified\":\"2022-03-29T11:42:05+00:00\",\"author\":{\"@id\":\"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3\"},\"breadcrumb\":{\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mcq-questions.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2\"}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3\",\"name\":\"Prasanna\",\"image\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/mcq-questions.com\/#personlogo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"caption\":\"Prasanna\"},\"url\":\"https:\/\/mcq-questions.com\/author\/prasanna\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2 - MCQ Questions","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/","og_locale":"en_US","og_type":"article","og_title":"NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2 - MCQ Questions","og_description":"These NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/ NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.2 Ex 9.2 Class 12 NCERT Solutions Question 1. y = ex + 1 : y”- y’ = 0 … NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2 Read More »","og_url":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/","og_site_name":"MCQ Questions","article_publisher":"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/","article_published_time":"2022-03-29T11:30:42+00:00","article_modified_time":"2022-03-29T11:42:05+00:00","og_image":[{"url":"https:\/\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png"}],"twitter_card":"summary_large_image","twitter_creator":"@ncertsolguru","twitter_site":"@ncertsolguru","twitter_misc":{"Written by":"Prasanna","Est. reading time":"5 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebSite","@id":"https:\/\/mcq-questions.com\/#website","url":"https:\/\/mcq-questions.com\/","name":"MCQ Questions","description":"MCQ Questions for Class 1 to 12","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mcq-questions.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/#primaryimage","inLanguage":"en-US","url":"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1","contentUrl":"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1","width":170,"height":17,"caption":"NCERT Solutions"},{"@type":"WebPage","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/#webpage","url":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/","name":"NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2 - MCQ Questions","isPartOf":{"@id":"https:\/\/mcq-questions.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/#primaryimage"},"datePublished":"2022-03-29T11:30:42+00:00","dateModified":"2022-03-29T11:42:05+00:00","author":{"@id":"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3"},"breadcrumb":{"@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-2\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mcq-questions.com\/"},{"@type":"ListItem","position":2,"name":"NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2"}]},{"@type":"Person","@id":"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3","name":"Prasanna","image":{"@type":"ImageObject","@id":"https:\/\/mcq-questions.com\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","caption":"Prasanna"},"url":"https:\/\/mcq-questions.com\/author\/prasanna\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/32214"}],"collection":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/comments?post=32214"}],"version-history":[{"count":3,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/32214\/revisions"}],"predecessor-version":[{"id":37776,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/32214\/revisions\/37776"}],"wp:attachment":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/media?parent=32214"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/categories?post=32214"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/tags?post=32214"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}