{"id":32216,"date":"2022-03-29T17:00:41","date_gmt":"2022-03-29T11:30:41","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=32216"},"modified":"2022-03-29T17:10:51","modified_gmt":"2022-03-29T11:40:51","slug":"ncert-solutions-for-class-12-maths-chapter-9-ex-9-1","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-1\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.1"},"content":{"rendered":"

These NCERT Solutions for Class 12 Maths<\/a> Chapter 9 Differential Equations Ex 9.1 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-1\/<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.1<\/h2>\n

\"NCERT<\/p>\n

Question 1.
\n\\(\\frac { { d }^{ 4 }y }{ { dx }^{ 4 } } +({ sin }y^{ “‘ })\\) = 0
\nSolution:
\nThe highest order derivatives is \\(\\frac { { d }^{ 4 }y }{ { dx }^{ 4 } }\\)
\n\u2234 Order of the equation is 4
\nThe differential equation is not a polynomial equation in its derivatives.
\nHence its degree is not defined.<\/p>\n

Question 2.
\ny’ + 5y = 0
\nSolution:
\nThe highest order derivative is y’
\n\u2234 Order is 1
\nThis is a polynomial equation in y’ and the
\nHence its degree is 1.<\/p>\n

\"NCERT<\/p>\n

Question 3.
\n\\({ \\left( \\frac { ds }{ dt } \\right) }^{ 4 }+3s{ \\left( \\frac { { d }^{ 2 }s }{ { dt }^{ 2 } } \\right) }\\) = 0
\nSolution:
\nThe highest order derivative is \\(\\frac{d^{2} s}{d t^{2}}\\)
\n\u2234 Order is 2
\nThis is a polynomial equation in \\(\\frac{d^{2} s}{d t^{2}}\\) and \\(\\frac{ds}{dt}\\) and the power of \\(\\frac{d^{2} s}{d t^{2}}\\) is one
\nHence its degree is one.<\/p>\n

Question 4.
\n\\({ \\left( \\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \\right) }^{ 2 }+cos\\left( \\frac { dy }{ dx } \\right) =0\\)
\nSolution:
\nThe highest order derivatives is \\(\\frac{d^{2} y}{d x^{2}}\\)
\n\u2234 Order of the equation is 2
\nThe differential equation is not a polynomial equation in its derivatives.
\nHence its degree is not defined.<\/p>\n

\"NCERT<\/p>\n

Question 5.
\n\\(\\frac { { d }^{ 2 }y }{ { dx }^{ 2 } }\\) = cos3x + sin3x
\nSolution:
\nThe highest order derivative is \\(\\frac{d^{2} y}{d x^{2}}\\)
\n\u2234 Order is 2
\nThis is a polynomial equation in \\(\\frac{d^{2} y}{d x^{2}}\\) and the power of \\(\\frac{d^{2} y}{d x^{2}}\\) is one
\nHence its degree is one.<\/p>\n

Question 6.
\n\\({ { (y }^{ ”’ }) }^{ 2 }+{ { ( }y^{ ” }) }^{ 3 }+{ { (y }^{ ‘ }) }^{ 4 }+{ y }^{ 5 }\\) = 0
\nSolution:
\nThe highest order derivative is y”‘
\n\u2234 Order is 3
\nThis is a polynomial equation in y”‘, y” and y’ the power of y” is two.
\nHence its degree is 2.<\/p>\n

Question 7.
\ny”‘ + 2y” + y\u2019 = 0
\nSolution:
\nThe highest order derivative is y”‘
\n\u2234 Order is 3
\nThis is a polynomial equation in y”‘, y” and y’ and the power of y”‘ is one.
\nHence its degree is 1.<\/p>\n

\"NCERT<\/p>\n

Question 8.
\ny’ + y = ex<\/sup>
\nSolution:
\nThe highest order derivative is y’.
\n\u2234 Order is 1
\nThis is a polynomial equation in y’ and the power of y’ is one.
\nHence its degree is 1.<\/p>\n

Question 9.
\ny” + (y’) +2y = 0
\nSolution:
\nThe highest order derivative is y”
\n\u2234 Order is 2
\nThis is a polynomial equation in y” and
\ny’ and the degree of y\u201d is one.
\nHence its degree is 1.<\/p>\n

Question 10.
\ny” + 2y’ + sin y = 0
\nSolution:
\nThe highest order derivative is y”.
\n\u2234 Order is 2
\nThis is a polynomial equation in y”, y’ and the power of y” is one.
\nHence its degree is 1.<\/p>\n

Question 11.
\nThe degree of the differential equation
\n\\({ \\left( \\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \\right) }^{ 3 }{ +\\left( \\frac { dy }{ dx } \\right) }^{ 2 }+sin{ \\left( \\frac { dy }{ dx } \\right) }+1=0\\)
\n(a) 3
\n(b) 2
\n(c) 1
\n(d) not defined
\nSolution:
\nThe differential equation is not a polynomial equation in derivatives. Hence the degree is not defined.<\/p>\n

\"NCERT<\/p>\n

Question 12.
\nThe order of the differential equation
\n\\({ 2x }^{ 2 }\\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -3\\frac { dy }{ dx } +y=0\\)
\n(a) 2
\n(b) 1
\n(c) 0
\n(d) not defined
\nSolution:
\nThe highest order derivative is \\(\\frac{d^{2} y}{d x^{2}}\\)
\n\u2234 Order is 2.<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.1 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-1\/ NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.1 Question 1. = 0 Solution: The highest order derivatives is \u2234 Order of the equation is 4 The …<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.1<\/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 9.1 - 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-9-1\/\" \/>\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 9.1 - 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