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 <\/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 <\/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
<\/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 \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
<\/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>\nQuestion 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 \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
<\/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 \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n