{"id":32327,"date":"2022-03-29T17:00:03","date_gmt":"2022-03-29T11:30:03","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=32327"},"modified":"2022-03-29T17:19:25","modified_gmt":"2022-03-29T11:49:25","slug":"ncert-solutions-for-class-12-maths-chapter-9-ex-9-5","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-5\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.5"},"content":{"rendered":"

These NCERT Solutions for Class 12 Maths<\/a> Chapter 9 Differential Equations Ex 9.5 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-5\/<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.5<\/h2>\n

\"NCERT<\/p>\n

Question 1.
\n(x\u00b2+xy)dy = (x\u00b2+y\u00b2)dx
\nSolution:
\n\"NCERT<\/p>\n

Question 2.
\ny’ = \\(\\frac { x+y }{ x }\\)
\nSolution:
\nWe have x.\\(\\frac { dy }{ dx }\\) = x + y
\nLHS as \\(\\frac { dy }{ dx }\\) and convert RHS as a function of \\(\\frac { y }{ x }\\) a homogeneous differential equation substitute v for \\(\\frac { y }{ x }\\) differential y w.r.t. x put the values of \\(\\frac { dy }{ dx }\\) and \\(\\frac { y }{ x }\\) in (1) variable separble equation of v and x Replace the value of v by \\(\\frac { y }{ x }\\)
\n\"NCERT
\nwhich the required general solution.<\/p>\n

\"NCERT<\/p>\n

Question 3.
\n(x – y)dy – (x + y)dx = 0
\nSolution:
\n(x – y)dy – (x + y)dx = 0
\ni.e., (x – y)dy = (x + y)dx
\n\"NCERT
\nis a homogeneous differential equation
\n\"NCERT<\/p>\n

Question 4.
\n(x\u00b2 – y\u00b2)dx + 2xy dy = 0
\nSolution:
\n(x\u00b2 – y\u00b2)dx + 2xy dy = 0
\n2xy dy = (x\u00b2 – y\u00b2)dx
\n\"NCERT
\nis a homogeneous differential equation
\n\"NCERT
\nwhich the required general solution.<\/p>\n

\"NCERT<\/p>\n

Question 5.
\nx\u00b2\\(\\frac { dy }{ dx }\\) = x\u00b2 – 2y\u00b2 + xy
\nSolution:
\n\\(\\frac { dy }{ dx }\\) = \\(\\frac{x^{2}-2 y^{2}+x y}{x^{2}}\\)
\n\\(\\frac { dy }{ dx }\\) = \\(1-2\\left(\\frac{y}{x}\\right)^{2}+\\left(\\frac{y}{x}\\right)\\) … (1)
\nis a homogeneous differential equation
\n\"NCERT<\/p>\n

Question 6.
\n\\(xdy-ydx=\\sqrt { { x }^{ 2 }+{ y }^{ 2 } } dx\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 7.
\n\\(\\left\\{ xcos\\left( \\frac { y }{ x } \\right) +ysin\\left( \\frac { y }{ x } \\right) \\right\\} ydx=\\left\\{ ysin\\left( \\frac { y }{ x } \\right) -xcos\\left( \\frac { y }{ x } \\right) \\right\\} xdy\\)
\nSolution:
\n\"NCERT
\nis a function of \\(\\frac { y }{ x }\\)
\n\u2234 The given differential equation is homogeneous.
\n\"NCERT
\nis the general solution of the differential equation.<\/p>\n

\"NCERT<\/p>\n

Question 8.
\n\\(x\\frac { dy }{ dx } -y+xsin\\left( \\frac { y }{ x } \\right) =0\\)
\nSolution:
\n\\(x\\frac { dy }{ dx } -y+xsin\\left( \\frac { y }{ x } \\right) =0\\)
\ni.e., x\\(\\frac { dy }{ dx }\\) = y – xsin\\(\\frac { y }{ x }\\)
\n\\(\\frac { dy }{ dx }\\) = \\(\\frac { y }{ x }\\) – sin(\\(\\frac { y }{ x }\\)) is a homogeneous differential equation.
\nPut \\(\\frac { y }{ x }\\) = v \u21d2 y = vx and \\(\\frac { dy }{ dx }\\) = v + x\\(\\frac { dv }{ dx }\\)
\n\"NCERT
\nis the general solution.<\/p>\n

Question 9.
\n\\(ydx+xlog\\left( \\frac { y }{ x } \\right) dy-2xdy=0\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 10.
\n\\(\\left( { 1+e }^{ \\frac { x }{ y } } \\right) dx+{ e }^{ \\frac { x }{ y } }\\left( 1-\\frac { x }{ y } \\right) dy=0\\)
\nSolution:
\n\"NCERT
\nis a homogeneous differential equation.
\nPut v = \\(\\frac { x }{ y }\\), \u2234 x = vy
\nDifferentiating w.r.t. y we get
\n\"NCERT
\n\\(x+y e^{\\frac{x}{y}}=C\\), is the general solution of the differential equation.<\/p>\n

\"NCERT<\/p>\n

Question 11.
\n(x + y) dy+(x – y)dx = 0,y = 1 when x = 1
\nSolution:
\n\"NCERT<\/p>\n

Question 12.
\nx\u00b2dy + (xy + y\u00b2)dx = 0, y = 1 when x = 1
\nSolution:
\nx\u00b2dy + (xy + y\u00b2)dx = 0
\nx\u00b2dy = – (xy + y\u00b2) dx
\n\"NCERT<\/p>\n

Question 13.
\n\\(\\left[x \\sin ^{2}\\left(\\frac{y}{x}\\right)-y\\right] d x+x d y=0 ; y=\\frac{\\pi}{2}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 14.
\n\\(\\frac { dy }{ dx }\\) – \\(\\frac { y }{ x }\\) + cosec\\(\\frac { y }{ x }\\) = 0; y = 0 when x = 1
\nSolution:
\n\\(\\frac { dy }{ dx }\\) – \\(\\frac { y }{ x }\\) + cosec\\(\\frac { y }{ x }\\) = 0 is a homogeneous differential equation.
\n\"NCERT<\/p>\n

Question 15.
\n\\(2xy+{ y }^{ 2 }-{ 2x }^{ 2 }\\frac { dy }{ dx } =0,y=2,when\\quad x=1\\)
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 16.
\nA homogeneous equation of the form \\(\\frac{d x}{d y}=h\\left(\\frac{x}{y}\\right)\\) can be solved by making the substitution,
\n(a) y = vx
\n(b) v = yx
\n(c) x = vy
\n(d) x = v
\nSolution:
\n\\(\\frac{d x}{d y}=h\\left(\\frac{x}{y}\\right)\\) is a homogeneous equation.
\nHence the substitution is \\(\\frac { x }{ y }\\) = v or x = vy<\/p>\n

Question 17.
\nWhich of the following is a homogeneous differential equation?
\n(a) (4x + 6y + 5)dy – (3y + 2x + 4)dx = 0
\n(b) \\((x y) d x-\\left(x^{3}+y^{3}\\right) d y=0\\)
\n(c) \\(\\left(x^{3}+2 y^{2}\\right) d x+2 x y d y=0\\)
\n(d) \\(y^{2} d x+\\left(x^{2}-x y-y^{2}\\right) d y\\)
\nSolution:
\n(d) \\(y^{2} d x+\\left(x^{2}-x y-y^{2}\\right) d y\\)
\n\"NCERT
\nHence it is a homogeneous differential equation.<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.5 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-5\/ NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.5 Question 1. (x\u00b2+xy)dy = (x\u00b2+y\u00b2)dx Solution: Question 2. y’ = Solution: We have x. = x + y …<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.5<\/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 9.5 - 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-9-5\/\" \/>\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 9.5 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.5 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-5\/ NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.5 Question 1. 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