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Ex 9.5, 8 - Show homogeneous: x dy/dx - y + x sin (y/x) = 0 - Ex 9.5

Ex 9.5, 8 - Chapter 9 Class 12 Differential Equations - Part 2
Ex 9.5, 8 - Chapter 9 Class 12 Differential Equations - Part 3 Ex 9.5, 8 - Chapter 9 Class 12 Differential Equations - Part 4

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Ex 9.5, 8 show that the given differential equation is homogeneous and solve each of them. + =0 Step 1: Find = y x sin Step 2. Put = F (x, y) and find F( x, y) F(x, y) = sin F( x, y) = sin = sin = F(x, y) = ( , ) F (x, y) is a homogenous function of degree 0 . So the differential equation is homogenous Step 3 : Let y = vx Solving = - sin Putting y = vx Diff w.r.t.x = x + v = x + v Putting value of = 2 + 2 2 + and y = vx in (1) = y x sin v + = sin v + = sin v = v sin v v = sin = sin = Integrating both sides = = log cot = log + log log cot + log = log log ( cot ) = log x (cosec v cot v) = C x 1 sin cos sin = C x (1 cos ) sin = C x(1 cos v) = C sin v Putting value of v = x = C sin

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.