Ex 9.5, 2 - Show homogeneous: y' = x+y / x - Solving homogeneous differential equation

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  1. Chapter 9 Class 12 Differential Equations
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Ex 9.5, 2 In each of the Exercise 1 to 10 , show that the given differential equation is homogeneous and solve each of them. = + Step 1: Find = + Step 2. Putting F(x, y) = and find F( x, y) So, F(x, y) = + F( x, y) = + = ( + ) = + = F(x, y) = F(x, y) Therefore F(x, y) Is a homogenous function of degree zero. Hence is a homogenous differential equation Step 3: Solving by putting y = vx Put y = vx. differentiating w.r.t.x = x + = + v Putting value of and y = vx in (1) = + + v = + + v = 1+ = 1+ = 1 = 1 Integrating both sides = v = log + Putting v = = x log + cx is the general solution of the given differential equation

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