Prove that X2 – Y2 = C(X2 + Y2)2 is the General Solution of the Differential Equation (X3 – 3xy2)Dx = (Y3 – 3x2y)Dy, Where C is Parameter

Question

Prove that x² – y² = c(x² + y²)² is the general solution of the differential equation (x³ – 3xy²)dx = (y³ – 3x²y)dy, where C is parameter

Solution

The given equation is:

(x³ – 3xy²)dx = (y³ – 3x²y)dy

`=> (dy)/(dx) = (x^3 - 3xy^2)/(y^3 - 3x^2y)`

which is a homogeneous equation.therefore substituting y=vx

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Methods of Solving Differential Equations> Homogeneous Differential Equations

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Q 18 Q 17 Q 19

2016-2017 (March) Delhi Set 1

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2016-2017 (March) Delhi Set 1 (with solutions)

Q 18 | 4 marks

2016-2017 (March) Delhi Set 2 (with solutions)

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