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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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