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

It is given that (x3–3xy2) dx = (y3–3x2y)dy - --------(1)

Now, let us take y = vx  Now, substituting the values of y and in equation (1), we get,      On integrating both sides we get, --------(2)

Now,  ---------(3)

Let    Now,  Let v2 = p    Now, substituting the values of I1 and I2 in equation (3), we get, Thus, equation (2), becomes,    (x2 – y2)2 = C’4(x2 + y2 )4

(x2 – y2) = C’2(x2 + y2 )

(x2 – y2) = C(x2 + y2 ), where C = C’2

Therefore, the result is proved.

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