Solution of the differential equation {1/x - y^2/(x-y)^2}dx + {x^2/(x-y)^2 - 1/y}dy = 0 is

Question

Solution of the differential equation \(\left\{ \frac 1x - \frac{y^2}{(x-y)^2}\right\}dx + \left\{\frac{x^2}{(x-y)^2} - \frac 1y\right\}dy = 0\) is

a. \(log_e\frac xy + \frac{xy}{x-y} = C\)

b. \( \frac{xy}{x-y} = C.e^{x/y}\)

c. \(log_e\frac xy =C+ \frac{xy}{x-y} \)

d. None of these

Answer 1

Correct option is a. \(log_e\frac xy + \frac{xy}{x-y} = C\)