Question

Find the general solution of the following differential equation:

(1 – x²) dy + xy (1 – y) dx = 0

Answer 1

(1 – x²) dy = - xy (1 – y)dx

(1 – x²) dy = xy (y – 1)dx

\(\frac{1}{y(y-1)}dy\) = \(\frac{1}{1-x^2}dx\)

Integrating on both the sides,

Comparing coefficients in both the sides, 

A = - 1, B = 1

RHS:

\(\int\frac{x}{1-x^2}dx\)

Multiply and divide 2

Therefore the solution of the given differential equation is