Question

Solve the following differential equation.

(x² − yx² ) dy + (y² + xy²) dx = 0

Answer 1

(x² − yx² ) dy + (y² + xy²) dx = 0

∴ x² (1 - y) dy = - y² (1 + x) dx

∴ `((1-y)/y^2)dy = - ((1+x)/x^2)dx`

Integrating on both sides, we get

`int(1/y^2- 1/y) dy = - int (1/x^2+1/x)dx`

∴ `-1/y - log |y| = - (-1/x + log  | x |)+c`

∴`(-1)/y - log |y| = 1/x - log  | x |+c`

∴ `log  | x | - log | y | = 1/x + 1/y + c`