Question

For the given differential equation, find the general solution: $y \ dx + (x - y^2) dy = 0$

Answer 1

Answer:

Step-by-step explanation:

Concept:

I have applied variable separable method to solve this differential equation.

$y\:dx+(x-y^2)dy=0\\\\y\:dx+x\:dy-y^2\:dy=0\\\\y\:dx+x\:dy=y^2\:dy\\\\x\:dy+y\:dx=y^2\:dy\\\\d(xy)=y^2\:dy\\\\Integrating\\\\\int{d(xy)}=\int{y^2}\:dy\\\\xy=\frac{y^3}{3}+c$