Question

Q\Determine the following ODEs are exact or not? Why?
(2xy)dx+2y^2dy=0

Answer 1

Differential equation $Mdx+Ndy=0$ is exact if and only if $\frac{\partial M }{\partial y}=\frac{\partial N }{\partial x}$.

$\frac{\partial M }{\partial y}=2x$

$\frac{\partial N }{\partial x}=2y^2.$

ODE is not exact.