I'd love your help with solving this following differential equation: $(2x^3y^2-y)dx+(2x^2y^3-x)dy=0.$
I tried to use check if this is an exact equation and find a integration, but it didn't work. Then I tried to divide the equation by some factor and to use some kind of assignment such as $z=\frac{y}{x}$, but it didn't work for me either.
Any suggestions?
($y$ is a function of $x$)
Even though Julian answer is great, I wonder if there's a solution without an integration depends both on x and y.
Thanks a lot!