Question

The solution of the differential equation $\left(2x-10y^3\right)\frac{dy}{dx}+y=0$ is $x{y}^n=2y^m+C$ then find $n+m$.

Answer 1

Answer: 7.00

$y\frac{dx}{dy}+2x=10y^3$
$\Rightarrow \frac{dx}{dy}+\frac{2x}{y}=10y^2$
$I.F.=e^{\int \frac{2}{y}dy}=y^2$
$x.y^2=\int 10y^{4}dy$
$\Rightarrow x{y}^2=2y^5+c$