Question

The solution of the differential equation:
$(2x-10y^3)\frac{dy}{dx}+y=0$ is

Answer 1

$(2x-10y^3)\frac{dy}{dx}+y=0$

$\Rightarrow$ $(2x-10y^3)+y\frac{dx}{dy}=0$

$\Rightarrow$ $y\frac{dx}{dy}+2x=10y^3$

$\Rightarrow$ $\frac{dx}{dy}+\frac{2x}{y}=10y^2$

I.F $=e^{\int \frac{2}{y}dy}=e^{2\log y}=y{}^2$

$\Rightarrow$$\frac{d}{dy}(x.y^2)=10y^4$

$\Rightarrow$ $y^{2}x=2y^5+c$

$\Rightarrow$ $x{y}^2=2y^5+c$