To solve differential equation ($xy^{3} + x^{2}y^{7}) \frac{dy}{dx} = 1$ The ODE is
($xy^{3} + x^{2}y^{7}) \frac{dy}{dx} = 1$
I have tried everything like integrating factor,it is not homogenous and not linear differential equation..What should be done now?

Re-arranging your differential equation, we have 
$$\frac{dx}{dy}=xy^3+x^2y^7$$
$$\frac{dx}{dy}-xy^3=x^2y^7$$
$$\frac{1}{x^2}\cdot \frac{dx}{dy}-\frac{1}{x}\cdot y^3=y^7$$
$$-\frac{d}{dy}\left(\frac{1}{x}\right)-y^3\cdot \left(\frac{1}{x}\right) =y^7$$
Put $u=\frac{1}{x}$
You get $$\frac{du}{dy}+uy^3=y^7$$
The integrating factor comes out to be $e^\frac{y^4}{4}$.
Then we have $$\frac{d}{dy}\left(ue^\frac{y^4}{4}\right)=y^7e^\frac{y^4}{4}$$
Now $$\int y^7e^\frac{y^4}{4} dy = \int y^4 e^\frac{y^4}{4} \cdot y^3 dy$$
$$=\int 4ze^z dz$$
where $z=\frac{y^4}{4}$.
Can you complete the integration now?
