The ODE with unknow r

[khanhzodoi]

$$x^2y^4 + x\frac{dy}{dx} + y = 4x^r + x^r\ln \left( x \right) $$
r is a real number.



I dont know what kind of this equation is and how to solve it, anybody help me please!!!

[HallsofIvy]

As to what kind of equation, this is a first order, nonlinear, nonhomogeneous differential equation, non-separable differential equation. I don't see any method to solve it other than numerical integration.