How to solve the ODE y' = (4 + y +1)^2

[mohdfasieh]

hello genius guys,
can u people tell me the solution of differential equation dy/dx=(4x+y+1)^2

please replyy
thz in advance

 

[arildno]

Introduce the new function: u(x)=4x+y(x)+1
Then, you have:
$$\frac{du}{dx}=4+\frac{dy}{dx}=4+u^{2}$$
The diff.eq in u is separable.