How Can This Nonlinear Differential Equation Be Solved?

[Pachito]

Hi everybody.
Not very good in solving DE's. Here is one for the better:

ay'+by = (y'+cy)^2+d

where a,b,c and d are real positive constants.

I know that : y(0)=0 and y''(0)=k*d (k= real positive constant)

Any possible suggestions?
Thanks
Pachito

 

[JJacquelin]

I know that : y(0)=0 and y''(0)=k*d (k= real positive constant)

Two initial conditions are too much for a first oreder ODE. This implies a relationship between the coefficients of the ODE. If this relationship is not satisfied, no valid solution can be derived. See attachment :

 

[Pachito]

Thank you very much for the illumination