How Can This Nonlinear Differential Equation Be Solved?

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Pachito
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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
 
Last edited:
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 :
 
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  • Handwritten-style derivation of a first-order nonlinear ODE, showing y' solutions via the quadratic formula, derivation of y'' and initial conditions y(0)=0, y''(0)=kδ, and a resulting relationship k=..., ending with the implicit integral x=∫dθ/(...) giving x(y).
    EDO.JPG
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