I need help with solving this differential equation
(y'')^2 + y' + y = f (x)
please suggest me how to solve this differential equation.
Thank you for your time
I would rewrite it as a first order system,
v'=sqrt(f-v-y); y' = v
and solve it numerically, keeping the two possible signs of the square root in mind.
I don't think there is much hope for analytic solutions, except perhaps for very special cases of f(x).
I am searching for applications of third-order linear differential equations.
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