I'm trying to solve a second order ODE in the form of Ay''+By'+1=0. This is part of a genetics problem I have, but I haven't taken DiffEq in a very long time and can't quite remember how to go about solving this. Can anyone help?
I would write the ODE as follows:
The characteristic roots are:
and so the homogeneous solution is:
I would next assume a particular solution of the form:
Now, we may use the method of undetermined coefficients to find :
and we have:
By superposition, we now may write the general solution: