# Forming a new solution of ODE

## Main Question or Discussion Point

Is it possible to form a new solution of a second order ODE by multiplying it by an exponential factor?

## Answers and Replies

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Not clear what you mean. In a second-order LINEAR diff eq, if you have one solution u(x) you can find the general solution by trying the form f(x)u(x) ... This should be in standard ODE textbooks.

What I mean is that I have two particular solutions even and odd that diverge at infinity, but I noted that if I multiply them by exp(-z^2 / 4) they behave properly. I'm trying to justify this procedure. Substituting the product of each back into the differential equation doesn't seem to work.

HallsofIvy