# Forming a new solution of ODE

1. Apr 17, 2010

### intervoxel

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

2. Apr 18, 2010

### g_edgar

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.

3. Apr 18, 2010

### intervoxel

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.

4. Apr 18, 2010

### HallsofIvy

Staff Emeritus
In general, no. Multiplying a solution to a d.e. by another function, exponential or not, does NOT give a new solution.