Tricky....
Reduce u'' + (ax+b)u = 0 to u'' + tu = 0 by a suitable change of variables.
this can surely not be the whole story, since by just chosing $\displaystyle t=ax+b$ your problem will already be solved...
can you give a bit more information?
I suppose it should read like this:
$\displaystyle \frac{d^{2}u(x)}{dx^{2}}+(ax+b)u(x)=0$
and you want to make a substitution such that you end up with
$\displaystyle \frac{d^{2}u(z)}{dz^{2}}+tu(z)=0$
??