Reduce u'' + (ax+b)u = 0 to u'' + tu = 0 by a suitable change of variables.
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Let ax+b = t, then by differenciating u(x) with respect to t twice using the chain rule you will get (a^2)u'' + tu = 0. Is this what you wanted?
this can surely not be the whole story, since by just chosing your problem will already be solved...
can you give a bit more information?
I suppose it should read like this:
and you want to make a substitution such that you end up with
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