Change of Variables

• Feb 26th 2010, 08:27 AM
joeyjoejoe
Change of Variables
Tricky....

Reduce u'' + (ax+b)u = 0 to u'' + tu = 0 by a suitable change of variables.
• Feb 26th 2010, 09:36 AM
sashikanth
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?
• Feb 26th 2010, 09:39 AM
Mauritzvdworm
this can surely not be the whole story, since by just chosing $t=ax+b$ your problem will already be solved...

I suppose it should read like this:

$\frac{d^{2}u(x)}{dx^{2}}+(ax+b)u(x)=0$

and you want to make a substitution such that you end up with

$\frac{d^{2}u(z)}{dz^{2}}+tu(z)=0$

??