- #1
buffordboy23
- 548
- 2
Homework Statement
Solve the differential equation:
[tex] A\left(x\right)\frac{d^{2}u}{dx^{2}} + A'\left(x\right)\frac{du}{dx} + \frac{1}{A\left(x\right)}u = 0 [/tex]
where
[tex] u\left(x\right) = exp\left(c\int^{x}A\left(x'\right)^{q}dx'\right) [/tex]
for some contants c and q.
The Attempt at a Solution
I tried substitution to obtain the constants c and q and also tried solving for A(x). I did not post my work since I don't even know if the approach is correct. I never saw a problem like this. The textbook does not offer any assistance, nor could I find anything on the internet. I do know that there should be two linear independent functions since it is a second-order equation. Any hints on solving the problem or suggestion of topics to research to help solve the problem would be appreciated.