(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

How does one find all the permissible values of [itex]b [/itex] for [itex]-{d\over dx}(-e^{ax}y')-ae^{ax}y=be^{ax}y[/itex] with boundary conditions [itex]y(0)=y(1)=0[/itex]?

Thanks.

2. Relevant equations

See above

3. The attempt at a solution

I assume we have a discrete set of [itex]\{b_n\}[/itex] where they can be regarded as eigenvalues? After that how does one find the corresponding [itex]\{y_n\}[/itex]? I am sure we substitute the [itex]\{b_n\}[/itex] into the equation, but then I still don't know how this equation is solved. Please help! Perhaps it is easier to find the permissible [itex]b[/itex]'s if we write the equation in the form [itex]y''+ay'+(a+b)y=0[/itex]?

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# Eigenvalues and eigenfunctions

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