Please, I can help with this problem of differential equations

[herguz]

For -π < x < π, consider the boundary value problem
u′′+25u=αx²⁰²¹sin(3x)+βsin(5x),
u(-π)=0,u(π)=0.
Use the Fredholm alternative theorem to determine the parameter values for α and β that yield existence of
a solution to this problem. If solutions exist, how many are there? Do not try to find the solution(s).

 

[Deleted member 4993]

For -π < x < π, consider the boundary value problem
u′′+25u=αx²⁰²¹sin(3x)+βsin(5x),
u(-π)=0,u(π)=0.
Use the Fredholm alternative theorem to determine the parameter values for α and β that yield existence of
a solution to this problem. If solutions exist, how many are there? Do not try to find the solution(s).

Please define:

the Fredholm alternative theorem​

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