In: Advanced Math
Consider the ODE u" + lambda u=0 with the boundary conditions u'(0)=u'(M)=0, where M is a fixed positive constant. So u=0 is a solution for every lambda,
Determine the eigen values of the differential operators: that is
a: find all lambda such that the above ODE with boundary conditions has non trivial sol.
b. And, what are the non trivial eigenvalues you obtain for each eigenvalue