Consider the ODE u" + lambda u=0 with the boundary conditions u'(0)=u'(M)=0, where M is a...

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Consider the ODE u" + lambda u=0 with the boundary conditionsu'(0)=u'(M)=0, where M is a fixed positive constant. So u=0 is asolution for every lambda,

Determine the eigen values of the differential operators: thatis

a: find all lambda such that the above ODE with boundaryconditions has non trivial sol.

b. And, what are the non trivial eigenvalues you obtain for eacheigenvalue

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