Consider the fourth order Dirichlet (biharmonic) boundary value problem(adsbygoogle = window.adsbygoogle || []).push({});

y^(4) + [ lambda - q(t)] y = 0 in ( 0,1),

y(0) = y'(0) = 0

y(1) = y'(1) = 0

Where q : [0,1] -> R is continuous function. Prove that if phi(t, lambda 1) and phi(t, lambda 2) are solutions of this equation corresponding to distinct values of lambda, i.e., lambda 1 doesn't equal lambda2, then functions phi(t, lambda 1) and phi(t, lambda2) are orthogonal on (0,1).

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# Homework Help: Fourth order Dirichlet bounday value problem

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