- #1
ODEMath
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Consider the fourth order Dirichlet (biharmonic) boundary value problem
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).
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).