Question

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solve the Sturm Liouville problem

Y"+hY=0,

NB: h means lambda

y(0)+y'(0)=0
y(1)+3y'(1)=0

Answer 1

well, you know that
y = c1*sin(√k x) + c2*cos(√k x)
y' = √k(c1*cos(√k x) - c2*sin(√k x))
so,
(0+c2)+√k(c1-0) = 0
c2 = -√k*c1
thus,
y = c1√k sin(√k x) - √k*c1 cos(√k x)
y = c√k (sin(√k x)-cos(√k x))
and so
c√k(sin(√k)-cos(√k)) = 0
sin(√k)=cos(√k)
√k = π/4 or 5π/4