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(Solved): Find the eigen-values n and eigen-functions of the differential equation dx2d2y+y=0;> ...

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Find the eigen-values

?_{n}

and eigen-functions of the differential equation

\frac{d ^{2} y}{d x ^{2}} + ? y = 0; ? > 0

with

y (0) = 0

and

y^{?} (?) = 0

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Expert Answer

Given differential equation is

Case 1 :
then

On applying initial condition

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