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Asked Nov 8, 2019
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2. Eigenvalue Problem with first derivative in linear operator.
Find the eigenvalues and eigenfunctions for the boundary value problem,
y"+4yA 0 on 0<x <, /(0) = 0, y'(n) = 0.
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2. Eigenvalue Problem with first derivative in linear operator. Find the eigenvalues and eigenfunctions for the boundary value problem, y"+4yA 0 on 0<x <, /(0) = 0, y'(n) = 0.

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Expert Answer

Step 1

The given boundary value problem,

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y4y'y0 on 0< x<T y'(0)0 y'(z)0

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Step 2

Find the eigen values and eigenfunctions of the given boundary value problem in the following.

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y"4yAy0 The auxiliary equation of this equation is m24m 0 The roots of this equation is, m -2t8-2 such that m =-28-a m, -2-8-2

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Step 3

Therefore, the solution o...

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y Ae"Be"* where m and m, are the roots of the given boundary value problem. and A and B are the constants.

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