Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

Use the method if eigenvalue expansions to solve 

y"+lamda*y=x^2

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

Expert Solution
Check Mark
Step 1

We will be solving y''+λy=x2, along with the boundary conditions y'(0)=0, y'(1)=0 by the eigenvalue expansions method.

First, we will solve the corresponding homogeneous equation, that is y''+λy=0 satisfying the boundary conditions y'(0)=0, y'(1)=0.

Now, the auxiliary equation is m2+λ=0. Then m=±iλ.

So, the general solution is y=c1 cosλx + c2 sinλx. 

 

 

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