(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

a) Solve for the BVP. Where A is a real number.

b) For what values of A does there exist a unique solutions? What is the solution?

c) For what values of A do there exist infintely many solutions?

d) For what values of A do there exist no solutions?

2. Relevant equations

y'' + y = A + sin(2x)

y(0) = y'([tex]\pi[/tex]/2) = 2

3. The attempt at a solution

y = y_{h}+ y_{p}

0 = 1+ [tex]\lambda[/tex]^{2}

y_{h}=c_{1}*cos(x) + c_{2}*cos(x)

y_{p}= A + B*sin(2x)

y = A + B*sin(2x)

y'' = -4B*sin(2x)

A + sin(2x) = A -3B*sin(2x)

A = A, B = -1/3

y_{p}= A - 1/3*sin(2x)

y = A - 1/3*sin(2x) + c_{1}*cos(x) + c_{2}*sin(x)

y' = - 2/3*sin(2x) - c_{1}*sin(x) + c_{2}*cos(x)

2 = A + c_{1}

2 = 2/3 + c_{2}

c_{2}= 8/3

y = A - 1/3*sin(2x) + c_{1}*cos(x) + 8/3*sin(x)

I'm confused about answering the questions. A would be equal to all real numbers, since one could solve for c_{1}. How can I give the solution? There is a unique solution for each value of A, which I would have to write infinte solutions. And there is no value of A when there is an inifiite amount of solutions or no values.

IF A is defined, what would the answer be?

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# Homework Help: Boundary value problem

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