# Where Did I Go Wrong In Solving This PDE?

It is a 1-D wave equation problem with fixed ends, no initial velocity, and initial displacement of $$2sin(\pi x)$$ on the interval 0<x<4, t>0.

See my attached documents of my work. I end up with a c_n value of 0 based on the integration. I am pretty confident I set up the problem correctly as it follows a similar, generalized problem in my class notes. Obviously I used actual numbers in this problem. Can anyone spot any errors in my work? Thanks for your help.

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Anyone?

Have you tried to read the thumbnails, ColdFusion85. The quality is poor.

No they aren't. Place your cursor over the picture, the magnifying glass appears. Just click and you will be able to see it fine.

unless you have a mac and then you use SHIFT +

Looking for help again. Can anyone figure out what's wrong?

Try moving this thread to the section Differential Equations...looks like thats what this is. You'll probably have a higher chance of getting help there.

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At the end of your first page, knowing that $\sqrt{\lambda} = \frac{n \pi}{4}$ you went from
$$T^{\prime \prime} - 9 \lambda T = 0 \text{ to } T^{\prime \prime} + \frac{9 n^2 \pi ^2}{16} T = 0$$.
Why'd you switch sign?

HallsofIvy
$$\sum C_n Sin(\frac{n\pi x}{4})= 2 Sin(\pi x)$$