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

u[itex]_{t}[/itex]=3u[itex]_{xx}[/itex] x=[0,pi]

u(0,t)=u(pi,t)=0

u(x,0)=sinx*cos4x

2. Relevant equations

3. The attempt at a solution

with separation of variables and boundry conditions I get:

u(x,t)= [itex]\sum[/itex]B[itex]_{n}[/itex]e[itex]^-3n^{2)}}*sinnx[/itex]

u(x,0)=sinx*cos4x

f(x)=sinx*cos4x=[itex]\sum[/itex]B[itex]_{n}*sinnx[/itex]

And here is where I am stuck! I tried computing B[itex]_{n} by computing it like a Fourier coeff. of f(x) but all I got was zero... I don't really know where to go from here.

I'm having a hard time with Fourier analysis, that's why I have bombarded this forums with question these last couple of days. I really appreciate the help I get.

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# Homework Help: PDE: heat equation

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