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u_t=u_xx, x is in [0,1], t>0

with

u(0,t)=u(1,t)=0, t>0

u(x,0)=sin(pi*x)-sin(3*pi*x), x is in (0,1)

i think its solution is of the form

u(x,t)=sigma(n=1 to infinity){a_n*sin(n*pi*x)*exp(-n^2*pi^2*t)

where a_n=2*integral(0 to 1){ (sin(pi*x)-sin(3*pi*x)) * sin(n*pi*x) }

but i have a_n = 0, for all n..

i don't know where is my mistake..

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# 1-dimensional heat equation

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