problem
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) }...