Please solve the following question in python language.

1. The analytic solution to the heat equation tT(t,x)=2x22T(t,x) subject the boundary conditions T(t,0)=T(t,)=0 and initial condition T(0,x)=x(x) is T(t,x)=8n=1(2n1)2sin((2n1)x)exp((2n1)22t). Generate a 2D plot where you show the temperature profiles at t=0,1,2,3,4 using 5 and 100 modes for =0.5 (in other words, rather than calculate an infinite sum, only sum the first 5 or 100 terms). Clearly label your plots. The figures should look like