2024 Final Exam questionSolve the transient heat or mass diffusion PDE with insulated ends:deludelt=del2udelx2,00where is a constant, and u(x,t) can b= either temperature or concentration as a Linetionof position x and time t. The PDE is subject to the following conditions:Initial condition:u(x,t=0)=f(x),0xLBoundary cunditions:deludelx(x=0,t)=0,t>0deludelx(x=L,L)=0,t>0x,f(x),hy a Fourier cosincseries:a0=2L0Lf(x)dx{:an=2L0Lf(x)cos(nLx)dx.)f(x)=12a0+n=1ancos(nLx),0xwhere a0=2L0Lf(x)dx and {:an=2L0Lf(x)cos(nLx)dx.)