Hi, I need help to solve this problem, about 1-D heat equation
\partialu / \partialt = k (\partial2u / \partialx2)-2u (0< x <1)
u(x,0)=e-x
u(0,t)=e-2t
u(1,t)=0
I need to solve it with separation variable
I have a problem about Sturm-Liouville, and i can't solve it, maybe someone can help me
x2 y''+ 2xy'+ λy=0
and y(0)=0, y(e2)=0
What is the eigen value and eigenfunction of the equation?