Toronto Math Forum
APM3462019 => APM346Lectures & Home Assignments => Home Assignment 2 => Topic started by: Wanying Zhang on February 27, 2019, 10:30:59 PM

The problem is given:
$$u_{tt}  u_{xx} = (x^2 1)e^{\frac{x^2}{2}}$$
$$u(x,0) = e^{\frac{x^2}{2}}, u_t(x,0) = 0$$
I have already got the general solution as followed, but I have trouble solving the integral,
$$\int_{0}^{t} \int_{xt+s}^{x+ts} (y^21)e^{\frac{x^2}{2}}dyds$$
and I tried $\Delta$ method, but it seems to make the equation more complex. Professor, could you please give a hint of solving this problem?

Here is my work.
For the source, the function should be f (y,t).Hoping it could help you.