### Author Topic: 2.4 problem4  (Read 62 times)

#### Wanying Zhang

• Full Member
• Posts: 21
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##### 2.4 problem4
« 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,
$$\int_{0}^{t} \int_{x-t+s}^{x+t-s} (y^2-1)e^{-\frac{x^2}{2}}dyds$$
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?

#### shuxian

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##### Re: 2.4 problem4
« Reply #1 on: March 14, 2019, 02:42:23 PM »
Here is my work.
For the source, the function should be f (y,t).Hoping it could help you.