Deadline to submit an answer is this Sunday.
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my guess(wolfram alpha) is sin(t)sin(x)
Haha nice guess. Heres a hint the answer is is in the form
u(t,x) = sin(pi×x) + sin(2pi×x) + sin(3×x).
You have to find the particular solution (nonhomogenous)
Then you have to compare the particular solution to f(x) = sin(2pi×x) (homogenous) part using the formula lossu gave in my discord to find what Bn is equal to. Then you multiply sin(2pi×x) above by Bn & e^(n²pi²t).
Basically, you have to find nonhomogenous part. Its diffiucult but do-able. If no one submits a close answer by friday I will post a better hint.
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I only got as far as diffeq not partial diffeq 
I got the answer somwhere ill get to u by the weekend