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# Help with a partial differential equation question?

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- MathguyLv 51 month ago
I'll give it a shot......

u_xx - xt^2 = 0 u_xx = xt^2 u_x = ∫ xt^2 dx = (1/2)x^2 t^2 + C1

where C1 = f(t)

u = ∫ [ (1/2)x^2 t^2 + C1 ]dx = (1/6) x^3 t^2 + ( C1 ) x + C2

where C2 = g(t)

Now boundary conditions.....

u(0,t) = 0 + 0 + C2 = t^2 + 1 so C2 = t^2 + 1

u(1,t) = (1/6)t^2 + C1 + t^2 + 1 = (4/3)t^2

C1 = (4/3)t^2 - (1/6)t^2 - [ t^2 + 1 ]

C1 = (1/6)t^2 - 1

u(x,t) = (1/6) x^3 t^2 + ( (1/6)t^2 - 1 )x + ( t^2 + 1 )

double checking... u_x = (1/2)x^2 t^2 + (1/6)t^2 - 1

u_xx = x t^2 + 0 so u_xx - xt^2 = 0 :-) I think this works !!!

It's been awhile since I've done PDE but I used to solve them all the time before !!! don't forget to choose a Best Answer.....

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