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## Homework Statement

I have found the general solution to a second order pde to be

U(x,t) = f(3x + t) + g(-x + t) where f and g are arbitrary functions

I have initial conditions

U(x,0) = sin(x)

Du/dt (x,0) = cos (2x)

## The Attempt at a Solution

I have found that

U(x,0) = f(3x) + g(-x) = sin(x)

Du/dt(x,0) = f'(3x) + g'(-x) = cos(2x)

From this point I am not sure what to do. I have tried differentiating u(x,0) with respect to x which i think gives me

Du/dx (x,0) = 3f'(3x) - g'(-x) = cos (x)

I thought i would then equate the equations but I am not actually sure ths helps.

Could someone please point me in the right direction for this question

Thanks