Solving Coefficient not using Fourier Series coefficient

[Alana02011114]

Given the Laplace's equation with several boundary conditions. finally i got the general solution u(x,t).
One of the condition is that:
u(1,y)=y(1-y)

After working on this I finally got:
∑An sin(π n y )sinh (π n) = y(1-y)

However, i was asked to find An, by not using Fourier series coefficient, Is it possible to do so? Cheers

 

[LCKurtz]

Given the Laplace's equation with several boundary conditions. finally i got the general solution u(x,t).
One of the condition is that:
u(1,y)=y(1-y)

After working on this I finally got:
∑An sin(π n y )sinh (π n) = y(1-y)

However, i was asked to find An, by not using Fourier series coefficient, Is it possible to do so? Cheers

No, I don't think so. That hint usually arises in a situation where, if your equation were$$\sum_{n=1}^\infty A_n\sinh(\pi n)\sin(n\pi y) = 5\sin(3\pi y)$$where you could immediately say$$A_3 \sinh(3\pi) = 5$$ and all the other $A_n=0$.