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By first looking for a separable solution of the form u(x, y)=X(x)Y(y), find the general solution of the equation given above.

Determine the u(x,y) which satisfies the boundary condition u(1,y)=1+siny

For the separable form I have u(x, y)=A(x^c)(y^2c), could someone please show me how to do the rest of it.

Thank you.