Solving a PDE using separation of variables

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  • Typed boundary value problem for Laplace's equation: v_xx + v_yy = 0 for x>0, y>0; v_x(0,y) - hv(0,y) = 0 for y>0; v(x,0) = T_0 for x>0; v(x,y) to 0, v_x and v_y to 0 as x^2 + y^2 to infinity.
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Have you tried looking for a solution of the form $v(x,t)=X(x) \cdot T(t)$ ?
 

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