Solve the partial differential equation 2² dr² ¥(x, y) + ¡V(x, y) = 0 2² дуг using the separattion of variables technique for partial differential equations. That is, let V(x, y) = f(x)g(y) and obtain two ordinary differential equations, one for f(x) and the other for g(y). Choose your separation constant to be k². Then, obtain the general solution to each of the ordinary differential equations. Finally, obtain the general solution for (x, y).

Solve the partial differential equation 2² dr² ¥(x, y) + ¡V(x, y) = 0 2² дуг using the separattion of variables technique for partial differential equations. That is, let V(x, y) = f(x)g(y) and obtain two ordinary differential equations, one for f(x) and the other for g(y). Choose your separation constant to be k². Then, obtain the general solution to each of the ordinary differential equations. Finally, obtain the general solution for (x, y).