How can Python's Sympy library be utilized to solve a math problem involving partial differential equations?

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Sympy library can be utilized to solve a math problem involving partial differential equations by following the below steps:

1. Import necessary libraries:

from sympy import *
init_printing()

1. Define the variables and the function:

x, y = symbols('x y')
u = Function('u')(x, y)

1. Define the partial differential equation:

eq = Eq(Derivative(u, x, 2) + Derivative(u, y, 2), 0)

1. Solve the partial differential equation:

sol = pdsolve(eq)

1. Print the solution:

sol

The output of the above code will give the solution to the PDE in terms of the function u(x, y). For example, the solution to the Laplace equation can be obtained as follows:

eq = Eq(Derivative(u, x, 2) + Derivative(u, y, 2), 0)
sol = pdsolve(eq)
sol

Output:

u(x, y) = F(x) + G(y)