Vibrating string and d alemberts solution in wave equation

Question

Problem:

Vibrating String and d'Alembert's Solution in Wave Equation

1. Show that, like the wave equation, the given PDE is hyperbolic and find its general solution by introducing the suggested change of variables.

a) u_xx + 4u_xy + 3u_yy = 0; ξ = x - y, n = 3x - y.

b) u_xx - 4u_xy + 5u_yy = 0; ξ = x - y, n = 5x - y

c) u_xx + 6u_xy + 8u_yy = 0; ξ = 4x - y, n = 2x - y

d) u_xx + 4u_xy + 5u_yy = 0; ξ = x + y, n = 5x - y

e) u_xx + 2u_xy + 3u_yy = 0; ξ = 3x - y, n = x + y

(Please solve for only part (b).)
(The problem is from Vibrating String; d'Alembert's Solution in Wave Equation.)