+G(r+ct) u(x, 0) = 4e- SEPARATION OF VARIABLES 12.46. Solve each of the following boundary-value problems by the method of separation of variable ди อน (a) 3. +2. = 0, ax შეყ อน (b) = ди 2 + U, u(x, 0) =3e-5+2e-3x ax ди (c) = at ay Ju 4- მე2 * u(0,t) = 0, u(r,t) = 0, u(x, 0) = 2 sin 3x - 4 sin 5x 3 *#6 (d) 2 მა Ju ux(0, t) = 0, u(2,t) = 0, u(x, 0) = 8 cos - 6 cos at ax2 Solve the boundary-value problem J²y at2 = 4- อม 8x2 y(0,t) =y(5,t) = 0, y(x, 0) = 0, y(x, 0) = f(x). if (a) f(x) = 5 sin rx, (b) f(x) = 3 sin 2x - 2 sin 5rx.