In: Advanced Math
Solve the following initial value problems and graph the
solutions at times t = 1, 2, and 3:
(a) u_t − 3u_x = 0, u(0, x) = e^−x^{2}
(b) u_t + 2u_x = 0, u(−1, x) = x/(1 + x^2)
(c) u_t + u_x + 1/2u = 0, u(0, x) = tan^−1 x;
(d) u_t− 4u_x + u = 0, u(0, x) = 1/(1 + x^2)\