6. Suppose v"(x) = 9v(x) for 0 0 is given by u(t, x) - f(x - ct) + f(x + ct) 1 re+ct 1 prtc(t+s) + 2 g(y)dy + 2c Jo F(s, y) dyds. 2c Jx-ct Jx-c(t-8) Solve the forced initial value problem 2 u at2 272 + cost, u(0,x) = 1, at u(0, x) = 0, -00 09. (a) Use the definition f(k) = / e ika f(x)dx to compute the Fourier transform of the func- tion x , - 2