Problem 1: Solve for the general solution y (x): dy 2y - 3-= ye3x Also, write out the particular solution when y(x = 0) = 5. Problem 2: Solve for w(x, t) by Laplace transforms a2w a2 w aw ax2 = 100 at2 + 100 + 25w at subject to the following initial and boundary conditions: w(x, t = 0) = 0, x20 aw = 0, t 20 at Ix,t=0 w(x = 0, t) = sint , t 2 0 Problem 3: Solve for y(x): x2 day_ 2 + 0.7x-- 0.1y = 0 Problem 4: Use Fourier series to evaluate the following infinite sums 1 1 1 1=1+- + + +..: 00 27 64 1 1 12 = 1 -- + +...00 8 27 64 Problem 5: Evaluate v . ((V x w) x v) when v = [2y, 2z, 4x + z] and w = [3z2, x2 - y2, y2]. Problem 6: Evaluate ff F . nidA on the surface x2 + y2 + 4z2 = 4, z 2 0 when F = [1,1,1]