Suppose that X' = k1X1 with aX1 (0) + bX;(0) = 0 and cX1(L) + dX; (L) = 0 and X2 = K2X2 with aX2(0) + bX2(0) = 0 and cX2(L) + dX2(L) = 0 where a, b, c, d, L, k1 and k2 are constants and L > 0. Prove that if k1 * k2, then X1 (xx ) X2(x) dx = 0 Hint: Multiply the first ODE by X2 and multiply the second ODE by X1 and then subtract the two equations