Further Explorations 9. Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. To solve the equation y? + ty? + 4y = 0 you should use the trial solution y = e^rt. b. The equation y? + ty? + 4t^2y = 0 is a Cauchy-Euler equation. c. A second-order differential equation with constant real coefficients has a characteristic polynomial with roots 2 + 3i And-2 + 3i. d. The general solution of a second-order homogeneous differential equation with constant real coefficients could be y = c1 cos 2t + c2 sin r cos t. e. The general solution of a second-order homogeneous differential equation with constant real coefficients could be y = C1 cos 2t + c2 sin 3t.
