MTH 425 Lecture Notes - Lecture 14: Computer-Aided Technologies

Solve the Cauchy-Euler equation on the interval (0, 00).

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.