(10 point) Solve the following initial value problems. a) y"+ 4y' + 8y = 40cos(2x), y(0) = 8, y'(0) = 0 b) y" + 6y' + 13y = 12e-3xsin(2x), y(0) = 0, y'(0) = 0 (10 point) Find a general solution of each of the following nonhomogeneous equations. a) y" + 4y = 12x−8cos(2x) b) y(4)− 4y" = 16+32sin(2x)
Solve the initial value problem y" – 4y' + 4y = 0, y(0) = -3, y'(0) = -17/4
3) Solve the initial value problem. a) nie - 2x(y2 – 2y) = 0, with y(0) = 4 b) (-4y cos x + 4 sin I Cos I + sec? x)dx + (4y - 4 sin x)dy = 0, with y ) = 1
17. Use the Laplace transform to solve the initial value problem: y" + 4y' + 4y = 2e-, y(0) = 1, (O) = 3. 18. Use the Laplace transform to solve the initial value problem: 4y" – 4y + 5y = 4 sin(t) – 4 cos(1), y(0) = 0, y(0) = 11/17.
Solve the initial value problem: 34" + 4y' – 4y = e-2 with y(0) = 2, y(0) = 0. (Use the Euler-Cauchy method of characteristics, or the Laplace transform).
5. Solve the initial value problem y" + 4y = 2 + 3e", y(0) = 0, y(0) = 2.
Solve the given initial value problem. y'' + 4y' = 0; y(0) = 6, y'(0) = - 16 The solution is y(t) = _______
Solve the given initial value problem. y'' – 4y'' +10y' - 12y = 0; y(0) = 1, y'(0) = 0, y''(O) = 0 y(t)=
Use the Laplace transform to solve the given initial-value problem. Y" – 4y' + 4y = t3e2t, y(0) = 0, y'0) = 0 y(t) = 2016-2 Need Help? Read It Talk to a Tutor
Use the Laplace transform to solve the initial value problem: y' + 4y = cos(2t), y(0) = 0, y'(0 = 1.