3) Solve for the following ODE using Variation of Parameters y' – 4y' + 4y = x?e? a) Determine the characteristic equation and its roots, and solve for the complementary solution yn (6 marks) b) Solve for particular solution Yp using Variation of Parameters (13 marks) c) What is the general solution y ? (1 mark)
Question 1. Solve the following 30d order homogeneous linear ODE which has constant coefficients y" +3y" - 4y'-6y = 0.
Solve: y' – 4y' + 3y = 9t – 3 y(0) = 3, y'(0) = 13 y(t) = Preview
Solve the following IVPs using Laplace Transform: 2) y" + 4y' + 3y = 3 ezt; y(0) = y'(0) = 0
Solve the initial-value problem. a) y', _ y'-12y = 0, y(0) = 3, y'(0) = 5 b) y"-4y'+3y 9x2 +4, y(0)-6, y(0) 8 Solve the initial-value problem. a) y', _ y'-12y = 0, y(0) = 3, y'(0) = 5 b) y"-4y'+3y 9x2 +4, y(0)-6, y(0) 8
5. Solve the linear, constant coefficient ODE y" – 3y' + 2y = 0; y(0) = 0, y'(0) = 1. 6. Solve the IVP with Cauchy-Euler ODE x2y" - 4xy' + 6y = 0; y(1) = 2, y'(1) = 0. 7. Given that y = Ge3x + cze-5x is a solution of the homogeneous equation, use the Method of Undetermined Coefficients to find the general solution of the non-homogeneous ODE " + 2y' - 15y = 3x 8. A 2...
5. Use the Laplace transform to solve the problem 2t y" + 3y' – 4y e2, = y(0) = 0, y'(0) = 0.
9. Solve the IVP with Cauchy-Euler ODE: xy"txy+4y-0; y(1)-o, y )--3 = 0 , use Variat 0 10. Given that y = GXtar2 is a solution of the Cauchy-Euler ODE x, "+ 2xy-2 Parameters to find the general solution of the non-homogeneous ODE y+2xy-y homogeneoury"rQ&)e-ar)-
(10 pts) Solve the initial value problem by Laplace transform: y" – 4y + 3y = ezt, y(0) = 0, y'(0) = 0.
Solve the following initial-value problem. y" + 3y + 4y = 282(t) - 385(t) y(0) = 1, y'(0) = -2