Problem 6 Solve the following IVP: a) y" – 4y" +20y'=0 ; y0)=2 , y'(0)=0, y"(0)...
4. Solve the IVP y" + 4y = 36t² + 34t, y(0) = 0, y0) = 0 b) 4y" - y'= 4 + 122, y(0) = 0, 7(0) = 0, y"0) = 0
Mathematical Physics 2 H.W.4 y"+y-6y y+4y+4y y"+y0 y(0) 2 and y '(0) Subject to the initial conditionns 1 y"-y0 y(0) 2 and y'(0) = 1 Subject to the initial conditions yy'-12y 0 y(0) 2 and y '(0) 1 Subject to the initial conditions y"-4y xe Cos2x y"-2y'x+ 2e y"+y=sinx "-4y'+13y= e cos3x Solve the boundary-value problem y(0) = 1 and y(1) = 3 y"+ 2y'+y=0 Solve the initial-value differential equation y"+ 4y'+4y=0 subject to the initial conditions y (0) =...
4. (10 points) Solve the given IVP: y'"' + 8y" +22y' + 20y = 0; y(0) = 0, y'(0) = 1, y" (0) = 2.
Consider the IVP y" - 4y' + 4y = 0, y = -2, y'(0) = 1 a. Solve the IVP analytically b. Using step size 0.1, approximate y(0.5) using Euler's Method c. Find the error between the analytic solution and the approximate solution at each step
Solve the IVP: y''+4y=0 with y(0)=-3 and y'(0)=6 Please show how you get yP.
Question 1: [25 pts] Consider the IVP y" – 4y' - 5y = 0, y(0) = 1, y0) = 2. a) Find the solution of the given IVP using the corresponding characteristic equation. b) Find the solution of the IVP using the Laplace Transform. c) Does the solution change if we would change the second initial condition as y'(0)=3? Explain.
Use the Laplace Transform to solve the following IVP y' + 4y = t2 , y(0) = 0
Solve the following IVP: dy/dx + 4y - e^-x = 0 ; y(0) = 4/3
6. Solve the given initial value problem, with y0 = 2 and y'0) = 5: y" - 6y' + 5y = 20t +1
use method of undetermined coefficients to solve ivp y" - 4y' - 12y = 3e^5x, y(0) = 18/7, y'(0) = -1/7