Consider the initial value problem y'' – 2y' – 8y = 0, y(0) = a, y'(0)...
Consider the initial value problem y'' + 2y' – 15y = 0, y0) = a, y'0 = 1 Find the value of a so that the solution to the initial value problem approaches zero as t → a= Preview Get help: Video Points possible: 2 Unlimited attempts.
Solve 2y'' – 5y' – 25y = 0, y(0) = -6, y'(0) = – 15 (t) = Consider the initial value problem y' + 3y' – 10y = 0, y(0) = a, y'(0) = 3 Find the value of a so that the solution to the initial value problem approaches zero as t + oo a = 1
21. Solve the initial value problem y" - y-2y= 0, y(0) = a , y ( 0) the solution approaches zero as t 0o. 2. Then find a so that
Consider the initial value problem y'' + y' – 12y = 0, y(0) = a, y'(0) = 5 Find the value of a so that the solution to the initial value problem approaches zero ast → a = Preview
(2 points) Consider the initial value problem y' +8y +41y = g(t), y(0) = 0, y(0) = 0, where g(t) = if 9 t<oo. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y() by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below) ! help (formulas) b. Solve your equation for...
Consider the initial value problem for function y, y" – ' - 20 y=0, y(0) = 2, 7(0) = -4. a. (4/10) Find the Laplace Transform of the solution, Y(8) = L[y(t)]. Y(8) = M b. (6/10) Find the function y solution of the initial value problem above, g(t) = M Consider the initial value problem for function y, Y" – 8y' + 25 y=0, y(0) = 5, y(0) 3. a. (4/10) Find the Laplace Transform of the solution. Y(s)...
please show all steps , thank you 6. Consider the initial value problem y" + 2y' + 2y = (t – 7); y(0) = 0, y'(0) = 1. a. Find the solution to the initial value problem. (10 points) b. Sketch a plot of the solution for t E (0,37]. (5 points) c. Describe the behavior of the solution. How is this system damped? (5 points)
Consider the differential equation y" + 8y' + 15 y=0. (a) Find r1 r2, roots of the characteristic polynomial of the equation above. = 11, 12 M (b) Find a set of real-valued fundamental solutions to the differential equation above. yı(t) M y2(t) M (C) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = 4, y(0) = -3. g(t) = M (10 points) Solve the initial value problem y" - 54' +...
Consider the initial value problem y" +3y' +2y = (t-1)+r(t), y(0) = y(0) = 0, where 8(t-1) is Dirac's delta function and S4 if 0<t<1 r(t) 8 if t > 1 (a) Represent r(t) using unit step functions. (b) Find the Laplace Transform of 8(t-1)+r(t). (c) Solve the above initial value problem. {
Find the solution to y" + 2y' – 8y =0.