Question 5 < > Given the differential equation y' + 5y' + 4y = 0, y(0)...
please solve with steps and explain thanks Question 5 Given the differential equation y'' + 5y' + 4y = 0, y(0) = 2, y'(0) = 1 Apply the Laplace Transform and solve for Y(8) = L{y} Y(8) = Now solve the IVP by using the inverse Laplace Transform y(t) = L-'{Y(s)} g(t) =
Given the differential equation y"' + 5y' – 4y = 4 sin(3t), y(0) = 2, y'(0) = -1 Apply the Laplace Transform and solve for Y(s) = L{y} Y(s) = 1
Given the differential equation y” + 5y' – 4y = 4 sin(3t), y(0) = 2, y'(0) = -1 Apply the Laplace Transform and solve for Y(s) = L{y} Y(s) = (293 +52 + 188 +21) (52 +58 - 4)( 92 +9)
Consider the initial value problem O if 0 t<3 y+5y={11 if 3 <5 if 5 t00, y(0) = 10 (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. Do not move any terms from one side of the equation to the other (until you get to part (b) below). 11 A-3s)/5-11e-5s)/5+10 (S+5)Y (b) Solve your equation for Y Y =Lly) (c) Take...
Given the differential equation y' + 367 - ezt, y(0) = 0, y'(0) = 0 Apply the Laplace Transform and solve for Y(s) = L{y} Y(s) = Now solve the IVP by using the inverse Laplace Transform y(t) = L-1{Y(s)} g(t) =
Given the differential equation y'' – 9y = - ett + 3e8t, y(0) = 0, y'(0) = 4 Apply the Laplace Transform and solve for Y(8) = L{y} Y(s) = Preview Now solve the IVP by using the inverse Laplace Transform y(t) = L '{Y(8)} g(t) = Preview
if t < 41 8(t) = 41 if t > 41 Solve the differential equation y(0) = 6, 7(0) = 5 y" +4y = g(t), using Laplace transforms. ift < 41 if t > 411
Given the differential equation y" – 4y' + 3y = - 2 sin(2t), y(0) = -1, y'(0) = 2 Apply the Laplace Transform and solve for Y(8) = L{y} Y(S) -
Consider the following IVP y″ + 5y′ + y = f (t), y(0) = 3, y′(0) = 0, where f (t) = { 8 0 ≤ t ≤ 2π cos(7t) t > 2π (a) Find the Laplace transform F(s) = ℒ { f (t)} of f (t). (b) Find the Laplace transform Y(s) = ℒ {y(t)} of the solution y(t) of the above IVP. Consider the following IVP y" + 5y' + y = f(t), y(0) = 3, y'(0) =...
Solve the following ode using Laplace transform: y' - 5y = f(t); y(0) - 1 t; Ost<1 f(t) = 0; t21