determine la solucion no trivial x=x(t) del p.v.i tx^n(t)+tx´(t)-x(t)=0, x>0; x(0)=0
15) 5. Use Laplace transforms to solve the initial value problem y" + y = g(t),...
cometeness and clarity please ! 1. Solve the initial value problem using Laplace transforms. ſi ost<5 y" - 5y + 4y = 0 t25 y(0) = 0, 7(0) = 1
So 0<t<5 Using the Laplace transform, solve the initial value problem y' + y = 3 t5 y'(0) = 0. 9
Use the Laplace transform to solve the given initial-value problem. so, 0 <t< 1 y' + y = f(t), y(0) = 0, where f(t) 17, t21 y(t) = + ult-
2. Use the Laplace Transform to solve the initial value problem y"-3y'+2y=h(t), y(O)=0, y'(0)=0, where h (t) = { 0,0<t<4 2, t>4
Use the Laplace Transform to solve each of the following initial-value problem (b) y'(t) + 16y(t) = f(t), y(0) = 2, y'(0) = 1. where f(t) is defined by (t) = , 1, 0 <t<, 10, t>,
QUESTION 3 Use Laplace Transform to solve the initial value problem y" + 9y = f(t) ,y(0) = 1, y'(0) = 3 where 6, f(t) 0 <t<nt i < t < 0
(10 pts) Use Laplace Transforms to solve the initial value problem y" - 6y +9y = t?e3 y(0) = 0,(0) = 0.
4. Use the Laplace transform to solve the initial value problem y" + y = f(1) = -2, ost<2 13t+4, 122 y(0) = 0, y'(0) = -1
2. Use the methods of Laplace transforms to solve the initial value problem y" – yr e-t sin 2t, y(0) = 0, y'(O) = 0.
Use the Laplace transform to solve the given initial-value problem. Use the table of Laplace transforms in Appendix III as needed. y" + 25y = f(t), y(0) = 0, y (O) = 1, where RE) = {cos(5€), Ostan (Σπ rce) = f sin(51) + (t-1) -sin 5(t-T) 5 Jault- TE ) X