Use the Laplace transform to solve initial value problems
Use the Laplace transform to solve initial value problems 4. x" + 4x' + 13x =...
use laplace transform 4. x" + 4x' + 13x = te-t, x(0) = 0, x'(0) = 2.
Use the Laplace transform to solve initial value problems 5. *" + 4x = f(x); x(t) = 35. f(t – 1) sin 27 dt, x(0) = x'(0) = 0 (use a convolution theorem).
Use the Laplace transform to solve initial value problems 1. *" + 4x' + 8x = e, x(0) = x'(0) = 0.
Use the Laplace transform to solve initial value problems 3. tx" + 2(t-1)x' - 2x = 2, x(0) = 0.
Use the Laplace transform to solve initial value problems 2. x" + 6x' + 18x sin 2t, x(0) = -1, x'0) = 1.
Transform the second-order initial-value proben x"+ 4x + 13x = 40 cost, for [0,1], with X(o)=3, x'(o)=4 into a system of first order initial value problems, and use the Euler nethod with 4=0.2 to approxiuste the solution.
Solve initial value problem using Laplace transform Problem 4 Solve the initial value problems given below --ез, y(0) 2. a. b. f ty 3 cos t, y(0)-
Use the Laplace transform to solve initial value problems 6. tx" - 2x' + tx = 0, x(0) = 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
In Problems 41 , use the Laplace transform to solve each system. 41 x' + y=t 4x+y'=0 x(0,-1, y(0)-2 41 x' + y=t 4x+y'=0 x(0,-1, y(0)-2