(write After use Laplace Transform to transform the following initial value problem x" + 3x' +...
QUESTION 1 use to following initial value problem (write fraction as After Laplace Transform transform the x" + 3x' + 2x=2e-t, x(0) = x'(0)=0, you should get X(s)= S-2 (S-2)/(5-4)(s+6) for (s-4)(s+6) -). Then, find x(t)= L-(x(s))= 5 -3t (write 5/6 by 6' ; e^{-3t} by e and sin(2t) or cos(3t) by sin(2t) or cos(3t)).
(write After use Laplace Transform to transform the following initial value problem x" + 2x' +x=3, x(0)=0,x'(0)=1, you should get X(s)= S-2 fraction as (S-2)/(S-4)(8+6) for -). Then, find x(t) = £-2(x(s)= (s-4)(3+6) (write 5/6 by 5 -3t 6' , e^{-3t} by e and sin(2t) or cos(3t) by sin(2t) or cos(3t)).
QUESTION 2 use to the following initial value problem (write fraction as (s- After Laplace Transform transform x" + 2x' +x=3, x(O)=0,x'(0)=1, you should get X(s)= S-2 2)/(S-4)(s+6) for (s-4)(8+6) -). Then, find x(t)= L-(x(s))= 5 -3t (write 5/6 by 6' e^{-3t} by e and sin(2t) or cos(3t) by sin(2t) or cos(3t)).
(write fraction as After use Laplace Transform to transform the following initial value problem rret, x(O)= 1,x'(0)=1, you should get X(s)= S-2 (S-2)/(5-4)(8+6) for -). Then, find x(t) = L-?{x(s)}= (s – 4)(s+6) 5 -3t (write 5/6 by 6' , e^{-3t} by e and sin(2t) or cos(3t) by sin(2t) or cos(3t)).
QUESTION 3 After use Laplace Transform to transform the following initial value problem X" +x=e-t, x(0) = 1,x'(0) = 1, S-2 you should get X(s)= (write fraction as (S-2)/(5-4)(8+6) for -). Then, find (s-4)(8+6) x(t)= L-?{X(s)}= (write 5/6 by 5 -30 6' e^{-3t} by e and sin(2t) or cos(3t) by sin(2t) or cos(3t)).
1 point) Consider the initial value problem dy 29y--9e cos( dt dt2 dt Write down the Laplace transform of the left-hand side of the equation given the initial conditions Y(sA2-10s+29)+3s-24 Your answer should be a function of s and Y with Y denoting the Laplace transform of the solution y. Write down the Laplace transform of the right-hand side of the equation -9(s-5(S-5)A2+9) Your answer should be a function of s only. Next equate your last two answers and solve...
Use the Laplace transform to solve the following initial value problem: 44" + 2y + 18y = 3 cos(3t), y(0) = 0, y(0) = 0. a. First, take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation and then solve for L{y(t)}. Do not perform partial fraction decomposition since we will write the solution in terms of a convolution integral. 3s L{y(t)}(s) = (452 + 25 +2s + 18)(52+9) b. Express the...
Hollie work #2 (Due April 1 δ) Problem Obtain the Laplace transform of each of the following functions: 2t (a) et cos 3tu(t) (c) e3 cosh 2tu(t) (e) te sin 2tu(t) (b) e2t sin 4tu(t) (d) e4 sinh tu(t) Problem 2. Find the Laplace transform of each of the following functions (b) 3f* e^ut) (c) 2n1(t)-4". δ(t) (e) 5u(t/2) (d) 2e) u(t) 2p-(t-1) (f) 6el3 u(t) d" dt" Problem 3. Find the Laplace transform of the following signals (a) f(t)-(2t...
D Question 5 D Question 7 20 pts Find the Laplace transform. £{/0) of the following function: Solve the following Initial Value Problem: " + 4y = sint - Ul(t - 2) sin(t - 2n), y(0) -0,(0) = 0 * (+64 +5) +ed (cos(36) + sin(5t)) None of the given answers is correct Owt) --sint + sin(2t) - (t - 2x)} sin(t - 2x) - sin(21 – 2*))] (t) = sint - sin(2) - 11(- 21) sin(-2) - sin(2t -...
17. Use the Laplace transform to solve the initial value problem: y" + 4y' + 4y = 2e-, y(0) = 1, (O) = 3. 18. Use the Laplace transform to solve the initial value problem: 4y" – 4y + 5y = 4 sin(t) – 4 cos(1), y(0) = 0, y(0) = 11/17.