1 point) Consider the initial value problem dy 29y--9e cos( dt dt2 dt Write down the Laplace transform of the left-hand...
(1 point) Consider the initial value problem d'y dy dt2 dt dt Write down the Laplace transform of the left-hand side of the equation given the initial conditions 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 Your answer should be a function of s only. Next equate your last two answers and solve for Y. You...
(1 point) Consider the initial value problem d2y dy 8 +41y8 cos(2t), dt dy (0) y(0) = -2 -6 dt dt2 Write down the Laplace transform of the left-hand side of the equation given the initial conditions (sA2-8s+41)Y+2s-18 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 (-8s+32)/(sA2-8s+20) Your answer should be a function of s only...
(1 point) Consider the initial value problem a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of v(t) 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) (sh2+4)Y(s)-(8s+5) Solve your equation for Y(s) b. c. Take the inverse Laplace transform of both sides of the previous equation to solve for...
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" + 3x' + 2x=2e-t, x(O) = x'(0)=0, you should get X(s)= S-2 fraction as (S-2)/(S-4)(s+6) for (s-4)(3+6) -). Then, find x(t) = L-2(x(s)= 5 (write 5/6 by 6 -3t 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)).
(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)).
1 point) Consider the initial value problem y" + 36y-cos(61), y(0)-6 (0)-8, 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(t) 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. Solv e your equation for Y (s) Y(s) = L { y(t)) = c. Take the inverse...
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)).
use the Laplace transform to solve the given initial value problem: Only problem 4,8 and 12 please 4. y" – 4y' + 4y = 0; y(0) = 1, y'(0) = 1 5. y" – 2y' + 4y = 0; y(0) = 2, y'(0) = 0 Σ Answer Solution = e 6. y" + 4y' + 297 - 2t sin 5t; y(0) = 5, 7. y" +12y = cos 2t, 22 # 4; y(0) = 1, : > Answer > Solution...