The following IVP will be used for Question 1 and Question 2 on this quiz. Solve...
please do at least 2 and show every step (3) Solve the IVP using the Laplace transform +e sin( 2e cos(2t 7--2t
Please show work Question 14 5 pts Use the Laplace transform to solve the given initial-value problem. y" + 4y=f(t – 2), y(0) = 1, y (0) = 0 Oy(t) = cos(2t) + U (t – 2) · sin[2(t – 2)] Oy(t) = {U (t – 2) sin(2t) Oy(t) = {U (t – 2) sin(2(t – 2)] Oy(t) = cos(2t) + U (t – 2) sin(2t)
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)).
Detailed answer with another method then the Laplace transforms Solve the IVP using the method of Laplace transforms AND one other method of your choice. y" +5y' +6y= 2e ; y(0)=1, y'(0) = 3 TABLE 7.2 Properties of Laplace Transforms L{f'}(s) = s£{f}(s) - f(0) L{f"}(s) = s?L{f}(s) – sf(0) – f'(0) . TABLE 71 Brief Table of Laplace Transforms 50 F(x) = ${f}(s) s>0 S 1 => a S a p", n=1,2,... s>0 +1 sin bt s > 0...
Detailed answer using the Laplace Transforms method Solve the IVP using the method of Laplace transforms AND one other method of your choice. y" +5y' +6y= 2e ; y(0)=1, y'(0) = 3 TABLE 7.2 Properties of Laplace Transforms L{f'}(s) = s£{f}(s) - f(0) L{f"}(s) = s?L{f}(s) – sf(0) – f'(0) . TABLE 71 Brief Table of Laplace Transforms 50 F(x) = ${f}(s) s>0 S 1 => a S a p", n=1,2,... s>0 +1 sin bt s > 0 . s?...
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)).
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) =...
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)).
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...
PROBLEMS Solve for y. 3.1. - x + 4x + sin 6x 3.4. y + 3x = 0 3.5. (x-1)? ydx + x? (y - 1)dy = 0 Just find a solution. Solving for y is tough. Test for exactness and solve if exact. 3.6. (y - x) dx + (x? - y) dy - 0 3.7. (2x + 3y) dx + (3x + y - 1) dy - 0 3.8. (2xy Y + 2xy + y) dx + (x*y*el...