d?x dy -y = 0, dt? dt dx 2- dt dz +- z = 0, dt dx dy + 3x + dt -4y+ 3z 0; dt dx x(0) = 0, (0) = = 1, y(0) = 0, z(0) = 0 dt

Q: L{t + et} =+ I. L{t + e3t} = = 1 %3D II. S-3 52 5-3 L{t + e*} =+ L{t + e#} = - III. IV. S+3 52 543

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Q: (c) Use the Laplace transform to solve the following IVP y -2y -3y = e cos(t) y (0) = y(0) = 0.

A: The objective here is to solve the given differential equation using Laplace transform: Given…

Q: (d) f"(t) - 4f (t) = sin 2t where f(0) = 1 and f'(0) = -2

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Q: (a) f(t) = cosh² t (b) f(t) = 2 sinh? 2t 2

A: To find the Laplace transforms of the given functions we will use the following table of Laplace…

Q: 5 6. (s+3)² 7. 3 s2-32 8. L{f(t)}: 3s²-1 s²+8+1

A:

Q: ut

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Q: Consider the following IVP: y"-3y'+2y = e*; y(0) = 0, y'(0) = 0 Find the general solution.

A: We solve the given DE  y"-3y'+2y=e3t.......(1) y(0)=y'(0)=0......(2)

Q: use the laplace transform to solve

A: Hi! As per norm we will be answering only the first question since both of the solutions are long.…

Q: a k 2 + k² S 2 + k² k

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Q: 5. 2cos?t 6. cosh²t

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Q: t3 - 3t2 + 5t – 8

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Q: -31 19. f(t) =re

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Q: b) F(s) = |NIN S (s+2)²+4

A: Inverse Laplace transform

Q: 3t x(t) = to

A: We have to apply the Laplace transform of the given function.

Q: x* (t) – x(t) = 4 cost with x(0) = 0, x' (0) = 1 %3D y = 2e with y(0) = – 1 y - y = e -* with y(0) =…

A: Take the Laplace transform on both sides of the equation.

Q: (ii): f(t) = sin (t + 7)+ e³' cosh 5t

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Q: f(t) = 6te-3t + te-5t sin5t + t² %|

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Q: y" + 3y - 4y = 6e²t-3, y(1.5) = 4, y'(1.5) = 5

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Q: sin 3t 4. f (t) t

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Q: Consider the following IVP: y" -3y' -10y = 1, y(0) = -1, y'(0) = 2 Find the general solution. 13 5r…

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Q: dy 2х dx - y = 6e3t, dt dt dy 3x + dt dx - 3y = 6e3t; | dt x(0) = 3, У (0) 3 0.

A: Given, dxdt-2x-dydt-y=6e3t2dxdt-3x+dydt-3y=6e3t, x0=0, y0=0   We use the Laplace transforms…

Q: on the function fcs) 35 - 17 s- 65+25 %3D

A: Inverse Laplace transform of function is : 12e3t(6cos4t-sin4t

Q: 2s – 10 -5s

A: We have to solve given problems:

Q: 4. Solve the following initial value problems using the Laplace transform: a) y' + 3y = 0, y(0) =…

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Q: Find the Laplace transform of 4t2 + 5t3.

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Q: 50 (s² + 15s + 2) 25s2 + 202s + 25

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Q: Consider the following IVP: y"- y = 4cos t; y(0) = 0, y'(0) = 1 Find the general solution. A y (1) =…

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Q: 3. F(s) = = 3s+2 (s-4) (s+1)(s-3) 4. F(s) = 5s-2 s³+3s²+s

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Q: 17 s + 675 7 270 2 s - 4s + 85

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Q: 0 9. f(t)=t-n 0 if t 2π

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Q: FIND THE INVERSE LAPLACE TRANSFORM

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Q: Find L (t*ett)

A: You asked to find inverse Laplace transform.but your image is for Laplace transform.

Q: f4(t) = costu(t-1) F4(s) = s² + 1 [s(cos 1") sin 1"]

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Q: f (t) = 3e " cosh (In 2r)

A: This is a problem of Laplace Transform.

Q: Solve the Laplace transform of: 3 cos 8t + 2 sin 8t

A: