) x -い×+ 8X =e 3€ %3D t=0,X=0 X =2

Q: (b) L-¹{12} 8²-68+12}

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Q: у" +у%3D0.001t?, У (0) %3D 0, у'(0) %3D 1.5

A:

Q: Example 7.5 Determine the Inverse Laplace Transform of the following expressions using Partial…

A: We use the table of Laplace transform to solve the given question.

Q: 1. Solve: 2y' — y y (1) = es; y (0) = 2 ? Which of the following is within 0.01 of the right answer:…

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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: t¢ (0, 5 te (0, 5 æ' (t) + 3.x (t) = f (t), x (0+) = -2, ƒ (t) = 10 sin t

A:

Q: f(d) = e-2d d4

A:

Q: t3 - 3t2 + 5t – 8

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Q: L[sin(3t - 4n)]

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Q: #o5 Selve the simultem Eou) equatis m3 using ん·T. プ=1; (()=onx() ナ? -0;1()=y() dt

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Q: Solve the equation subject to the given conditions. d'y dy dx² dx 6y=4, y(0)=3, y'(0)=2

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Q: 5 sinh (3t) +4 cosh (3t)

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Q: Solve the laplace transform 3x-6x= Sin 2t %3D given when t=0

A: Use the laplace transformation table and derivative formula

Q: ) 3x - 4x= sin社 ; at t=0,x==

A:

Q: y"" + 3y" +3y' + y = 0, y(0) = 7, y'(0) =-7, y"(0) = 11

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Q: 8. Solve using Laplace transform: y" + 2y – 3y = 8e¬t + 8 (t – ), y(0) = 3, y' (0) = –5.

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Q: tsin 3t fre>=5. ー3七

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Q: Solve the given symbolic initial value problem. у'+ 9y'+ 20y 3D е ""6(t-3); у(0) 3 2, у'(0)%3 - 9…

A: We have to solve the given differential equations using Laplace transform.

Q: Using second-shifting theorem find, F(s) where f(t) = e-4t sin 3t

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Q: dy - 4 - 5y = dy -3t sin(4t) ; y (0) = 3, y (0) = 10 dt2

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

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Q: x" (t) – x' (t) = te*, x (0+) = 1, x' (0+) = 0. --

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Q: 3 cos(wt - a), where w and a are constants

A: We find the Laplace transform

Q: Find the Laplace transform of the following signal which is periodic with period 20. 20 15 20 t -201

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Q: Q18: y′ − 2y + [y(2) dz=e², y(0) = 0.

A: The given equation is         y' - 2y + ∫0tyzdz = et  . . . . . . (1)     With condition y(0) = 0 .…

Q: y" +y' = e' + 1; y(0) = y'(0) = 0 %3D

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Q: According to Kirchoff's voltage law, the sum of the voltage drops across these elements is equal to…

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Q: 5. * + 9x = cos 2t

A: