12. x Ct) = cosh 3t Sin 3t te

Q: 8. x(t) = e2" (t³ + 3t) %3D

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Q: f(x)= (ae if x>0 MX ае -Nx +be

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Q: y ct) = sin 2t cos 34

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Q: 6. 7. 5 (s+3)² 3 s2-32

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Q: xct) = 3(t/4) e 6.

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Q: t° cos(5t) + cos(2at) cos (3at) COS

A: 1) Ltnf(t)=(-1)ndndsnLf(t) 2) Lcos(at)=ss2+a2

Q: sin 3t f(t) t

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Q: a k 2 + k² S 2 + k² k

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Q: 7. co sh?t CO 9.

A: The given problem is to find the Laplace transform of the given function f(t). Given function f (t)…

Q: t も c6 10. XCt)> { -8 + -8 t ct-6)? » t >6

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Q: f(t) = e-2tsin²tcos²t

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Q: f(t) = te¯3t cos² 2t -3t cos 2t

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Q: yct)= sin 2t cos 34

A: Given: y(t)=sin2t cos3t

Q: SOLVE FOR THE LAPLACE TRANSFORM. Provide the step-by-step solution

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

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Q: f(t) = cosh wt sin wt

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Q: G(t) = t5 – e-9t + 5(t – 1)?

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Q: y(^) – y = sin ht,y(0) = y'(0) = y"(0) = 0,y"'(0) = 1 %3D %3D

A: The given equation is, y4-y=sinh t                  ............1 The given initial condition is,…

Q: y" - 4y + 13y = sin(2t) y(0) = y'(0) = 0

A: We have to solve the differential equation  by Laplace transformation.

Q: 0 9. f(t)=t-n 0 if t 2π

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Q: fCt) = 3e 4t C1- 3t + 2t?)

A: The Laplace transformation formulas are Lekt=1s-k, Ltnft=-1nFns, where Lft=Fs. Simplify the given…

Q: Find the Fourier Sine Transform of the function   if a = 7,  b = 7 , m = 5 , and n = 4. Then,…

A: The formula for the Fourier Sine Transform is :-  f^a=2π∫0∞fxsinaxdx   And we are given the function…

Q: Solve for the Laplace transform cosh2t

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Q: f(t) = t²sinh3t

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Q: 2s-1 's²-6s+18*

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Q: - 2t 1 y Ct) = 5e COS 67 CoS

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Q: 2Ct -4)4 fct) = 4. 2Ct -4) %3D

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Q: 5. XCt) Ct +2)Sin Ct - 4) %D

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Q: 2. fct) = 3e +t C1-3t + 2t 2) -4t (1-3t + 2t2)

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Q: 11. 3北 x(t) = e to

A: We have to find the Laplace transform of Xt=e3t-1t

Q: Solve the shifted data IVP by the Laplace transform. Show the details.

A: We have given a initial value problem, y''-2y'-3y=0 with initial conditions y4=-3, y'4=-17 This is…

Q: 3. f Ct) 2 (3t-5) e 4t

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Q: Solve by the Laplace transform, showing the details and graphing the solution:

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Q: 3北 X(t) = e - | 1. t

A: If f(t) is a function of t defined for all positive values of t, then the Laplace transform of the…