Use Laplace Transform to solve यु y=4e ーt %3D given ylo)= 2 and u lo) = -l

Q: Find the Laplace transform L(2te3t cos 4t + u(t – 1/2) sin 2t)

A: Here we apply formulas of lapses transformation.

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

A: We will use following Laplace transformation…

Q: The Laplace transform of f (t) = cos(2t) + 2e-3t + 3t? is: %3D

A: Note the following results : Lcos at=ss2+a2  Leat=1s-a Ltn=n!sn+1 ; n=1,2,3,…… Linearity property…

Q: Find the Laplace Transform 1.f(t)=(sint-cost)?

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Q: Use Laplace transform to solve: du ди -x = 0; u(x,0) = e*, u(0,t) = 0. at %3D %3D ax

A: Solution

Q: Use Laplace transform to solve f(t) if y" + 3y' + 2y = t + 1 with y(0) = 1, y'(0) = 0

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: Solve by Laplace transforms. (Do not use Heaviside coverup.) Y – 2 y(7)dr = 2t?. -

A: Given that y-2∫0tyτdτ=2t2. Solve this using the laplace transform.

Q: Use Laplace transform to solve the given IVP. 1. (D – 1)y = 2 sin 5t, y(0) = 0

A: According to our guidelines if there are multiple questions, we have to solve the first question…

Q: I. Find the Laplace Transform of the following: Sje-2t sin 5t dt а.

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Q: The Laplace transform off (t) = e2t sin(7t) + te3t is:

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Q: Find the Laplace transform of 1. f(t) = [1u₂n(t)](2 sint - sin 2t) 2

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Q: Use Laplace transform to solve the DE. d²y_3dy = 9 dx² dx where x=0, x=0 and dy=0 dx

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Q: 3t x(t) = to

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

Q: Solve the following DE using Laplace Transform y" + 2y + y = 0, y(0) = -1, (0) = 1

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Q: Use Laplace transform to solve the given IVP. 1. (D – 1)y = 2 sin 5t , y(0) = 0

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Q: Use Laplace transform to solve the DE y" + 4y' + 6y = 1 + e¯*, y(0) = 0, y'(0) = 0. %3D

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Q: Solve the IVPS by the Laplace transform. 1. y' + 5.2y = 19.4 sin 21, y(0) = 0

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Q: Use the Laplace transform to solve y" – 4y' + 4y = t³, y(0) = 1, y'(0) = %3D

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Q: Use Laplace transform to solve the ODE. y" – 4y' + 3y = 8cos4t, y(0)= 0, y'(0)=3 %3D

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Q: Use Laplace transform technique to solve, y"+2y'+2y = e given y(0) = -2 and y'(0) = -1

A: According to our guides, we are allowed to answer the first question only. Kindly re post the second…

Q: Use Laplace transform to solve. y" – 6y' = 0 y(0) = 2 y'(0) = 3

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Q: Use Laplace transform to solve the given IVP. 3. у" — у' %—D еХ cos x, у(0) %3D 0, у'(0) — 0

A: We have y''-y'=excosx  , y0=0 , y'0=0 Now,  Ly'=sYs-y0Ly''=s2Ys-sy0-y'0 Take Laplace transform on…

Q: Find the Laplace transform of u2(t)cos(t − 2)

A: This is laplace transform shift problem

Q: Use Laplace transforms to solve the IVP y''+1=0, y(0)=1, y'(0)=1

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Q: Find the Laplace Transform 1.ft'est 2.[5sinh3t 3.[t - 8t2 + 1

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Q: Find the Laplace transform of 1. _ƒ(t) = ½ [1 − U2„(t)](2 sin t – sin 2t) - - 2

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: I t los 2t e-を

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Q: y” − 2y' + 5y 8e¯ª, y (0) ³, y (0) = 2, y’(0) = 12 =

A: It is known that: L{f(n)}=snF(s)−sn−1f(0)−sn−2f'(0)−⋯−sf(n−2)(0)−f(n−1)(0) Hence, it can be written…

Q: Solve for the Laplace Transform of f(t) = t²sin 2t

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Q: 2. t5/2 sinh 4t

A: The solution is given as

Q: Use the Laplace transform to solve y" + 9y = cos 3t, y(0) = 4, y'(0) = 2. %3D %3D %3D

A: Given that, y"+9y=cos3t, y0=4,y'0=2

Q: Find the Laplace transform of f(t)=sin(4t + ?/3)

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Q: Solve the following Euler type DE using Laplace transform:  y''+2ty'-4y=1 where y(0)=0 and y'(0)=0

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Q: 2ィ 4= e そーを 4(t) dt

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Use Laplace transform to solve the given IVP. 5. y' + y = x sin x, y(0) = 0

A: To solve: The differential equation y'+y=xsinx, y0=0. Concept used: Laplace formulas…

Q: Use Laplace transform to solve IVP shown below: y" - 5y' + 6y = 2tet – 3et y(0) = 1, y'(0) = -1. %3D…

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Q: Which is the correct inverse Laplace transform of U (s)=+ O u(t) = 6t + sinh(4t) + cosh(4t) %3D O u…

A: Recall:  L-11sn=tn-1(n-1)! L-1ss2+a2=cos at L-11s2+a2=1asin at

Q: Find the Laplace transform of f(t) = t cosh 2tsinh 3t.

A: To find the Laplace transform of ft=t cosh2t sinh3t.

Q: Use Laplace transform to evaluate the integral J te-2t sin(2t) dt A 8. B Not Defined 4s (s? + 4)2…

A: Here, the objective is to evaluate the given integral using Laplace transformation ∫0∞te-stsin2tdt

Q: Use a Laplace transform to solve y" + 16y = 6 (1 –).y(0) = 1, y'(0) = 0. %3D 4

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Q: Use Laplace transform to solve the ODE. y"- 4y +3y - Bsinst, y(0)= 0, y'(0)-3

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Q: show that the Laplace transform of f(t)=te^(at)

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Q: " + 8y' + 25y = 13e-2t y(0) = -1, y' (0) = 18 %3D

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Q: The Laplace transform of f (t) = cos(2t) + 2e-3t + 3t? is:

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Q: By using Laplace transform to solve y + y = cosht y (0) = 0, what would the particular solution be?…

A: the given equation is y'+y=cosh t  y(0)=0 taking Laplace of the given transform Ly'+y=Lcosh t…

Q: Solve the following IVP using Laplace Transform.  (ii) y′′−6y′+15y=2sin(3t), y(0)=−1, y′(0)=−4

A: Given differential equation is y''−6y'+15y=2sin3t and y0=−1 and y'0=−4 Take Laplace transform of…

Q: Solve the following DE using Laplace Transform y" + 2y' + y = 0, y(0) = -1, y(0) = 1

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Q: Evaluate using Laplace Transform: tsin3 3t dt e-3t f(t) = 0,

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