Use the Laplace transform to solve the given initial-value problem. y" + 10y' + 34y = 8(t - n) + 6(t - 37), y(0) = 1, y'(0) = 0 %3D %3D %3D

Q: Find y as a function of x if y(1) = 1, y'(1) = 4. y = x²y"-7xy' + 16y=x6,

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Q: Find y as a function of x if

A: The given differential equation y'''-4y''-y'+4y=0D3-4D2-D+4=0D+1D-1D-4=0D=-1, 1, 4

Q: Find y as a function of t if y(4) = 6, y (4) = 4. y = 121y" - 132y +36y = 0,

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Q: use LaPlace transforms find solutions for dx/dt+3x=e^-2t, given that t=0 and x=2.

A: The objective of this question is to solve the given differential equation dx/dt + 3x = e^-2t using…

Q: Solve y""-2y"-5y'+6y=-12xe +2e¹; y(0)=2, y(0)=7, y"(0)=9 using the method of aplace transforms. Feel…

A: We will use the Laplace transform method to solve the above differential equation by taking the…

Q: let h(y)=(y-3y2)5(y2+2)6  h'(y) in simplified form.

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Q: 0st<"/2 – "/2) tz"/2 Solve using Laplace transforms. y" –- 3y' - y = } y(0) = y'(0) = 0 cos(t SHOW…

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Q: Integrate (a) S2(* dt (b) S(x+1)³ dx (c) cos(-x)(x²)dx

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Q: Find y as a function of a if y(1) = -4, y'(1) = -9. y x²y" + 2xy' - 6y = 0,

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Q: Find dy/dx if y = (*+*) А. 1 В. 2х + 2 D. 1/x C. 2x + 4 csc(2b) sec(2b) Find da/db if a A. 2sec (2b)…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: Find y as a function of a if y(1) = 8, y'(1) = 6. y = x²y" + 3xy' - 35y = 0,

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Q: 5

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Q: * Find y as a function of æ if y" – 8y" – y' + 8y = 0, y(0) = 4, y'(0) = -6, y" (0) = 130. y(x) =

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Q: Integrate (2x - 5) with respect to x from x = 2 to x = 5.

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Q: Find the function satisfying y' x + 3 and y(0) = 2 ... 2y + 5

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Q: Apply variation of parameters to find a particular solution of y ''' - y' = tan x

A: The given differential equation is y''-y' = tan x.We have to solve this using the variation of…

Q: y'' + 4y = cos2t y(0) = -2 and y'(0) = 0 Solve the IVP using the Laplace Transform.

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Q: y''-3y'+10y=e-2t , y(0) =0, y'(0)=1

A: We have to solve given problem:

Q: Evaluate dy/dx if y = (sec2x - tan2x)/(2cos2x-1)

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Q: Obtain general solution of ODE y''-y=exp(x) + cos(2x)

A: Step 1. Homogeneous Solution (y_h):We start by assuming the solution for the homogeneous equation…

Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)