6) Use Laplace transforms to solve the differential equation: d²y dy -72+10y=e2* +20, given that when x=0, y=0 dx² dx dy and dx 113

Q: Solve the differential equation using Laplace Transform. (b) y" – y" + 4y' – 4y = 10e-t, y(0) = 5,…

A: We will find out the required solution.

Q: Solve the differential equation dx/dt-6x=3e6t under the initial condition x(0)=6-2 by using the…

A: The solution is given as

Q: Solve the differential equation using Laplace Transform. (a) y" – 2y' + 5y = 8e'sin2t, y(0) = 1,…

A: a. The given differential equation is                                     y''-2y'+5y=8etsin2t   ,…

Q: 2. y' + y = e2t ; y(0) = 0

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Q: Solve the differential equation y" + 4y' + 5y = 0 given y (0) = 1 and y' (0) = - 4 using Laplace…

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Q: Evaluate the differential equations: Integrating Factor by Formula a) (2y2 + 2y + 4x2)dx + (2xy +…

A: Given:  a) 2y2+2y+4x2dx+2xy+xdy=0b) y2cosxdx+4+5ysinxdy=0

Q: Solve the differential equation using the Laplace transform у" — 5y — бу %3Dеs", y(0) 3D 0; у' (0)…

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Q: y" – 2y' + 5y = 8e'sin2t, y(0) = 1, y'(0) = -1 %3D

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Q: y"(x) + 9y(x) = 40e* ; y(0) = 5, y'(0) = -2

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

Q: 7. Find the solution of the differential equation using Laplace Transform. y" – 3y' + 2y = e3x when…

A: We need to solve DE.

Q: Find the general solution of differential equation 3y" + 2y' - 8y = 0. Solve for the Laplace…

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Q: Determine the order of the differential equation. (dy/dt)^2+7 dy/dt+9y=3t

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Q: Use Laplace transforms to solve the differential equation: y' +y – et = 0 where y (0) = 0, y (0) = 0

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Q: dy %3D ху + 3х — 2у — 6 dx -

A: We have dydx=xy+3x-2y-6 Now, we can write it as…

Q: Use the Laplace transform to solve the differential equation: y' – 2 +y = e', y(0) = 0, y (0) =

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Q: What is the solution of the differential equation using Laplace Transform y'' - 3y' + 2y = e3x when…

A: What is the solution of the differential equation using Laplace Transform y'' - 3y' + 2y = e3x when…

Q: Solve the differential equation by using Laplace Transform y''+4y'=15et y(0)=5,y'(0)=-2

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Q: y" – 3y' + 2y = est ; y(0) = y'( %3D

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Q: Solve y(x) in the differential equation using Laplace Transform. y" + 4y + 10 = e-³x + sin(x); y(0)…

A: I am attaching image so that you understand each and every step.

Q: :Q1: Use Laplace transforms to solve the differential equation d² y - 24Y + dy + 2y = 3ex cos 2xr,…

A: Given:  d2ydx2-2dydx+2y=3excos2x      ......(1) y0=2 and y'0=5 We want to solve the given…

Q: Convert the differential equation d²y - 3y + 2y = 4 sin x dx² dx with the initial conditions y(0) =…

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Q: Solve the differential equation y" +4y' +4y 6e", y(0) =-2, y'(0)=8. using Laplace transform

A: Given differential equation:y''+4y'+4y=6e-t ; y0=-2 and y'0=8To find: solution by using the laplace…

Q: Using Laplace transform, find the solution to the differential equation y" – 4y' + 4y = -16 cos 2t…

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Q: y" – 2y' + 3y = 2t²e3t 3 where y'(0) = y(0) = 0

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Q: The solution of the differential equation using dy + 6y = 7e-3t is dt Laplace transform „given that…

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Q: Use the Laplace transform to solve the differential equation dy x – 2y dx with the initial condition…

A: Solved below

Q: Given a second order differential equation dx 2x = e³t dt where t = 0, x = -5. Using Laplace…

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Q: Determine the solution of the differential equation using Laplace and Inverse Laplace Transforms.…

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Q: Use Laplace transforms to solve the differential equation ,, Y +6y' + 13y = 0, given y(0) = 3 and y'…

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Q: Solve the differential equation using Laplace Transform. (a) y" – 2y' + 5y = 8e'sin2t, y(0) = 1,…

A: According to the given information, it is required to solve the given differential equation using…

Q: y" + 9y = 5t + 2, y(0) = 2 y'(0) = -1 |

A:

Q: Use Laplace transformation to solve the differential equation: y(0) = 1 and y'(0) = -2 where y" +…

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Q: y" + 5y' + 4y = 0, y(0) = 1 y'(0) = 0

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Q: Transform the differential equation -3y + 4y - 4y = sin(at) y(0) = Therefore Y = = -4 y = -4 into an…

A: Given -3y''+4y'-4y=sina t Also given y0=-4,   y'0=-4   To transform the equation into an algebraic…

Q: Transform

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Q: Solve the given differential equation using Laplace Transform (D2 – 6D + 15)y = 2 sin 3t - With the…

A: GIVEN (D2-6D+15)y=2 sin 3twith intian condition y(0)=-1, y(0)'=-4we need to solve the equation using…

Q: 6y = -12 y (0) = 1, y' (0) =4. y" (0) = -2 %3D 3.) at + 4 dt

A: Take laplace on both sides of the given equation and then Use-…

Q: 4- dt2 d²y(t) dy(t) + 4 dt + 10y(t) = sin 2t u(t)

A:

Q: 3. Find the solutions for the given linear systems of differential equations using Laplace…

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Q: Solve the given differential equation using Laplace Transform (D² – 6D + 15)y = 2 sin 3t With the…

A: Given differential equation is D2-6D+15y=2 sin 3t with initial conditions y0=-1, y'0=-4. Applying…

Q: Solve the differential equation using Laplace transformation y" – 2y' + 3y = 2t²e3t where y'(0) =…

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Q: B) Solve the differential equation by using Laplace transform y" - y = -t² y(0) 2 and y'(0)=0

A: The given equation is;  y''-y=-t2, y(0)=2, y'(0)=0.

Q: x"(t) + 9x(t) 5sin (2t) when t = 0,x = 3,x' = 1

A: Solve the differential equation by using Laplace transferom

Q: Use Laplace transforms to solve the differential equation y' + 2 y = 10 e3t , if y(0) = 6

A: The given equation is: y'+2y=10e3t,y(0)=6...(1) Taking Laplace transform on both sides of equation…

Q: Given a second order differential equation dx 2x = e³t dt where t = 0, x = -5. Using Laplace…

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Q: Solve the differential equation using either the method of undetermined coefficients or Laplace…

A: The given equation is y″′+y″+y′+y=e^(-t)+4t.

Q: y"+16y = cos4t, y(0)= 0, y'(0) = 1,

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Q: y" + 6y + 9y = t

A: Given: y"+6y'+9y=t