dx Solve the simultaneous equations dt dy - 2x + 2y = 1-2t, dt +x= 0. Given that dt *0, y= 0, dr =0 when t= 0, by using Laplace transforms. 空山 2.

Q: y"- y'- 2y = 0; y(0) = -2,

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Q: у" — Зу' + 2у %3D2е3t y(0) 3D 0 у'(0) — 4 |-

A: Given differential equation is  y''-3y'+2y=2e3t given condition is  y(0)=0 ,y'(0)=4

Q: Q.5: Solve the initial value problems by Laplace transforms. у" - 2 у'- Зу%3D 0, y(4) = -3, У (4)…

A: Given,  y'' - 2y' - 3y = 0,     y(4) = -3,     y'(4) = 6

Q: dx Solve the differential equation dt - Mx = 3eMt under the initial condition x(0) = M – 2 by 4) %3D…

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Q: (a) Solve the following differential equation using Laplace transformation technique: y- 3y +2y =…

A: Given differential equation y''-3y'+2y=e-x and y0=c0, y'0=c1 And Ly'=sLy-y0  Ly''=s2Ly-sy0-y'0 Let…

Q: Use Laplace transforms to find the solutions to the following first order differential equations.…

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Q: Solve the system of differential equations by using the Laplace transform method: x" + y' = cos t y"…

A: Here we will find out the required value.

Q: b) Solve the given system of differential equation by laplace transformation dx = x- y dt dy — 5х -…

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Q: Q.5: Solve the initial value problems by Laplace transforms. у" - 2 у' — Зу %3D0, y(4) = -3, У (4)…

A: y"-2y'-3y=0,    y4=-3, y'4=6 Let t=x-4⇒x=t+4 The original differential equation is y"x-2y'x-3yx=0 ,…

Q: Q:- solve the differential equation by Laplace transform : y" – 3y' + 2y = e3t %3D Where the initial…

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Q: Use laplace transform to solve the initial value problem; a) y''+9y=cos3t,y(0)=2, y'(0)=5.

A: We shall use Laplace and inverse Laplace transform to solve this

Q: If y(t) satisfies the initial value problem  ((d2y)/(dt2)) -(5(dy/dt))-6y=126H(t-2), y(0)=3,…

A: Given differential equation is d2ydt2-5dydt-6y=126Ht-2 Taking Laplace transform on both sides,…

Q: find the solution of following differential equation using Laplace transformation. y" + 3y + 2y = ex…

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

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Q: TM a) Solve the initial value problem using Laplace transform UTM UTM UTM y + 2y = 26 sin 3t, y(0) =…

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Q: y" – 2y' + y = 0 y(0) = 1, y'(0) = 0 Solve the initial value problem using Laplace transform.

A: y"-2y'+y=0 Applying Laplace Transform and using the fact that it is linear we get Ly"-2Ly'+Ly=0…

Q: Using Laplace transform, solve the simultaneous differential equations dx +2x+6y 0, dt dy x+ -3y =…

A: To find the solution of the simultaneous differential equation using the Laplace method.  Given…

Q: Using Laplace transformation, the solution of the following differential equation y" +y = 3, with…

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Q: (B) Use Laplace transformation to solve the differential equation √√2e-¹ y+16ym. +6+8y' csc 2x+…

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Q: Solve the initial value problem using Laplace Transform: a. y" – 2y' + 5y = -8e-t, y(0) = 2, y'(0) =…

A: We have apply Laplace transform to solve the given problem.

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

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Q: Solve the folowing differential equations using Laplace transform method. (1) y"+4y'+5y = 50t, y(0)…

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Q: Using Laplace transform, solve the simultaneous differential equations dx +2x +6y 0, dt dy x+-3y =…

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Q: Use laplace transform to solve the initial-value problem; a) y'+y=B(t-1), y(0)=2

A: Given below the detailed solution

Q: y" — y' = 2x, y (0) = 1, y'(0) = -2

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Q: y" + 3y' + 2y = 6e-t, y(0) = 1, y'(0) = 2 Solve the initial value problem using Laplace transform.

A: Given initial  value problem is  y"+3y'+2y=6e-t, y0=1, y'0=2

Q: Use laplace transform to solve the given system of differential equation; a) {dx/dt=2y+e^t…

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Q: 10. Use the method of Laplace transform to solve the initial value problem y" – 2ay + (a? + B²)y =…

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Q: Using Laplace transforms, solve the initial value problem y" − 2y' + 10y = 0, y(0) = -3, y'(0) = 3.…

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Q: b. (e2t – e-2t)2

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Q: Use Laplace transform technique to solve y" +2y +2y= e-, v(0) = – 3, y'(0) = 2

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Q: у"+ 2y' + 5у %3D0, у(0) — — 1, у'(0) %3D

A: We have to solve the initial value problem y''+2y'+5y=0,  y(0)=-1, y'(0)=6

Q: Determine the Laplace transform of the differential equation 3y’’’ – y’ = e-3t t5 - 9y’’ + 4y With…

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Q: y – y = e3t y(0) = 1

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Q: Solve the initial value problem by Laplace transform, y"+ 5y'+4y 0, y(0) = 1, y'(0)=0 %3D

A: Taking Laplace transform in the both the direction:…

Q: Transforms

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Q: 2. Solve y" – 2y + y = 25 cos(2t), y(0) = 0, y(0) = 0 with Laplace transforms.

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Q: Use Laplace transform technique to solve y" + 2y +2y= e¬, Y(0) = - 4, y'(0) = - 2

A: Laplace transform

Q: 1. Use Laplace transform to solve y" + 3y + 2y = u(t – 2) y(0) = 0, y'(0) = 1

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Q: Solve the given initial value problem using method of Laplace Transform: y" - 2y' +y = e2* +…

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

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Q: Determine the Laplace transform of the differential equation. y² + 4y y (0) = 0 = Cost;

A: Sol:- y' +4y=costTake Laplace transform of both sides of the equationLy'…

Q: 4. Solve the particular solution of y" + 3y' + 2y = 6et, y(0) = 1,y'(0) = 2, using b. Laplace…

A: Solve the differential equation, by using Laplace transferom

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: Using Laplace transforms, solve the initial value problem y" - 2y + 10y = 0, y(0) = -3, y'(0) = 3.

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Q: Consider the partial differential equation D 0°C V or? 1 ƏC Ox r ôr C=C,x=0 0,r = 0 - D- Or : KC,r=1…

A: Given partial differential equation is ∂C∂x=DV∂2C∂r2+1r∂C∂r                        (1)C=C1,…

Q: Solve these second order differential equations by applying the Laplace transform. (i) 6y" – 5y – y…

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