Solve equation using Laplace transform ÿ +9y = 6 (t -) sin(t), y(0) = 0, y(0) = 0 %3D

Q: Using the linearity of the inverse Laplace transform, solve for the solution of the differential…

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Q: y''+y'=0 where y(0)=0, y'(0)=1 laplace transform of derivatives

A: Given that:-  y" + y' = 0 and y(0)= 0, y'(0) =1 We find laplace transform of this differential…

Q: Using Laplace transform to solve y' +y = sin(t), y(0) = 1.

A: Applying Laplace transformation,

Q: Solve using the Laplace transform y' - y = et , y(0) = 2

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Q: Solve by Laplace transform method. y '"-3 y '+2 y = 4 , where y(0) = 2; y'(0) = 3.

A: The given differential equation is  y''-3y'+2y=4,   y(0)=2 , y'(0)=3 Laplace transform of few…

Q: y" +y = e-2t Sint initial condition for the differential equation y(0) = 0, y'(0) = 0 are given…

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Q: Solve the equation dy y ху-з dx II +

A: The given equation is of the bernoulli's equation form.

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

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Q: Problen ts) Find the solution of the following differential equation using the Laplace transform…

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Q: Solve equation using Laplace transform ÿ + 9y = 8 (t -) |sin(t), y(0) = 0, ý(0) = 0

A: Formulae:  1. Lf(t)δ(t-a)=e-asf(a) 2. Lf''(t)=s2F(s) - sf(0)-f'(0) 3. L-1e-asF(s)=H(t-a)f(t-a),…

Q: What is the Laplace transform of the given differential equation? y" 2y1 = 0, y (0) = 0, y

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Q: Solve the differential equation using Laplace Transform and Inverse Laplace transform y" – 4y' + 4y…

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Q: The solution of the differential equation using Laplace transform - + 5y given that y(0) -0 O 1- O…

A: the given differential equation is dydt+5y=5, given y(0)=0 taking Laplace transform on both sides…

Q: Using Laplace transform, How would I solve the given initial-value problem dy/dt + 7y = u2(t),…

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Q: Using Laplace transforms. Solve y" + 4y′ + 3y = e^t. When, y(0) = 0 and y′(0) = 0. Whole Solution

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Q: Solve using the Laplace transform y' - y = e3t , y(0) = 2

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Q: Q2) Solve the initiai value problem by Laplace transform. y" +4y=cos 2t y(0) = 1 , y'(0) = 1

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Q: azu(x, t) a?u(x, t) (-00 0) at2 ax2 u(x,0) = 4e-5|x| %3D (x,0)30 at

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Q: y' – 5y = e5x ;y(0) = 0 %3D

A: The give question is related with differential equation and Laplace transform. Given that,…

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

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Q: Using Laplace Transform, solve y" + 2ty' – y = t when y(0) = 0, and y'(0) = 1. %3D

A: Given:y''+2ty'-y=t,y(0)=0,y'(0)=1

Q: Solve using Laplace transform y" - y = e' cost, y(0)= 0, y'(0)=0

A: Solve the differential equation by using lapalce transformation

Q: ve the differential equation using Laplace Transform and Inverse Laplace transform y" - 4y' + 4y =…

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Q: Use Fourier transform to solve the partial differential equation: ди d²u ax² du(0,1) -10u: x>0,t> 0…

A: Given: The partial differential equation and the conditions are: ∂2u∂x2-10u=∂u∂t, x>0, t>0…

Q: Solve the initial value problem using Laplace Transform: y" + 2ty' – 4y = 1, y(0) = y'(0) = 0 %3D

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Q: estion 4 Use the Laplace transform method to solve initial value problem. Provide sufficient…

A: Laplace transform in calculus is the integral transform of the derivative function and changes the…

Q: Using Laplace transform, find the solution to the differential equation y" + 4y' + 3y = 8te' + 6e²…

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Q: Application of the Laplace transform (Solution of partial differential Equations) dy учу where…

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Q: Laplace transform to solve the given initial-value problemn. y"+ 2y" y' 2y – sin(3t), y(0) = 0 y'0)…

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Q: Laplace under initial conditions x '+ y' + x= 0 and x '+ 2y' = 1 equation system x(0) = y (0) = 0…

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Q: Using Laplace transform, solve y" +y = cos x, where y (0) = 0 = y'(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: Using Laplace Transform, solve the following initial value problem Зу' - 4y — sin 2t У) --

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Q: Transform

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Q: Solve the initial value problem using Laplace Transform Method y' + 9y = 0 y(0) = 2 2 y(t) = -3-sin…

A: The given initial value problem is y'+9y=0, y0=2 use the Laplace transform Ly'=sYs-y0 use the…

Q: Solve the shifted data IVP by the Laplace transform method showing your work in details. y"-xy'-y=0…

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Q: Using Laplace Transform, evaluate the integro-differential equation y' - y=e-t ;    y(0)=1

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Q: Solve the differential equation using Laplace Transform and Inverse Laplace transform y" – 4y' + 4y…

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Q: Solve the differential equation using Laplace Transform: y''+2y'+y=sin⁡t        ,y(0)=-2…

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Q: y" +y' = e' + 1; y(0) = y'(0) = 0 %3D

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Q: 8. Using the Laplace transform, find the solution to y" + y = sin t, y(0) =0, y'(0) = -1. %3D

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Q: Solve using Laplace transform method: y + y = 1 y(0) = 2 [y' (0) = 0

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Q: Using Laplace transform solve the initial value problem: y''+4y'-5y=e2t , y(0)=1, y'(0)=-1

A: Given initial value problem is  y''+4y'-5y=e2t  ,    y(0)=1 , y'(0)=-1

Q: 4. Solve using the Laplace transform: y' + 2y = cos 3t , y(0) = 4.

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Q: Solve by using Laplace transform y" + y = cost, y(0) = 0, y'(0) = -1.

A: The given initial value problem is y''+y=cost,y(0)=0 and y'(0)=-1. Apply Laplace transform on both…

Q: у" — у 3D 4 сosx У (0) %3D0 ,у'(0) — 2

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Q: 4. Use Laplace transform technique to solve , y"+2y'+2y = e given y(0) = -2 and y'(0) =-1 %3D

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Q: Solve the differential equation using Laplace Transform and Inverse Laplace transform y" – 4y' + 4y…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.