CALCD LA TE THE SOLUCIO4 USING LAPLACE TRANSFORM. t et 0 st<- y't y'- Gy= Cos 2t et Sen 2t T st< t∞ GIVEU THAT y(0)= 1 y'l0)=2

Q: y" + 4y' + 3y = x² Solve this equation using Laplace transform

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

A: We will use following Laplace transformation…

Q: use laplace transform to solve y'-y=2cos(t), y(0) = 4

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Q: Use the Laplace transform to solve the following initial-value problem for a first-order equation.…

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Q: Solve the equation using Laplace transform y" - 6y' +9y t²e³t, y(0) = 2, y'(0) = 6. =

A: Introduction: There are many different ways that are applied to solve an initial value problem. One…

Q: Solve the following DE using Laplace Transform 3. y" - y' -2y = 5 sinx y(0) = 1, v'(0) = -1

A: The given differential equation .We have to solve the differential equation using the Laplace…

Q: A function f(t) is given as f(t) = e' cos 2t cos t %3! Find the Laplace transform of this function.

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Q: Solve using the Laplace transform y' + 2y = 12 e3t , y(0) = 3

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Q: Q2 \ Determine the Laplace transforms of the following function: t | e-4tt sin? 3t dt L

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Q: Use Laplace transforms to solve the IVP y''-y=0, y(0)=2, y'(0)=3. Show the complete solution.

A: Given initial value problem is, y''-y=0, y(0)=2, y'(0)=3

Q: 3. 2y" + Зу" — Зу' — 2у %3D е-t, con y(0) 3D 0, у'(0) — 0, у" (0) %3 1

A: Given: 2y'''+3y''-3y'-2y=e-t, y(0)=0=y'(0), y''(0)=1 To find: Solution of given differential…

Q: 1 dt. 1+ vt Let G(x) Find G'(9).

A: Given that: G(x) = ∫2x211+tdt

Q: solve: y" - Hý + 4y = 4szt; y(0)=2₁ y(a)=5 using Laplace transform

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Q: Solve the IVP using Laplace Transform y" = y + 2y, y(0) = -2, y (0) = 3.

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Q: Solve the DE using Laplace transform. y" – by' + 13y = 0, y(0) = 0, y'(0) = -3

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Q: b) Solve by using Laplace transform y + 2x = e • x' - 2 y = 1+ t; where, x(0) = 1, y(0) = 2 %3D

A: To find the solution of the given system first we take the Laplace transform of both the equations…

Q: Let Y(s) be the Laplace transform of y(t). Find the equation satisfied by Y(s) when solving the…

A: Introduction: The Laplace transformation is a very important tool in solving an initial value…

Q: Solve the following ODE 3t. y" – 6y' + 9y = t²et; y(0) = 0, y'(0) = %3D

A: Given The given ODE is y"-6y'+9y=t2e3t. y0=0,    y'0=1 Apply formula…

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

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Q: Use the Fourier transform method to solve du k at ax2-Yu, -o∞ 0 u(x, 0) = f(x).

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Q: y = sin 3t dt – y

A: Calculated integration and the applied laplace transformation in both sides

Q: 22) Solve using Laplace Transform y" + 2y' +5y = etsint where y(0) = 0, y'(0) = 1

A: Solution to the differential equation by using Laplace transform

Q: | sin 3t dt – y' y =

A: To find the Laplace of function y=f(t) first evaluate the integral ∫0t sin 3τ dτ .…

Q: ii. f(t)= e*tsinhrt 't sinh at

A: Laplace transform formulae: 1. Ltnf(t)=(-1)ndndsnLf(t) 2. Leatf(t)=Lf(t)s→s-a Given: f(t)=e3ttsinhπt

Q: Find the value of dr / dt at t = 0 if r = (θ2 + 7)1/3 and θ2t + θ = 1.

A: Consider the provided equation, r=θ2+713 and θ2t+θ=1 Find the value of drdt at t=0. Apply the chain…

Q: Using Laplace transform, solve y"+25y=t, y(0)=1 and y'(0)=0.04

A: Given that, y''+25y=t, y(0)=1, y'(0)=0.04 The laplace transform for, Ly''=s2y(s)-sy(0)-y'(0)Lt=1s2…

Q: Use the Laplace transform to solve y' - v = te'sint, y(0) = 0

A: To solve the given IVP, first we take the Laplace transform of differential equation and then we use…