Question

Use method of Laplace transforms to solve and explaine step by
step the following differential equation:
2y''+3y'-2y=te^{-2t} with y(0)=0 and y'(0)=2.

Can we do this using partial fractions? if so, how? Thank you so much!

Answer #1

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Solve the following differential equation using the method of
Laplace Transforms. ? ′′ + 2?′ + ? = 3,
?(0) = 0,
? ′ (0) = 0.

Solve the following differential equation by Laplace transforms.
The function is subject to the given conditions.
y''-y=5sin2t, y(0)=0, y'(0)=6

Use the method of laplace transforms to solve the following
Initial Value Problem:
y"+2y'+y=g(t), y'(0)=0

Use the Laplace Transform method to solve the following
differential equation problem: y 00(t) − y(t) = t + sin(t), y(0) =
0, y0 (0) = 1
Please show partial fraction steps to calculate
coeffiecients.

Use the method of Laplace transforms to solve the following
initial value problem. y'' + 6y' + 5y = 12e^t ; y(0) = −1, y'(0) =
7

Solve the following differential equation using Laplace dy/dt
+2y=12sin4t y(0) =10

Use Laplace transforms to find the solution of ?′′(?) + 2?′(?) +
2?(?) = 2 with ?(0) = 0 and ?′(0) = 0
First, find an equation for ?(?), the Laplace transform of ?(?)
Second, simplify ?(?) using partial fractions if necessary Third,
find the inverse transform of ?(?)

use the method of undetermined coefficients to solve the
differential equation)
y'' + 2y' - 3y = (x2 + x + 1) + e-3x

Use Laplace transforms to solve 3y ′′ − 48y = δ(t − 2), y(0) =
1, y ′ (0) = −4.

Solve the initial value problem below using the method of
Laplace transforms. y"+11y'+30y=280e^2t, y(0)=1, y'(0)=32

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