Explore Laplace Transform Equations

Use Laplace transform to solve the folowing initial value problem $y " + 2 y^{'} + 2 y = 0$
$y (0) = 2$
$y^{'} (0) = - 1$

Brittney Lord 2020-12-24

Find the laplace transform of the following function
$f (t) = t u_{2} (t)$

sanuluy 2020-12-24

Determine the Laplace transform of
$f (t) = t^{4} - t^{2} e^{3 t} + 2$

ringearV 2020-12-24

Find the laplace transform of the following:
MULTIPLICATION BY POWER OF t
$g (t) = (t^{2} - 3 t + 2) \sin (3 t)$

Chesley 2020-12-24

Solve the following differential equations using the Laplace transform
$\frac{(d y)}{(d t)} - 4 y = 4 - 2 t,$
$y (0) = 0$

he298c 2020-12-22

Find the laplace transform of the following
1) SHIFTING
$f (t) = (1 + t e^{- t})^{3}$

tinfoQ 2020-12-21

Solve the IVP with Laplace Transform:
${\begin{cases} y " + 4 y^{'} + 4 y = (3 + t) e^{- 2 t} \\ y (0) = 2 \\ y^{'} (0) = 5 \end{cases}$

babeeb0oL 2020-12-17

Solve the initial value problems in Problems and graph each solution function x(t):
$x " + 4 x = δ (t) + δ (t - π)$
$x (0) = x^{'} (0) = 0$

lwfrgin 2020-12-17

Find the Laplace transform Y(s), of the solution of the IVP
$y " + 3 y^{'} + 2 y = \cos (2 t)$
$y (0) = 0$
$y^{'} (0) = 1$
Do not solve the IVP

CoormaBak9 2020-12-17

use the Laplace transform to solve the given initial-value problem. $y " + y^{'} - 2 y = 10 e^{- t}, y (0) = 0, y^{'} (0) = 1$

Falak Kinney 2020-12-17

Solve by using Laplace Transform and explain the steps in brief
$\frac{d^{2} x}{{d t}^{2}} + 2 \frac{d x}{d t} + x = 3 t e^{- t}$
Given $x (0) = 4, x^{'} (0) = 2$

CMIIh 2020-12-17

determine a function f(t) that has the given Laplace transform
$F (s) = \frac{4 s + 5}{s^{2} + 9}$

Reeves 2020-12-16

Existence of Laplace Transform
Do the Laplace transforms for the following functions exist? Explain your answers. (You do not need to find the transforms , just show if they exist or not)
a) $f (t) = t^{2} \sin (ω t)$
b) $f (t) = e^{t^{2}} \sin (ω t)$

Yulia 2020-12-16

solve the initial value problem with using laplace
$Y^{'} + 3 Y = 6 e^{- 3 t} \cos 6 t + 24$
$Y (0) = 0$

geduiwelh 2020-12-15

Find the solution of the following differential equation by Laplace transforms:
$y^{‴} - 5 y " + 7 y^{'} - 3 y = 20 \sin (t), y (0) = y^{'} (0) = 0, y " (0) = - 2$

Aneeka Hunt 2020-12-15

determine the Laplace transform of f.
$f (t) = 3 t e^{- t}$

Ava-May Nelson 2020-12-12

Use the Laplace transform table and the linearity of the Laplace transform to determine the following transform
$L {3 e^{- 4 t} - t^{2} + 6 t - 9}$

Tahmid Knox 2020-12-09

With the aid of Laplace Transform, solve the Initial Value Problem
$y (t) - y^{'} (t) = e^{t} \cos (t) + \sin (t), y (0) = 0, y^{'} (0) = 0$

Emeli Hagan 2020-12-07

Find the particular solution of a non-homogeneous equation using Laplace transformation,
$y (0) = 0,$
$y^{'} (0) = 0,$
$y " (0) = 0$
$y^{‴} - 5 y^{″} - 22 y^{'} + 56 y = 12 - 32 e^{- 8 x} + 2 e^{4 x}$

beljuA 2020-12-06

Use the Laplace transform to solve the given initial-value problem.
$y^{″} + 8 y^{'} + 41 y = δ (t - π) + δ (t - 3 π), y (0) = 1, y^{'} (0) = 0 y (t) = ?$

If you came across the necessity of Laplace transform, it is most likely that you are coming from a mechanical engineering or electrical background. The concept is used to solve differential equations, which is why it is vital to consider Laplace transform examples as you are looking through the questions and connect the dots as the equations are being approached. Remember to look through our list of answers as these will help you to address various Laplace transform problems and find solutions to complex Laplace transform questions as you are dealing with your Laplace transform equation homework.

Differential Equations

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