Explore Laplace Transform Equations

In your own words - What is the nature of the convolution theorem?

coexpennan 2021-02-03

The Laplace transform of $t u (t - 2) = e^{- 2 s} [\frac{s + 2 s^{2}}{s^{3}}]$
True or False?

Carol Gates 2021-02-02

Solve the following differential equations using the Laplace transform and the unit step function
$y " + 4 y = g (t)$
$y (0) = - 1$
$y^{'} (0) = 0, where g (t) = {\begin{cases} t & , t \leq 2 \\ 5 & , t > 2 \end{cases}$
$y " - y = g (t)$
$y (0) = 1$
$y^{'} (0) = 2, where g (t) = {\begin{cases} 1 & , t \leq 3 \\ t & , t > 3 \end{cases}$

e1s2kat26 2021-02-02

Obtain the Laplace Transform of
$L {t^{3} - t^{2} + 4 t}$
$L {3 e^{4 t} - e^{- 2 t}}$

e1s2kat26 2021-02-01

Find Laplace transform for
$x " - 3 x^{'} + 2 x = 1 - e^{2 t}$

Anish Buchanan 2021-01-31

Please solve
partial differential equations by laplace transforms,partial differential equations by laplace transforms
$\frac{\partial^{2} y}{\partial t^{2}} = a^{2} \frac{\partial^{2} y}{\partial x^{2}} - 9$
$y (x, 0) = 0$
$y (0, t) = 0$
$\frac{\partial y}{\partial t} = (x, 0) = 0$
$lim_{x \to \infty} y_{x} (x . t) = 0$

ruigE 2021-01-31

Find Laplace transform for
$\frac{s + 8}{s^{2} + 4 s + 5}$

CoormaBak9 2021-01-31

Compute the Inverse Laplace Transform of $F (s) = \frac{s}{R^{2} s^{2} + 16 π^{2}}$
take $R = 70$

he298c 2021-01-31

Solve the initial value problem below using the method of Laplace transforms.
$y " - 4 y^{'} + 40 y = 225 e^{5 t}$
$y (0) = 5$
$y^{'} (0) = 31$

Clifland 2021-01-31

Find the solutions for the given linear systems of differential equations using Laplace Transforms.
$w - 2 y + 3 w = 0 : y " + w = 2 \sin x$
$y (0) = w (0) = 2, y^{'} (0) = - 1$

opatovaL 2021-01-31

Find the Laplace Transform of the function
$f (t) = t$

babeeb0oL 2021-01-30

Use Laplace transform to find the solution of the IVP
$2 y^{'} + y = 0, y (0) = - 3$
a) $f (t) = 3 e^{- 2 t}$
b) $f (t) = 3 e^{\frac{t}{2}}$
c) $f (t) = 6 e^{2 t}$
d) $f (t) = 3 e^{- \frac{t}{2}}$

chillywilly12a 2021-01-28

Operate the Laplace Transform on the following
$(i) f (t) = \cos (3 t)$
$(ii) f (t) = t^{\frac{1}{2}}$

Aneeka Hunt 2021-01-27

Prove $F (s) = \frac{1}{s - 2} then f (t)$ is
a) $e^{2 t} u (t)$
b) $u (t + 2)$
c) $u (t - 2)$
d) $e^{- 2 t} u (t)$

Caelan 2021-01-27

Please solve the 2nd order differential equation by (PLEASE FOLLOW GIVEN METHOD) LAPLACE TRANSFORMATION
ALSO, USE PARTIAL FRACTION WHEN YOU ARRIVE
$L (y) = [\frac{w}{(s^{2} + a^{2}) (s^{2} + w^{2})}] \cdot b$
Problem 2 Solve the differential equation
$\frac{d^{2} y}{d t^{2}} + a^{2} y = b \sin (ω t)$ where $y (0) = 0$
and $y^{'} (0) = 0$

Carol Gates 2021-01-27

Derive the transform of $f (t) = \sin k t$ by using the identity $\sin k t = \frac{1}{2} u (e^{i k t} - e^{- i k t})$

permaneceerc 2021-01-27

If the Laplace Transforms of fimetions $y_{1} (t) = \int_{0}^{\infty} e^{- s t} t^{3} d t, y_{2} (t) = \int_{0}^{\infty} e^{- s t} \sin 2 t d t, y_{3} (t) = \int_{0}^{\infty} e^{- s t} e^{t} t^{2} d t$ exist , then Which of the following is the value of $L {y_{1} (t) + y_{2} (t) + y_{3} (t)}$
$a) \frac{3}{(s^{4})} + \frac{2}{(s^{2} + 4)} + \frac{2}{(s - 1)^{3}}$
$B) \frac{(3!)}{(s^{3})} + \frac{s}{(s^{2} + 4)} + \frac{(2!)}{(s - 1)^{3}}$
$c) \frac{3!}{(s^{4})} + \frac{2}{(s^{2} + 2)} + \frac{1}{(s - 1)^{3}}$
$d) \frac{3!}{(s^{4})} + \frac{4}{(s^{2} + 4)} + \frac{2}{(s^{3})} \cdot \frac{1}{(s - 1)}$
$e) \frac{3!}{(s^{4})} + \frac{2}{(s^{2} + 4)} + \frac{2}{(s - 1)^{3}}$

allhvasstH 2021-01-25

Use the Laplace transform to solve the given system of differential equations.
$\frac{(d^{2} x)}{(d t^{2})} + \frac{(d^{2} y)}{(d t^{2})} = \frac{t}{2}$
$\frac{(d^{2} x)}{(d t^{2})} - \frac{(d^{2} y)}{(d t^{2})} = 4 t$
$x (0) = 5, x^{'} (0) = 0,$
$y (0) = 0, y^{'} (0) = 0$

Rui Baldwin 2021-01-23

Laplace transform of $\sin (2 t) + e^{t} \sin (t)$

Lewis Harvey 2021-01-22

Use Laplace transform to solve the folowing initial value problem $y " + 2 y^{'} + y = 4 e^{- t} y (0) = 2 y^{'} (0) = - 1$

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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