Explore Laplace Transform Equations

find Laplace transform
$L^{- 1} \frac{5}{s^{2} + 2 s - 3}$

Rivka Thorpe 2021-09-26

$F (t) = 0$
$= \sin (t)$
$0 \leq t < π$
$π < t < 2 π$
Find $L (f (t)) =$ ?

Yasmin 2021-09-26

Solve by Laplace transformation method the following D.E.
(1) $y^{″} - 3 y^{'} + 2 y = 4^{2} e^{t}$ given that $y (0) = - 3, y^{'} (0) = 5$

Aneeka Hunt 2021-09-26

Find the Laplace transform for the functions:
$f (t) = t u_{2} (t)$
$f (t) = u_{π} (t) \sin (t)$

tabita57i 2021-09-26

Use Laplace transforms to solve the following initial value problem.
$x^{″} + x = 3 \cos 3 t, x (0) = 1, x^{'} (0) = 0$
The solution is $x (t) = ?$

Cabiolab 2021-09-25

Find the inverse Laplace transform $f (t) = L^{- 1} {F (s)}$ of the function $F (s) = \frac{8 e^{- 4 s}}{s^{2} + 64}$
Use h(t-c) for the Heaviside function h_c(t) if necessary.
$f (t) = L^{- 1} {\frac{8 e^{- 4 s}}{s^{2} + 64}} =$

Tobias Ali 2021-09-24

Obtain Laplace transforms for the function $\sin (t - π)$ step $(t - π)$

Lipossig 2021-09-24

The Laplace transform of $u (t - 2)$ is
(a) $\frac{1}{s} + 2$
(b) $\frac{1}{s} - 2$
(c) $e^{2} \frac{s}{s} (d) \frac{e^{- 2 s}}{s}$

Jason Farmer 2021-09-24

Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the Laplace tranform of the function below.
${(1 + e^{- 4 t})}^{2}$

Clifland 2021-09-24

Use Laplace transform to solve the following initial value problem:
$y^{″} + 5 y = 1 + t, y (0) = 0, y^{'} (0) = 4$
A) $\frac{7}{25} e^{t} \cos (2 t) + \frac{21}{10} e^{t} \sin (2 t)$
B) $\frac{7}{2} + \frac{t}{5} - \frac{t}{25} e^{t} \cos (2 t) + \frac{21}{10} e^{t} \sin (2 t)$
C) $\frac{7}{25} + \frac{t}{5}$
D) $\frac{7}{25} + \frac{t}{5} - \frac{7}{25} e^{t} \cos (2 t) + \frac{21}{10} e^{t} \sin (2 t)$
E) non of the above
F) $\frac{7}{25} + \frac{t}{5} - \frac{7}{5} e^{t} \cos (2 t) + \frac{21}{10} e^{t} \sin (2 t)$

Cabiolab 2021-09-23

Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the Laplace tranform of the function below.
$e^{- 2 t} \cos 6 t + e^{5 t} - 1$

ka1leE 2021-09-23

Using Laplave Transform, evaluate the integro-differential equation
$y^{″} (x) + 9 y (x) = 40 e^{x}; y (0) = 5, y^{'} (0) = - 2$

Ernstfalld 2021-09-23

If $L f (t) = F (s), then L f (4 t)$
a) $\frac{1}{4} F (s)$
b) $F (\frac{s}{4})$
c) $4 F (s)$
d) $\frac{1}{4} F (\frac{s}{4})$

defazajx 2021-09-23

Find the inverse Laplace transform of $F (s) = \frac{7 s - 6}{s^{2} - 4}$

Dillard 2021-09-23

L[y(x)]=Y(s) the following equation has been obtained when Laplace transformation has been applied to an initial value problem in y(x). find y(0)
$Y (s) = \frac{25 (5 - s^{2})}{s (s^{2} + 25)}$
25
-26
-25
27
-27

Tabansi 2021-09-23

find inverse Laplace transform of the given Function
$L^{- 1} \frac{s - 5}{{(s - 5)}^{2} - 9}$

kuCAu 2021-09-23

The Laplace transform of a continuous function over the interval $[0, \infty) [0, \infty)$ is defined by $F (s) = \int_{0}^{\infty} e^{- s x} f (x) d x .$
This definition is used to solve some important initial-value problems in differential equations, as discussed later. The domain of F is the set of all real numbers s such that the improper integral converges.
Find the Laplace transform F of the following functions and give the domain of F. $f (x) = \cos (2 x)$

remolatg 2021-09-23

find the Laplace transform of f (t).
$f (t) = t^{2} \cos 2 t$

rocedwrp 2021-09-23

Let f(t) be a function on $[0, \infty]$ . The Laplace transform of f is the function F defined by the integral $F (s) = \int_{0}^{\infty} e^{- s t} f (t) d t$ . Use this definition to determine the Laplace transform of the following function.
$f (t) = e^{- 4 t} \sin 9 t$

Emeli Hagan 2021-09-22

determine the Laplace transform of f.
$f (t) = e^{- 2 t} \sin (t - \frac{π}{4})$

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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