Explore Laplace Transform Equations

solve the given initial value problem
$y^{‴} + 3 y^{″} - 13 y^{'} - 15 y = 0, y (0) = y^{'} (0) = 0, y^{″} (0) = 1$

Kyran Hudson 2021-09-16

Find the solution of the given system of differential equations by Operator method or Laplace transform.
$2 \frac{d x}{d t} + \frac{d y}{d t} + x + 5 y = 4 t$
$\frac{d x}{d t} + \frac{d y}{d t} + 2 x + 2 y = 2$
$x (0) = 3, y (0) = - 4$

Kye 2021-09-15

Find laplace transform of the following functions
$f (t) = t \sin h (2 t)$

Tazmin Horton 2021-09-15

Laplace transforms A powerful tool in solving problems in engineering and physics is the Laplace transform. Given a function f(t), the Laplace transform is a new function F(s) defined by
$F (s) = \int_{0}^{\infty} e^{- s t} f (t) d t$
where we assume s is a positive real number. For example, to find the Laplace transform of $f (t) = e^{- t}$ , the following improper integral is evaluated using integration by parts:
$F (s) = \int_{0}^{\infty} e^{- s t} e^{- t} d t = \int_{0}^{\infty} e^{- (s + 1) t} d t = \frac{1}{s + 1}$
Verify the following Laplace transforms, where u is a real number.
$f (t) = \cos a t \to F (s) = \frac{s}{s^{2} + a^{2}}$

Marvin Mccormick 2021-09-15

Consider the following initial value problem:
$y'' - 4 y' - 45 y = \sin (7 t), y (0) = 1, y' (0) = - 4$
Using Y for the Laplace transform of y(t), i.e., Y=L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)=?

FizeauV 2021-09-15

Solve the differential equation by variation of parameters
$y y = \sin x$

sanuluy 2021-09-15

Find the initial value for the function $f {t} = 2 u (t) + 3 \cos u (t)$
a) 2
b) 3
c) 5
d) 4

OlmekinjP 2021-09-15

Calculate the Laplace transform $L {f}$ of the function $f (t) = e^{4 t + 2} - 8 t^{6} + 8 \sin (2 t) + 9$ using the basic formulas and the linearity of the Laplace transform

ankarskogC 2021-09-15

Find the Laplace transform by the method of definition.
$f (t) = e^{\frac{t}{5}}$

zi2lalZ 2021-09-15

Solve the following differential equations using the Laplace transform
$y 2 y^{'} + y = t + 3$
$y (0) = 1, y^{'} (0) = 0$

Reeves 2021-09-15

Evaluate $L^{- 1} (\frac{3 x}{x^{2} + 9})$ where $L^{- 1}$ is inverse Laplace transformation?
a) $2 \cos (2 x)$
b) $3 \sin (3 x)$
c) $3 \cos (9 x)$
d) $3 \cos (3 x)$
e) $2 \cos (3 x)$

allhvasstH 2021-09-15

Find the Laplace transform of $3 e^{- 7 t}$

Daniaal Sanchez 2021-09-15

Find the inverse Laplace transform of the following:
$(\frac{7}{2}) \log (\frac{s - 8}{s + 8})$

glasskerfu 2021-09-15

Use the Laplace transform table and the linearity of the Laplace transform to determine the following transform
$L {t^{4} + t^{3} - t^{2} - t + \sin \sqrt{2} t}$

Chaya Galloway 2021-09-15

Find Laplace transform $L {10 e^{- 5 t} \sin \frac{t}{2}}$

Lewis Harvey 2021-09-15

Which of the following is a TRUE statement?
A) $L^{- 1} {\frac{6}{s^{7}}} = t^{6}$
B) $L^{- 1} {\frac{3}{s^{2} + s}} = 3 - 3 e^{t}$
C) $L^{- 1} {\frac{6!}{(s + 4)^{8}}} = t^{6} e^{4 t}$
D) $L^{- 1} {\frac{s}{s^{2} + 5 s + 6}} = 3 e^{- 3 t} - 2 e^{- 2 t}$
E) $L^{- 1} {\frac{5!}{(s + 2)^{3}}} = t^{5} e^{- 2 t}$

Jason Farmer 2021-09-15

Invert the following system to the time domain using partial fraction
$f (s) = \frac{6}{s^{2} (s + 2) (s + 4)}$

Cheyanne Leigh 2021-09-15

Determine the solution of y(t) for the following equations
$\frac{d y}{d t} + 5 \int_{0}^{t} y d t + 2 y = 10 with y (0) = 0$

Ernstfalld 2021-09-14

Solve the laplace transforms
$\dot{x} - 2 \ddot{x} + x = e^{t} \cdot t$
fiven $t = 0$ and $\dot{x} = 0$ and $x = 1$

lwfrgin 2021-09-14

If the $L {y} = \overset{―}{y},,then the L {y "}$ is
a) $s \overset{―}{y} - y (0)$
b) $s^{2} \overset{―}{y} - s y (0) - y^{'} (0)$
c) $s^{2} \overset{―}{y} + s y (0) + y^{'} (0)$
d) None of these

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

Learn Laplace Transform Equations with Plainmath