Explore Laplace Transform Equations

Solve by Laplace transforms
$y " - 3 y^{'} + 2 y = 2 δ (t - 1)$
$y (0) = 1$
$y^{'} (0) = 0$

emancipezN 2020-11-09

Use Laplace transform to evaluate the integral
$\int_{0}^{\infty} t e^{- 2 t} \sin (2 t) d t$
a) $\frac{1}{B}$
b) not defined
c) $\frac{4 s}{(s^{2} + 4)^{2}}$
d) $\frac{4 (s + 2)}{(s^{2} + 4 s + 8)^{2}}$

Amari Flowers 2020-11-09

Solve the inital value problem by using Laplace transform:
$y^{″} - 5 y^{'} + 6 y = - 8 \cos (t) - 2 \sin (t), y (\frac{π}{2}) = 1, y^{'} (\frac{π}{2}) = 0$

Khadija Wells 2020-11-09

Solve the third-order initial value problem below using the method of Laplace transforms
$y^{‴} - 2 y " - 21 y^{'} - 18 y = - 18$
$y (0) = 2$
$y^{'} (0) = 7$
$y " (0) = 95$

Line 2020-11-08

How to solve this equation $y - 4 y + 2 y - 16 y = 4 x + 1$ using Method of Undetermined Coefficient, Variation of Parameters and Laplace Transformation

CoormaBak9 2020-11-08

The Laplace transform of the product of two functions is the product of the Laplace transforms of each given function. True of False?

Kaycee Roche 2020-11-08

Find the solution of the Differentional equation by using Laplace Transformation
$2 y^{'} - 3 y = e^{2 t}, y (0) = 1$
$y " + y = t, y (0) = 0 a n d y^{'} (0) = 2$

opatovaL 2020-11-07

Write down the qualitative form of the inverse Laplace transform of the following function. For each question first write down the poles of the function , X(s)
a) $X (s) = \frac{s + 1}{(s + 2) (s^{2} + 2 s + 2) (s^{2} + 4)}$
b) $X (s) = \frac{1}{(2 s^{2} + 8 s + 20) (s^{2} + 2 s + 2) (s + 8)}$
c) $X (s) = \frac{1}{s^{2} (s^{2} + 2 s + 5) (s + 3)}$

Tobias Ali 2020-11-06

Find Laplace transform of the given function
$t e^{- 4 t} \sin 3 t$

sagnuhh 2020-11-05

Explain First Shift Theorem & its properties?

boitshupoO 2020-11-05

Find the inverse laplace transform of the function
$Y (s) = \frac{e^{- s}}{s (2 s - 1)}$

Dolly Robinson 2020-11-02

Use the Laplace transform to solve the given integral equation
$(s) = 2 t^{2} + \int_{0}^{t} \sin [2 (t - τ)] x (τ) d τ$

BenoguigoliB 2020-11-02

$y + y = e^{- 2 t} \sin t, y (0) = y' (0) = 0$
solution of given initial value problem with Laplace transform

generals336 2020-11-02

Find the Laplace transform $L {u_{3} (t) (t^{2} - 5 t + 6)}$
$a) F (s) = e^{- 3 s} (\frac{2}{s^{4}} - \frac{5}{s^{3}} + \frac{6}{s^{2}})$
$b) F (s) = e^{- 3 s} (\frac{2}{s^{3}} - \frac{5}{s^{2}} + \frac{6}{s})$
$c) F (s) = e^{- 3 s} \frac{2 + s}{s^{4}}$
$d) F (s) = e^{- 3 s} \frac{2 + s}{s^{3}}$
$e) F (s) = e^{- 3 s} \frac{2 - 11 s + 30 s^{2}}{s^{3}}$

Tazmin Horton 2020-11-01

Calculate the Laplace transform
$L {\sin (t - k) \cdot H (t - k)}$

pedzenekO 2020-11-01

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

smileycellist2 2020-11-01

Solve the following IVP using Laplace Transform
$y^{'} - 2 y = 1 - t, y (0) = 4$

UkusakazaL 2020-11-01

Solve $f (t) = e^{t} \cos t$

Tahmid Knox 2020-10-31

How to solve for the equation
$y^{‴} + 4 y^{″} + 5 y^{'} + 2 y = 4 x + 16$
using laplace transform method given that
$y (0) = 0, y^{'} (0) = 0, and y^{″} (0) = 0$

Bevan Mcdonald 2020-10-31

Find the laplace transform of the following
$f (t) = t u_{2} (t)$
Ans. $F (s) = (\frac{1}{s^{2}} + \frac{2}{s}) e^{- 2 s}$

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.

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