I've done the transform part and got a function -

$y(S)=\frac{2}{({s}^{2}+4)({s}^{2}+2s+5)}=\frac{A}{{s}^{2}+4}+\frac{Bs+C}{{s}^{2}+2s+5}$

Jonah Jacobson
2022-09-14
Answered

Solve the differential equation ${y}^{\u2033}+2{y}^{\prime}+5y=\mathrm{sin}2t$ using Laplace transform when y=0 and y′=0 when t=0

I've done the transform part and got a function -

$y(S)=\frac{2}{({s}^{2}+4)({s}^{2}+2s+5)}=\frac{A}{{s}^{2}+4}+\frac{Bs+C}{{s}^{2}+2s+5}$

I've done the transform part and got a function -

$y(S)=\frac{2}{({s}^{2}+4)({s}^{2}+2s+5)}=\frac{A}{{s}^{2}+4}+\frac{Bs+C}{{s}^{2}+2s+5}$

You can still ask an expert for help

asked 2022-09-15

Need to find the integral of the following function using Laplace Transform

$${\int}_{0}^{\mathrm{\infty}}\frac{\mathrm{cos}(6t)-\mathrm{cos}(4t)}{t}\phantom{\rule{thinmathspace}{0ex}}dt$$

$${\int}_{0}^{\mathrm{\infty}}\frac{\mathrm{cos}(6t)-\mathrm{cos}(4t)}{t}\phantom{\rule{thinmathspace}{0ex}}dt$$

asked 2021-09-03

Solve the following differential equations using the Laplace transform

asked 2022-01-18

Obtaining Differential Equations from Functions

is a first order ODE,

is a second order ODE and so on. I am having trouble to obtain a differential equation from a given function. I could find the differential equation for

using the orginal function and (1). Finally,

which is the required differential equation.

Similarly, if the function is

following similar steps as above.

asked 2021-12-09

Using the Laplace Transform Table in the textbook and Laplace Transform Properties,find the (unilateral) Laplace Transforms of the following functions:

$u\left(t\right)-u(t-1)$

asked 2021-02-13

Find the inverse laplace transforms for the following functions

$F(s)=\frac{{e}^{-3s}}{{s}^{2}}$

$F(s)=\frac{2{e}^{-5s}}{{s}^{2}+4}$

asked 2021-09-21

The Laplace transform function for the output voltage of a network is expressed in the following form:

$V}_{0}\left(s\right)=\frac{12(s+2)}{s(s+1)(s+3)(s+4)$

Determine the final value of this voltage. that is,

${\upsilon}_{0}\left(t\right)$ as $t\to \mathrm{\infty}$

a) 6V

b) 2V

c) 12V

d) 4V

Determine the final value of this voltage. that is,

a) 6V

b) 2V

c) 12V

d) 4V

asked 2022-09-16

Can the Inverse Finding the Laplace transform of $\frac{2s+1}{s(s+1)(s+2)}$ without using partial fractions?