Joanna Benson
2021-12-28
Answered

Find the general/particular solution of the following homogeneous linear differential equations with constant coefficients.

$({D}^{3}+{D}^{2}-21D-45)y=0$

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asked 2022-09-24

I need to find Laplace transform of this f(t)

$$f(t)=\frac{{e}^{at}-\mathrm{cos}bt}{t}$$

My approach:

$$F(s)=\mathcal{L}\left(\frac{{e}^{at}}{t}\right)-\mathcal{L}\left(\text{Re}\left(\frac{{e}^{ibt}}{t}\right)\right)$$

But I don't know how to solve such cases

$$f(t)=\frac{{e}^{at}-\mathrm{cos}bt}{t}$$

My approach:

$$F(s)=\mathcal{L}\left(\frac{{e}^{at}}{t}\right)-\mathcal{L}\left(\text{Re}\left(\frac{{e}^{ibt}}{t}\right)\right)$$

But I don't know how to solve such cases

asked 2021-12-18

Solve the given differential equation by separation of variables.

$\frac{dS}{dr}=kS$

asked 2022-01-20

What might be a solution to the differential equation of the form

$xy=c\frac{y}{y+d}$

where$y=y\left(x\right)$ and c,d are constants? I am supposed to simply state a solution to this, but I don;t think it is all that obvious.

where

asked 2021-12-31

Solve the following manually using separable differential equations method.

$mydx+nxdy=0$

asked 2022-01-24

laplace transform of ${2}^{\left[t\right]}$ where [] is greatest integer function <=t

asked 2021-09-03

Find the Laplace transform of $\mathrm{sin}ht-\mathrm{cos}ht$

asked 2021-09-16

Solve the initial value problem below using the method of Laplace transforms.