Use the definition of Laplace Transforms to show that:

Jason Farmer
2021-02-12
Answered

Use the definition of Laplace Transforms to show that:

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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 2021-10-23

Show that any separable equation $M(x,y)+N(x,y){y}^{\prime}=0$

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 2022-01-21

A simple question about the solution of homogeneous equation to this differential equation

Given that$t,1+t,{t}^{2},-t$ are the solutions to $y{}^{\u2034}+a\left(t\right)y{}^{\u2033}+b\left(t\right)y{}^{\u2033}+c\left(t\right)y=d\left(t\right)$ , what is the solution of homogeneous equation to this differential equation? What i have done is tried the properties of linear differential equation that

$L\left(t\right)=L(1+t)=L\left({t}^{2}\right)=L(-t)=d\left(t\right)$ so the homogeneous solution should be independent and i claim that $1,t,{t}^{2}$ should be the solution. However, i am not sure hot can i actually conclude that these are the solutions? It seems that it can be quite a number of sets of solution by the linearity.

Given that

asked 2022-01-15

Solve the differential equation:

$y}^{\prime}\left(x\right)=y\left(x\right)-x-1+\frac{1}{x-y\left(x\right)+2$

with initial condition$y\left(0\right)=0$

with initial condition

asked 2021-06-16