Solve the differential equation

Reeves
2020-11-16
Answered

Solve the differential equation

You can still ask an expert for help

Alix Ortiz

Answered 2020-11-17
Author has **109** answers

Divide both sides by x and further simplify it

It is of the form

Now find the integrating factor by using

Hence,

Hence,

Hence,

Simplify

asked 2022-04-28

I am stuck with this equation. If you can help me

$y{}^{\u2033}\left(t\right)+12{y}^{\prime}\left(t\right)+32y\left(t\right)=32u\left(t\right)$ with $y\left(0\right)={y}^{\prime}\left(0\right)=0$

I found the laplace transform for y(t)

$Y\left(p\right)=x=\frac{32}{\left(p({p}^{2}+12p+32)\right)}$

so i need the laplace transform of y(t) and then the solution for y(t).

I found the laplace transform for y(t)

so i need the laplace transform of y(t) and then the solution for y(t).

asked 2022-06-21

Consider $x{y}^{\u2033}+2{y}^{\prime}+xy=0$. Its solutions are $\frac{\mathrm{cos}x}{x},\phantom{\rule{thinmathspace}{0ex}}\frac{\mathrm{sin}x}{x}$.

Neither of those solutions (as far as I could find) can be the solutions of a first order linear homogeneous differential equation. However

$\frac{{e}^{\pm ix}}{x}$

Can be the solution of a first order linear homogeneous DE (${y}^{\prime}+(x\mp i)y=0$)

Can I always find a first order homogeneous linear DE whose solution also solves a second order homogeneous linear DE?

For example can I find a first order homogeneous linear DE whose solution is a particular linear combination of ${J}_{1}$ and ${Y}_{1}$?

(unrelated: also I'd like to know if there is a way of solving $x{y}^{\u2033}+2{y}^{\prime}+xy=0$ without noticing that it is a spherical bessel function or using laplace transform.)

Neither of those solutions (as far as I could find) can be the solutions of a first order linear homogeneous differential equation. However

$\frac{{e}^{\pm ix}}{x}$

Can be the solution of a first order linear homogeneous DE (${y}^{\prime}+(x\mp i)y=0$)

Can I always find a first order homogeneous linear DE whose solution also solves a second order homogeneous linear DE?

For example can I find a first order homogeneous linear DE whose solution is a particular linear combination of ${J}_{1}$ and ${Y}_{1}$?

(unrelated: also I'd like to know if there is a way of solving $x{y}^{\u2033}+2{y}^{\prime}+xy=0$ without noticing that it is a spherical bessel function or using laplace transform.)

asked 2021-05-18

Use the family in Problem 1 to ﬁnd a solution of

asked 2022-02-15

Throughout my engineering education, Ive

asked 2020-12-05

Solve the following ODE by using the Laplace transform

${y}^{\prime}(x)-8y(x)=0$

$y(0)=e$

asked 2020-11-08

A particle moves along the curve $x=2{t}^{2}y={t}^{2}-4t$ and z=3t-5 where t is the time.find the components of the velocity at t=1 in the direction i-3j+2k

asked 2022-04-16

Laplace transform of $f\left({t}^{2}\right)$

Suppose we know the Laplace transform of a function f(t):

$F\left(s\right)={\int}_{0}^{\mathrm{\infty}}f\left(t\right){e}^{-st}dt$

Suppose we know the Laplace transform of a function f(t):