Recent questions in Differential Equations

Differential EquationsOpen question

Jonalito Juan2023-05-12

- A body falls from rest against resistance proportional to the square root of the speed at any instant. If the body attains speed V1 and V2 feet per second, after 1 and 2 seconds in motion, respectively, find an expression for the limiting velocity.

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Eliza Shields 2023-04-01

The Laplace transform of $u(t-2)$ is

(a)$\frac{1}{s}+2$

(b)$\frac{1}{s}-2$

(c)$e}^{2}\frac{s}{s}\left(d\right)\frac{{e}^{-2s}}{s$ ??

(a)

(b)

(c)

Differential EquationsAnswered question

Gianna Johnson 2023-04-01

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

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nepojamanuszc 2023-03-23

1 degree on celsius scale is equal to

A) $\frac{9}{5}$ degree on fahrenheit scale

B) $\frac{5}{9}$ degree on fahrenheit scale

C) 1 degree on fahrenheit scale

D) 5 degree on fahrenheit scale

A) $\frac{9}{5}$ degree on fahrenheit scale

B) $\frac{5}{9}$ degree on fahrenheit scale

C) 1 degree on fahrenheit scale

D) 5 degree on fahrenheit scale

Differential EquationsAnswered question

inframundosa921 2023-03-21

The Laplace transform of $t{e}^{t}$ is A. $\frac{s}{(s+1{)}^{2}}$ B. $\frac{1}{(s-1{)}^{2}}$ C. $\frac{s}{(s+1{)}^{2}}$ D. $\frac{s}{(s-1)}$

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enrosca0fx 2023-01-03

What is the Laplace transform of $t\mathrm{cos}t$ into the s domain?

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Aydin Welch 2022-12-20

Find the general solution of the given differential equation:

${y}^{\u2033}-2{y}^{\prime}+y=0$

${y}^{\u2033}-2{y}^{\prime}+y=0$

Differential EquationsOpen question

Hailee S.2022-12-19

The rate at which a body cools is proportional to the difference in

temperature between the body and its surroundings. If a body in air

at 0℃ will cool from 200℃ 𝑡𝑜 100℃ in 40 minutes, how many more

minutes will it take the body to cool from 100℃ 𝑡𝑜 50℃ ?

Differential EquationsOpen question

Hailee S.2022-12-19

A body falls from rest against a resistance proportional to the velocity at any instant. If the limiting velocity is 60fps and the body attains half that velocity in 1 second, find the initial velocity.

Differential EquationsAnswered question

unecewelpGGi 2022-11-25

What's the correct way to go about computing the Inverse Laplace transform of this?

$\frac{-2s+1}{({s}^{2}+2s+5)}$

I Completed the square on the bottom but what do you do now?

$\frac{-2s+1}{(s+1{)}^{2}+4}$

$\frac{-2s+1}{({s}^{2}+2s+5)}$

I Completed the square on the bottom but what do you do now?

$\frac{-2s+1}{(s+1{)}^{2}+4}$

Differential EquationsAnswered question

hemotropS7A 2022-11-25

How to find inverse Laplace transform of the following function?

$X(s)=\frac{s}{{s}^{4}+1}$

I tried to use the definition: $f(t)={\mathcal{L}}^{-1}\{F(s)\}=\frac{1}{2\pi i}\underset{T\to \mathrm{\infty}}{lim}{\int}_{\gamma -iT}^{\gamma +iT}{e}^{st}F(s)\phantom{\rule{thinmathspace}{0ex}}ds$or the partial fraction expansion but I have not achieved results.

$X(s)=\frac{s}{{s}^{4}+1}$

I tried to use the definition: $f(t)={\mathcal{L}}^{-1}\{F(s)\}=\frac{1}{2\pi i}\underset{T\to \mathrm{\infty}}{lim}{\int}_{\gamma -iT}^{\gamma +iT}{e}^{st}F(s)\phantom{\rule{thinmathspace}{0ex}}ds$or the partial fraction expansion but I have not achieved results.

Differential EquationsAnswered question

phumzaRdY 2022-11-25

How do i find the lapalace transorm of this intergral using the convolution theorem? ${\int}_{0}^{t}{e}^{-x}\mathrm{cos}x\phantom{\rule{thinmathspace}{0ex}}dx$

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klupko5HR 2022-11-25

Find the inverse Laplace transform of $\frac{{s}^{2}-4s-4}{{s}^{4}+8{s}^{2}+16}$

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vegetatzz8s 2022-11-25

How can I solve this differential equation? : $xydx-({x}^{2}+1)dy=0$

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Ghillardi4Pi 2022-11-24

Сalculate which equation represents a line that passes through $(5,1)$ and has a slope of StartFraction one-half EndFraction?

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Alberanteb4T 2022-11-24

inverse laplace transform - with symbolic variables:

$F(s)=\frac{2{s}^{2}+(a-6b)s+{a}^{2}-4ab}{({s}^{2}-{a}^{2})(s-2b)}$

My steps:

$F(s)=\frac{2{s}^{2}+(a-6b)s+{a}^{2}-4ab}{(s+a)(s-a)(s-2b)}$

$=\frac{A}{s+a}+\frac{B}{s-a}+\frac{C}{s-2b}+K$

$K=0$

$A=F(s)\ast (s+a)$

$F(s)=\frac{2{s}^{2}+(a-6b)s+{a}^{2}-4ab}{({s}^{2}-{a}^{2})(s-2b)}$

My steps:

$F(s)=\frac{2{s}^{2}+(a-6b)s+{a}^{2}-4ab}{(s+a)(s-a)(s-2b)}$

$=\frac{A}{s+a}+\frac{B}{s-a}+\frac{C}{s-2b}+K$

$K=0$

$A=F(s)\ast (s+a)$

Differential EquationsAnswered question

hemotropS7A 2022-11-24

How to find the Direct Discrete Laplace Transform of $(}\genfrac{}{}{0ex}{}{2n}{n}{\textstyle )$

Differential EquationsAnswered question

ingerentayQL 2022-11-24

Laplace transform of $(3e{)}^{t}{\mathrm{sin}}^{2}t$

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Juan Lowe 2022-11-23

How to solve such fraction differential equation?

Here's my first-order differential equation:

$({x}^{3}-2x{y}^{2})dx+3y{x}^{2}dy=xdy-ydx$

I've tried to make it fraction, but it isn't separable differential equation, also it isn't differential equation in total differentials, so after it I lose any clue for answer.

Here's my first-order differential equation:

$({x}^{3}-2x{y}^{2})dx+3y{x}^{2}dy=xdy-ydx$

I've tried to make it fraction, but it isn't separable differential equation, also it isn't differential equation in total differentials, so after it I lose any clue for answer.

Speaking of differential equations, these are used not only by those students majoring in Physics because solving differential equations is also quite common in Statistics and Financial Studies. Explore the list of questions and examples of equations to get a basic idea of how it is done.

These answers below are meant to provide you with the starting points as you work with your differential equations. If you need specific help or cannot understand the rules behind the answers that are presented below, start with a simple equation and learn with the provided solutions..