 # Learn First Order Problems with These Differential Equations Examples

Recent questions in First order differential equations 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℃ ? 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. vegetatzz8s 2022-11-25

## How can I solve this differential equation? : Ty Moore 2022-11-18

## What is the general solution of the differential equation? : ${x}^{2}\frac{{d}^{2}y}{{dx}^{2}}+x\frac{dy}{dx}+{n}^{2}y=0$ Uroskopieulm 2022-11-16

## Solve the Differential Equation $\frac{dy}{dx}=2xy-x$? Aron Heath 2022-11-05

## What is a solution to the differential equation $xy\prime +2y=0$? Trace Glass 2022-10-27

## ${x}^{2}{y}^{″}+x{y}^{\prime }-y={x}^{2}$My attempt:Divided by ${x}^{2}$:${y}^{″}+\frac{{y}^{\prime }}{x}-\frac{y}{{x}^{2}}=1$Now to solve the homogenous equation using Euler's method${y}^{″}+\frac{{y}^{\prime }}{x}-\frac{y}{{x}^{2}}=0$To look for solution $y={x}^{r}$so ${y}^{\prime }=r{x}^{r-1}$${y}^{″}=r\left(r-1\right){x}^{r-2}$So:$r\left(r-1\right){x}^{r-2}+\frac{r{x}^{r-1}}{x}-\frac{{x}^{r}}{{x}^{2}}=0$Divided by ${x}^{r}$:$r\left(r-1\right){x}^{-2}+\frac{r{x}^{-1}}{x}-\frac{1}{{x}^{2}}=0$Is it correct so far?My problem: I don't know how to find ${r}_{1},{r}_{2}$ Jane Galura2022-10-26

## A metal is heated-up to a temperature of 500 degree Celsius. It is then exposed to a temperature of 38 degree Celsius. After 2 minutes, the temperature of the metal becomes 190 degree Celsius.a. when will the temperature be 100°C?b. what is the temperature after 4 minutes? benatudq 2022-10-22

## What is a second solution to the Differential Equation ${x}^{2}y\prime \prime -3xy\prime +5y=0$? erwachsenc6 2022-10-12

## How do you solve the differential equation given $f\prime \left(s\right)=6s-8{s}^{3}$? blackdivcp 2022-10-11

## What is a solution to the differential equation $y\prime =2x+1$? smetuwh 2022-09-30

## How to you find the general solution of $\frac{dy}{dx}=x{e}^{{x}^{2}}$? Ratuiszt 2022-09-30

## How do I solve the differential equation $xy\prime -y=3xy,{y}_{1}=0$? Parker Pitts 2022-09-30

## What is a solution to the differential equation $\frac{dy}{dx}=\frac{6\mathrm{sin}x}{y}$? Jamarcus Lindsey 2022-09-30

## How to do the ordinary differential equation? $\frac{dA}{dt}=\stackrel{.}{A}=-\frac{\alpha }{2m}A\to A\left(t\right)=A\left(0\right){e}^{-\frac{\alpha }{2m}t}$ mocatgesex 2022-09-30

## What is the solution of the differential equation? : $y\frac{dy}{dx}={\left(9-4{y}^{2}\right)}^{\frac{1}{2}}$ where x=0 when y=0 timberwuf8r 2022-09-30

## How to you find the general solution of $\frac{dr}{ds}=0.05r$? jhenezhubby01ff 2022-09-30

## What is the general solution of the differential equation $xyy\prime ={x}^{2}+1$ ? eukrasicx 2022-09-30
## How do you solve $\frac{dy}{dx}=x{y}^{2}$? eukrasicx 2022-09-30