First Order Differential Equations: Examples and Practice Problems

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Calculus and Analysis
Differential Equations
First order differential equations

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? : $x y d x - (x^{2} + 1) d y = 0$

Ty Moore 2022-11-18

What is the general solution of the differential equation? : $x^{2} \frac{d^{2} y}{{d x}^{2}} + x \frac{d y}{d x} + n^{2} y = 0$

Uroskopieulm 2022-11-16

Solve the Differential Equation $\frac{d y}{d x} = 2 x y - x$ ?

Aron Heath 2022-11-05

What is a solution to the differential equation $x y' + 2 y = 0$ ?

Trace Glass 2022-10-27

$x^{2} y^{″} + x y^{'} - y = x^{2}$
My attempt:
Divided by $x^{2}$ :
$y^{″} + \frac{y^{'}}{x} - \frac{y}{x^{2}} = 1$
Now to solve the homogenous equation using Euler's method
$y^{″} + \frac{y^{'}}{x} - \frac{y}{x^{2}} = 0$
To look for solution $y = x^{r}$
so $y^{'} = r x^{r - 1}$
$y^{″} = r (r - 1) x^{r - 2}$
So:
$r (r - 1) x^{r - 2} + \frac{r x^{r - 1}}{x} - \frac{x^{r}}{x^{2}} = 0$
Divided by $x^{r}$ :
$r (r - 1) x^{- 2} + \frac{r x^{- 1}}{x} - \frac{1}{x^{2}} = 0$
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 $x^{2} y'' - 3 x y' + 5 y = 0$ ?

erwachsenc6 2022-10-12

How do you solve the differential equation given $f' (s) = 6 s - 8 s^{3}$ ?

blackdivcp 2022-10-11

What is a solution to the differential equation $y' = 2 x + 1$ ?

smetuwh 2022-09-30

How to you find the general solution of $\frac{d y}{d x} = x e^{x^{2}}$ ?

Ratuiszt 2022-09-30

How do I solve the differential equation $x y' - y = 3 x y, y_{1} = 0$ ?

Parker Pitts 2022-09-30

What is a solution to the differential equation $\frac{d y}{d x} = \frac{6 \sin x}{y}$ ?

Jamarcus Lindsey 2022-09-30

How to do the ordinary differential equation? $\frac{d A}{d t} = \dot{A} = - \frac{α}{2 m} A \to A (t) = A (0) e^{- \frac{α}{2 m} t}$

mocatgesex 2022-09-30

What is the solution of the differential equation? : $y \frac{d y}{d x} = {(9 - 4 y^{2})}^{\frac{1}{2}}$ where x=0 when y=0

timberwuf8r 2022-09-30

How to you find the general solution of $\frac{d r}{d s} = 0.05 r$ ?

jhenezhubby01ff 2022-09-30

What is the general solution of the differential equation $x y y' = x^{2} + 1$ ?

eukrasicx 2022-09-30

How do you solve $\frac{d y}{d x} = x y^{2}$ ?

eukrasicx 2022-09-30

What is a general solution to the differential equation $\frac{d y}{d x} = \frac{x^{3}}{y^{2}}$ ?

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Differential Equations

Learn First Order Problems with These Differential Equations Examples