First Order Differential Equations: Examples and Practice Problems

College
Calculus and Analysis
Differential Equations
First order differential equations

Recent questions in First order differential equations

Painevg 2022-01-19

Find the general solution of the differential equation
$y^{'} = \frac{x - y + 3}{x - y}$

kramtus51 2022-01-19

Solve for G.S./P.S. for the following differential equations using the solutions by a change in variables as suggested by the equations.
$(t^{2} e^{t} - 4 x^{2}) d t + 8 t x d x = 0$

Mary Keefe 2022-01-19

I need help
Solve the following first order differential equation:
$3 t x^{'} - 2 x = \frac{t^{3}}{x^{2}}$

Roger Smith 2022-01-19

Dont

veksetz 2022-01-19

The Runge Kutta method is known as:
a. An analytical method of solving first order differential equations.
b. An accurate method of solving first order differential equations.
c. A numberical method of solving first order differential equations.
d. A complex method of solving first order differential equations.

Osvaldo Apodaca 2022-01-19

Need your help!
1. Identify the substitution method used to solve the given differential equations. Support your answer with the appropriate calculations.
2. Solve for the solution to the given differential equation that satisfies the given condition
$y^{'} = 2 {(3 x + y)}^{2} - 1; y (0) = 1$

William Collins 2022-01-19

Determine if the equation is linear or non-linear and indicate the order of the differential equation and would you tell me why please
$(2 x^{3} + y) d x - x d y = 0$
$y d x - (x + 6 y^{2}) d y = 0$
$(x + y) d x + \tan (x) d y = 0$
$6 x y d x + (4 y + 9 x^{2}) d y = 0$

nemired9 2021-12-26

What is the derivative of $h (x) = \sin 2 x \cos 2 x$

prelimaf1 2021-11-20

Find all first-order partial derivatives of the function at any point of the domain.
$f (x, y, z) = 4 x^{3} y^{2} - e^{z} y^{4} + \frac{z^{3}}{x^{2}} + 4 y - x^{16} + 2021$

tapetivk 2021-11-11

Look at the Chain Rule formula with a visual explanation of how it works:
${(h (x))}^{'} = {(g (f (x)))}^{'} = g^{'} (f (x)) \cdot f^{'} (x)$
$g (f (x))$ -outside function
$(f (x))$ -inside function
$g^{'} (f (x))$ -derivative of the otside at f(x)
$f^{'} (x)$ -derivative of the inside
Now, explain what happens in regards to calculating the derivative, if f(x) is also a composite function.

remolatg 2021-09-25

If $f (x) + x^{2} {[f (x)]}^{5} = 34$ and f(1) = 2, find f '(1).

CMIIh 2021-09-24

Verify, using the definition of convergence of a sequence, that the following sequences converge to the proposed limit.
a) $lim \frac{2 n + 1}{5 n + 4} = \frac{2}{5}$
b) $lim \frac{2 n^{3}}{n^{3} + 3} = 0$
c) $lim \frac{\sin (n^{2})}{\sqrt[3]{n}}$

Tobias Ali 2021-07-05

Write first-order differential equations that express the situation: The increase in the number of people who have heard a rumor in a town of population 20,00020,000 is proportional to the product of the number PP who have heard the rumor and the number who have not heard the rumor at time tt .

Lennie Carroll 2021-06-10

Write first-order differential equations that express the situation: A student in an engineering course finds the rate of increase of his grade point average GG is directly proportional to the number NN of study hours/week and inversely proportional to the amount AA of time spent on online games .

Zoe Oneal 2021-05-31

Identify the surface whose equation is given.
$ρ = \sin θ \sin ϕ$

nitraiddQ 2021-05-27

Write first-order differential equations that express the situation: A Walking Mode, l Construct a mathematical model to estimate how long it will take you to walk to the store for groceries. Suppose you have measured the distance as 11 mile and you estimate your walking speed as 33 miles per hour. If it takes you 2020 minutes to get to the store, what do you conclude about your model?

Jason Farmer 2021-05-26

Write the following first-order differential equations in standard form. $y^{'} = x^{3} y + \sin x$

Khaleesi Herbert 2021-05-23

Find the differential of each function.
(a) $y = \tan \sqrt{t}$
(b) $y = \frac{1 - v^{2}}{1 + v^{2}}$

Yasmin 2021-05-22

Write the following first-order differential equations in standard form. $\frac{d y}{d t} = y x (x + 1)$

facas9 2021-05-05

If $f (x) + x^{2} [f (x)]^{5} = 34$ and $f (1) = 2,$ find $f^{'} (1) .$

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Differential Equations

Learn First Order Problems with These Differential Equations Examples