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

Scoopedepalj 2022-02-15

If $p (x)$ is a solution to a first-order differential equation in the form of $\frac{d f}{d x} = g (f)$ , then $p (x + c)$ , with c-constant, is a solution as well.
I know the idea of the proof, but I am having trouble expressing it in a rigorous proof. Namely, my idea is that if we shift $p (x)$ to the left by $c$ , then both the LHS and RHS will shift by $c P$ (invoking the chain rule), so they are equal. Should I define $u = x + c$ and do a change of variable?

durants718 2022-02-01

so the problem ask if like what statement is always true? A. The sum of two irrational numbers is ratioanl. B. The product of two rational and irrational number is rational. C The sum of two ratioanl number is irrational . D.The productof two rational number is rational.

Kaspaueru2 2022-01-22

Write an equivalent first-order differential equation and initial condition for y.
$y = - 4 + \int_{1}^{x} (4 t - y (t)) d t$
What is the equivalent first-order differential equation?
What is the initial condition?

Marenonigt 2022-01-22

Important
Solve the bernoullis

veksetz 2022-01-22

Solve in two different methods.
$(y - x + 3) d x + (x + y + 3) d y = 0; x = 1; y = 4 .$

Michael Maggard 2022-01-22

Explain why or why not determine whether the following statements are true and give an explanation or counterexample.
a. The differential equation y+2y

maduregimc 2022-01-22

Quickly! Need help
Solve differential equation, subject to the given initial condition.
$x \frac{d y}{d x} + (1 + x) y = 3; y (4) = 50$

reproacht3 2022-01-22

Find the solution of the following differential equations.
First Order Differential Equations
$x (2 y - 3) d x + (x^{2} + 1) d y = 0$
$A n s w e r : (x^{2} + 1) (2 y - 3) = c$

regatamin2 2022-01-22

Maybe you know how to do it?
Write an equivalent first-order differential equation and initial condition for y
$y = \int_{1}^{x} \frac{1}{t} d t$
What is the equivalent first-order differential equation?
$y^{'} = ?$

Brock Brown 2022-01-22

Don`t have much time, help
Solving a first-order differential equation in exercise, find the general solution of the first-order differential equation x>0 by any appropriate method
$\frac{d y}{d x} = \frac{e^{2 x + y}}{e^{x - y}}$

Annette Sabin 2022-01-22

Solve the first-order differential equations:
$(x^{2} + 1) \frac{d y}{d x} = x y$

Quentin Johnson 2022-01-22

Solve the equation separable, linear, bernoulli, or homogenous
$1 . \frac{d y}{d x} = \frac{x^{4} + 4 x y^{2}}{2 x^{3} + x^{2} y + y^{3}}$
$2 . (e^{- y} \cos (x)) y^{'} = x^{4} + 6 x^{2} y^{3}$
$3 . y^{'} = \frac{y + y x^{3}}{x + x^{2}} \cos (\frac{x^{2}}{y^{2}})$

petrusrexcs 2022-01-22

Find the general solution to these first order differential equations.
$3 (3 x^{2} + у^{2}) d x - 2 x y d y = 0$

zagonek34 2022-01-21

Solve the following first order differential equation $y^{'} = \frac{x + 1}{y^{2} + 1}$ , and give the solution to the general first order differential equations $y^{'} = \frac{a x + b}{y^{n} + c}$ , where a, b and c are constants.

Reginald Metcalf 2022-01-21

Solve by using the Laplace Transform Method?
$y^{'} + y = 6 e^{t^{2}}, y (0) = 3$

aspifsGak5u 2022-01-21

Find the general solution of these first order differential equations
$(1 - x) y^{'} = y^{2}$

Irrerbthist6n 2022-01-21

${(y)}^{2} + 8 y^{'} = 4 t$ is:
a. Second order nonlinear differential equation.
b. First order linear differential equation.
c. Second order linear differential equation.
d. First order nonlinear differential equation.

Patricia Crane 2022-01-21

Are the following are linear equation?
$1 . \sin (x) \frac{d y}{d x} - 3 y = 0$
$2 . \frac{d^{2} y}{{d x}^{2}} + \sin (x) \frac{d y}{d x} = \cos (x)$

Patricia Crane 2022-01-21

Are the following are linear equation?
$1 . \frac{d P}{d t} + 2 t P = P + 4 t - 2$
$2 . \frac{d y}{d x} = y^{2} - 3 y$

Quentin Johnson 2022-01-21

Find the critical points and sketch the phase portrait of the given autonomous first order differential equation. Classify the each critical point as asmyptotically stable, unstable, or semi-stable.
$y^{'} = y^{2} (4 - y^{2})$

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Differential Equations

Learn First Order Problems with These Differential Equations Examples