# Differential equations questions and answers

Recent questions in Differential equations
2022-01-24

### laplace transform of 2^[t] where [] is greatest integer function <=t

Marenonigt 2022-01-22 Answered

### Important Solve the bernoulli's differential equation $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}{\left({x}^{{2}}{y}^{{3}}+{x}{y}\right)}={1}$$

veksetz 2022-01-22 Answered

### Solve in two different methods. $$\displaystyle{\left({y}-{x}+{3}\right)}{\left.{d}{x}\right.}+{\left({x}+{y}+{3}\right)}{\left.{d}{y}\right.}={0};\ {x}={1};\ {y}={4}.$$

Michael Maggard 2022-01-22 Answered

### Explain why or why not determine whether the following statements are true and give an explanation or counterexample. a. The differential equation y'+2y =t is first-order, linear, and separable. b. The differential equation $$\displaystyle{y}'{y}={2}{t}^{{2}}$$ is first-order, linear, and separable.

maduregimc 2022-01-22 Answered

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

reproacht3 2022-01-22 Answered

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

regatamin2 2022-01-22 Answered

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

Brock Brown 2022-01-22 Answered

### 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 $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{{e}^{{{2}{x}+{y}}}}}{{{e}^{{{x}-{y}}}}}}$$

Kaspaueru2 2022-01-22 Answered

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

Annette Sabin 2022-01-22 Answered

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

Quentin Johnson 2022-01-22 Answered

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

petrusrexcs 2022-01-22 Answered

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

Oberlaudacu 2022-01-21 Answered

### The equation $$\displaystyle{y}'={\frac{{{y}}}{{{x}}}}{\left({\ln{{y}}}-{\ln{{x}}}+{1}\right)}$$ is? 1. First order, Partial. 2. First order, Non-homogenous. 3. None of above. 4. First order, Homogenous.

killjoy1990xb9 2022-01-21 Answered

### Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. 1. The function $$\displaystyle{y}={t}+{\frac{{{1}}}{{{t}}}}$$, for t > 0, satisfies the initial value problem ty'+y=2t, y(1)=2.

piarepm 2022-01-21 Answered

### Convert the differential equation $$\displaystyle{u}{''}-{u}'-{2}{u}={e}^{{-{5}{t}}}$$ into a system of first order equations by letting x=u, y=u' $$\displaystyle{x}'=?$$ $$\displaystyle{y}'=?$$

Katherine Walls 2022-01-21 Answered

### Solve for G.S./P.S. for the following differential equations using the method of solution for Bernoulli and Ricatti differential equations. $$\displaystyle{9}{x}{y}'={\left({y}-{1}\right)}{\left({y}+{2}\right)};\ \ {y}_{{p}}=-{2}$$

Julia White 2022-01-21 Answered

### Solve the first order linear differential equation $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}+{x}{y}={x},\ \ {y}{\left({0}\right)}=-{6}$$

Carla Murphy 2022-01-21 Answered

### Which of the following is true about Lagrange's and Hamilton's equations a. Both sets of equations are first order differential equations b. Lagrange equations are first order differential equations and Hamilton's equations are second order differential equations c. Lagrange equations are second order differential equations and Hamilton's equations are first order differential equations d. Both sets of equations are second order differential equations

Krzychau1 2022-01-21 Answered

### Help to solve the following first order differential equations: a. $$\displaystyle{x}{y}^{{4}}{\left.{d}{x}\right.}+{\left({y}^{{2}}+{2}\right)}{e}^{{-{5}{x}}}{\left.{d}{y}\right.}={0}$$ b.$$\displaystyle{\left({x}+{1}\right)}{y}'={x}+{6}$$

b2sonicxh 2022-01-21 Answered

### Write an equivalent​ first-order differential equation and initial condition for y. $$\displaystyle{y}=-{1}+{\int_{{{0}}}^{{{x}}}}{\left({2}{t}-{5}{y}{\left({t}\right)}\right)}{\left.{d}{t}\right.}$$ What is the equivalent first-order differential equation? $$\displaystyle{y}'=?$$ What is the initial condition? $$\displaystyle{y}{\left({y}'=?\right)}=?$$

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..

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