# Differential equations questions and answers

Recent questions in Differential equations
hrostentsp6 2021-11-11 Answered

### Solve the initial value problem below using the method of laplace transforms. $$\displaystyle{y}{''}+{2}{y}'-{3}{y}={0},\ {y}{\left({0}\right)}={1},{y}'{\left({0}\right)}={9}$$

smismSitlougsyy 2021-11-11 Answered

### Determine the longest interval in which the given initial value problem is certain to have a unique twice differentiable solution. Do not attempt to find the solution. $$\displaystyle{\left({x}+{3}\right)}{y}{''}+{x}{y}'+{\left({\ln}{\left|{x}\right|}\right)}{y}={0},\ {y}{\left({1}\right)}={0},\ {y}'{\left({1}\right)}={1}$$

tapetivk 2021-11-11 Answered

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

Brittney Lord 2021-11-08 Answered

### Second derivatives Find y′′ for the following functions. $$\displaystyle{y}={x}{\sin{{\left({x}\right)}}}$$

emancipezN 2021-10-31 Answered

2021-10-28

### Solve the equation: $$L^{-1} = \frac{s}{(s^2-a^2)^2}$$

Chesley 2021-10-27 Answered

### The Laplace transform function for the output voltage of a network is expressed in the following form: $$\displaystyle{V}_{{0}}{\left({s}\right)}=\frac{{{12}{\left({s}+{2}\right)}}}{{{s}{\left({s}+{1}\right)}{\left({s}+{3}\right)}{\left({s}+{4}\right)}}}$$ ​Determine the final value of this voltage; that is, $$\displaystyle\upsilon_{{0}}{\left({t}\right)}$$ as $$\displaystyle{t}\rightarrow\infty$$ a) 6V b) 2V c) 12V d) 4V

Yasmin 2021-10-26 Answered

### Use the method of variation of parameters to find a particular solution of the given differential equation. $$\displaystyle{y}{''}+{y}={{\csc}^{{2}}{x}}$$

Alyce Wilkinson 2021-10-23 Answered

### Find the general solution of the given differential equation. $$\displaystyle{y}”−{2}{y}'−{3}{y}={3}{e}^{{{2}{t}}}$$

Brittney Lord 2021-10-20 Answered

### Find Laplace Transform of each following (a) $$\displaystyle{t}^{{n}}$$ , (b) $$cosωt$$

OlmekinjP 2021-10-14 Answered

### Use the Laplace transform to solve the given initial value problem.y"+2y'+5y=0;y(0)=2,y'(0)=−1

Falak Kinney 2021-09-30 Answered

### One property of Laplace transform can be expressed in terms of the inverse Laplace transform as $$L^{-1}\left\{\frac{d^nF}{ds^n}\right\}(t)=(-t)^n f(t)$$ where $$f=L^{-1}\left\{F\right\}$$. Use this equation to compute $$L^{-1}\left\{F\right\}$$ $$\displaystyle{F}{\left({s}\right)}={\arctan{{\frac{{{23}}}{{{s}}}}}}$$

Burhan Hopper 2021-09-30 Answered

### Solve the ordinary differential equation with initial conditions using Laplace transform. $$y''+4y'+13y=20e^{-t} , y_0=1 , y'_0=3$$ The solution of the above equation is given as $$\displaystyle{y}={A}{e}^{{{B}{x}}}+{e}^{{{C}{x}}}{\sin{{3}}}{t}-{e}^{{{D}{x}}}{\cos{{3}}}{t}$$

texelaare 2021-09-28 Answered

### Find the inverse Laplace Transform from the function below $$\displaystyle{F}{\left({s}\right)}={\frac{{{7}}}{{{\left({s}+{11}\right)}{\left({s}+{12}\right)}}}}$$

he298c 2021-09-27 Answered

### Let F(s) be the Laplace tranform of $$\displaystyle{f{{\left({x}\right)}}}={t}{\cos{{\left({2}{t}\right)}}}$$ find the value of F(1)

permaneceerc 2021-09-27 Answered

### Find the inverse Laplace transform of the function: $$\displaystyle{F}{\left({s}\right)}={\frac{{{2}{s}^{{3}}+{9}{s}^{{2}}+{11}{s}+{3}}}{{{\left({s}+{1}\right)}^{{3}}{s}}}}$$

Tahmid Knox 2021-09-26 Answered

### find Laplace transform $$\displaystyle{L}^{{-{1}}}{\frac{{{5}}}{{{s}^{{2}}+{2}{s}-{3}}}}$$

Rivka Thorpe 2021-09-26 Answered

### $$F(t)=0$$ $$\displaystyle={\sin{{\left({t}\right)}}}$$ $$\displaystyle{0}\leq{t}{<}\pi$$ $$\displaystyle\pi{<}{t}{<}{2}\pi$$ Find $$L(f(t))=$$?

Yasmin 2021-09-26 Answered

### Solve by Laplace transformation method the following D.E. (1) $$y''-3y'+2y=4^2e^t$$ given that $$y(0)=-3 , y'(0)=5$$​​​​​​​

Aneeka Hunt 2021-09-26 Answered

### Find the Laplace transform for the functions: $$\displaystyle{f{{\left({t}\right)}}}={t}{u}_{{2}}{\left({t}\right)}$$ $$\displaystyle{f{{\left({t}\right)}}}={u}_{{\pi}}{\left({t}\right)}{\sin{{\left({t}\right)}}}$$

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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