# Differential equations questions and answers

Recent questions in Differential Equations
sexoagotadorogyr 2022-04-01 Answered

### I am stuck with this equation. If you can help me$y{}^{″}\left(t\right)+12{y}^{\prime }\left(t\right)+32y\left(t\right)=32u\left(t\right)$ with $y\left(0\right)={y}^{\prime }\left(0\right)=0$I found the laplace transform for y(t)$Y\left(p\right)=x=\frac{32}{\left(p\left({p}^{2}+12p+32\right)\right)}$so i need the laplace transform of y(t) and then the solution for y(t).

Kason Palmer 2022-03-31 Answered

### I am having trouble finding the inverse Laplace transform of:$\frac{1}{{s}^{2}-9s+20}$I tried writing it in a different way:${L}^{-1}\left\{\frac{1}{{\left(s-\frac{9}{2}\right)}^{2}-{\left(\frac{1}{2}\right)}^{2}}\right\}=2{L}^{-1}\left\{\frac{\frac{1}{2}}{{\left(s-\frac{9}{2}\right)}^{2}-{\left(\frac{1}{2}\right)}^{2}}\right\}$

Amya Horn 2022-03-31 Answered

### Solve the differential equation by using method of variation of parametrs$y{}^{‴}+9{y}^{\prime }=\frac{1}{f\left(x\right)}$take $f\left(x\right)=\mathrm{cos}11x$

Roy Roth 2022-03-31 Answered

### ${\int }_{0}^{\infty }\frac{\mathrm{cos}\left(xt\right)}{1+{t}^{2}}dt$I'm supposed to solve this using Laplace Transformations.

jisu61hbke 2022-03-31 Answered

### $H\left(s\right)=\frac{s-5}{\left(s-3\right)\left(s-1\right)}$The inverse Laplace transform of H(s) is equal to$f\cdot g$

Alvaro Baca 2022-03-31

### y''-2y'-3y=0 for y(0)=3, y'(0)=2

ikramkeyslo4s 2022-03-30 Answered

### I am trying to take the laplace transform of $\mathrm{cos}\left(t\right)u\left(t-\pi \right)$. Is it valid for me to treat it as $\left(\left(\mathrm{cos}\left(t\right)+\pi \right)-\pi \right)u\left(t-\pi \right)$ and treat $\mathrm{cos}\left(t\right)-\pi$ as f(t) and use the 2nd shifting property, or is this not the correct procedure?

Milan Manandhar 2022-03-29

### Sketch grapf of f(y)=y for dy\dt = ay+by^2,a>0,b>0,y>0

wibawanyacl3q 2022-03-29 Answered

### Solve differential equation.$y{}^{″}+2{y}^{\prime }=3{x}^{2}+2x$

Kendall Daniels 2022-03-28 Answered

### A nonhomogeneous second-order linear equation and a complementary function ${y}_{c}$ are given. Find a particular solution of the equation.

atenienseec1p 2022-03-26 Answered

2022-03-26

### Find Laplace transform of L[tetsin4t] is

Sanai Huerta 2022-03-25 Answered

### Determine the Laplace Transform ${\left(t-1\right)}^{4}$?

Reuben Brennan 2022-03-25 Answered

### Find a second-order lincar equation for which $y\left(x\right)={c}_{1}{e}^{3x}+{c}_{2}{e}^{5x}+\mathrm{sin}\left(2x\right)$is the general solution

Coradossi7xod 2022-03-25 Answered

### Consider the following linear second-order homogeneous differential equation with constant coefficients and two initial conditions

Blackettyl2j 2022-03-25 Answered

### Solve the following linear second order homogeneous differential equation

Pizzadililehz 2022-03-25 Answered

### Find the general solution of the given differential equations$4y{}^{″}-4{y}^{\prime }-3=0$

Destinee Hensley 2022-03-25 Answered

### Find the general solution of the given second-order differential equations$2y{}^{″}+2{y}^{\prime }+y=0$

Jackson Floyd 2022-03-25 Answered

### Find ODE having the given function as its general solution.$y={x}^{2}+{c}_{1}{e}^{2x}+{c}_{2}{e}^{3x}$

kembdumatxf 2022-03-25 Answered

### Find the general solution to the following second order differential equations.$y{}^{″}-{6}^{\prime }+25y=0$

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..