# Differential equations questions and answers

Recent questions in Differential Equations
illusiia 2020-10-25

### Solve differential equation $dy/dx={e}^{4}x\left(y-3\right)$

Dolly Robinson 2020-10-25

### Create a 2nd order, homogeneous, linear IVP, that is not guaranteed to have a unique solution at ${x}_{0}=3$

Lewis Harvey 2020-10-23

### Write the first order differential equation for $y=2-{\int }_{0}^{x}\left(1+y\left(t\right)\right)\mathrm{sin}tdt$

illusiia 2020-10-23

Tyra 2020-10-20

### Find the general solution of $y{}^{″}-2{y}^{\prime }+2y=x{e}^{x}\mathrm{cos}x$

UkusakazaL 2020-10-19

### What is the Laplace transform of $x\left(t\right)={e}^{-t}\mathrm{cos}\left(\pi \right)t$?

tinfoQ 2020-10-18

### Laplace transforms A powerful tool in solving problems in engineering and physics is the Laplace transform. Given a function f(t), the Laplace transform is a new function F(s) defined by $F\left(s\right)={\int }_{0}^{\mathrm{\infty }}{e}^{-st}f\left(t\right)dt$ where we assume s is a positive real number. For example, to find the Laplace transform of $f\left(t\right)={e}^{-t}$, the following improper integral is evaluated using integration by parts: $F\left(s\right)={\int }_{0}^{\mathrm{\infty }}{e}^{-st}{e}^{-t}dt={\int }_{0}^{\mathrm{\infty }}{e}^{-\left(s+1\right)t}dt=\frac{1}{\left(s+1\right)}$ Verify the following Laplace transforms, where u is a real number. $f\left(t\right)=1\to F\left(s\right)=\frac{1}{s}$

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..