how do you form an differential equation? ...State me with an example !!!

Question

anonymous · Answer

You want a differential equation?

anonymous · Answer

y''+y'-2y=sinx

ash2326 · Answer

@ram_91 Welcome to Open Study
Suppose we have
$$y=e^x$$
Let's differentiate it
$$y'= e^x$$
so
$$y'=y$$
and therefore
$$y'-y=0$$
this is a differential equation voila!!!

anonymous · Answer

I just want to know whether we form on our own or there any laid down ways are procedures in which you should form it ?

anonymous · Answer

General solution + particular solution

ash2326 · Answer

@ram_91 generally we get differential equation and we try to find the solution to them
but if we try to create one, then there are innumerable ways

ash2326 · Answer

I could also write the differential equation I showed as
$$y''-y'=0$$
or
$$y''-y=0$$
or
$$y''+y'-2y=0$$
So we can create lot of Differential equations

anonymous · Answer

Can you suggest any book or open source to understand Calculus ? ...I really want to learn clearly and from the basics !!

ash2326 · Answer

Just a minute

ash2326 · Answer

http://ocw.mit.edu/high-school/calculus/

anonymous · Answer

Differential equations is different than calc. I wouldn't start if Diff. Eq. if you haven't taken calculus yet.

anonymous · Answer

*with

anonymous · Answer

I have done with calculus but during learning i just did it for the sake of clearing my exams.... but now while applying in finite element analysis .......i see the depth of its use ....i mean all calculus , ODE , numerical methods!!!

anonymous · Answer

thanks for your quick response and guidance !!!