20170617, 13:11  #1 
May 2017
3^{2} Posts 
Some noob questions about differential equation ?
https://s8.postimg.org/uzurdl8th/Eng...inition_01.png
How does a derivative component get inside an equation ? How do we solve a simple differential equation? Do we use integration to solve it ? What do we get after we solve a simple differential equation ? 
20170617, 13:40  #2 
Dec 2012
The Netherlands
7·239 Posts 
If we look for a number satisfying certain conditions, those conditions may involve basic operations on numbers such as addition and multiplication, e.g.
find all real numbers x for which \(x^23x+2=0\). If we look for a function satisfying certain conditions, those conditions may involve basic operations on functions such as differentiation, e.g. find all functions y(t) for which \(\frac{d^2y}{dt^2}+4y=t^2+2\). Sometimes we can solve an ordinary differential equation completely, giving a formula for a function that satisfies the conditions without any integral signs in it. Sometimes this is not possible and we have to be content with more general information about solutions, whether qualitative or quantitative. There are plenty of books on how to solve ordinary differential equations. Here is one: http://www.cambridge.org/nl/academic...UiCeUeylofa.97 Last fiddled with by Nick on 20170617 at 13:42 Reason: Typo 
20170617, 13:47  #3 
Banned
"Luigi"
Aug 2002
Team Italia
4,813 Posts 
Differential equations for dummies is another...

20170617, 13:52  #4  
May 2017
9_{16} Posts 
Thanks for the replies
Quote:
Quote:


20170617, 17:01  #5 
Aug 2006
3^{2}·5·7·19 Posts 

20170617, 20:43  #6 
May 2017
3^{2} Posts 
OK ,
What is a differential equation ? It is an equation involving an unknown function (solution) and its derivatives https://s7.postimg.org/a06uge72z/dif...l_equation.png Right ? 
20170617, 22:46  #7 
Dec 2012
The Netherlands
7·239 Posts 
Let n be a positive integer.
An nth order ordinary differential equation is an equation relating some or all of the following: \[ x,y,\frac{dy}{dx},\frac{d^2y}{dx^2},\ldots,\frac{d^ny}{dx^n}\] For example, \(\frac{dy}{dx}=x\) is a differential equation which we can solve simply by integrating, while \(\frac{dy}{dx}=y\) is trickier because it says that the solution must be a function equal to its own derivative. 
20170618, 07:25  #8 
May 2017
3^{2} Posts 
Thanks a lot ,
Found a good resource online for differential equations http://ncert.nic.in/textbook/textbook.htm?lemh2=36 
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