mersenneforum.org > Math Some noob questions about differential equation ?
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 2017-06-17, 13:11 #1 awholenumber     May 2017 32 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 ?
 2017-06-17, 13:40 #2 Nick     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 $$x^2-3x+2=0$$. 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 2017-06-17 at 13:42 Reason: Typo
 2017-06-17, 13:47 #3 ET_ Banned     "Luigi" Aug 2002 Team Italia 4,813 Posts Differential equations for dummies is another...
2017-06-17, 13:52   #4
awholenumber

May 2017

916 Posts

Thanks for the replies

Quote:
 A derivative simply specifies the rate at which a quantity changes. In math terms, the derivative of a function f(x), which is depicted as df(x)/dx, or more commonly in this book, as f'(x), indicates how f(x) is changing at any value of x. The function f(x) has to be continuous at a particular point for the derivative to exist at that point.
Quote:
 A derivative simply specifies the rate at which a point mass quantity changes. In math terms, the derivative of a function f(x), which is depicted as df(x)/dx, or more commonly in this book, as f'(x), indicates how f(x) is changing at any value of x. The function f(x) has to be continuous at a particular point for the derivative to exist at that point.
Is that the independent variable or the dependent variable ?

2017-06-17, 17:01   #5
CRGreathouse

Aug 2006

32·5·7·19 Posts

Quote:
 Originally Posted by awholenumber Is that the independent variable or the dependent variable ?
x is independent, f(x) dependent.

 2017-06-17, 20:43 #6 awholenumber     May 2017 32 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 ?
2017-06-17, 22:46   #7
Nick

Dec 2012
The Netherlands

7·239 Posts

Quote:
 Originally Posted by awholenumber What is a differential equation ?
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.

 2017-06-18, 07:25 #8 awholenumber     May 2017 32 Posts Thanks a lot , Found a good resource online for differential equations http://ncert.nic.in/textbook/textbook.htm?lemh2=3-6

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