Some noob questions about differential equation ?

[awholenumber]

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 ?

[Nick]

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

[ET_]

Differential equations for dummies is another...

[awholenumber]

Thanks for the replies

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.

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 ?

[CRGreathouse]

Originally Posted by awholenumber

Is that the independent variable or the dependent variable ?

x is independent, f(x) dependent.

[awholenumber]

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 ?

[Nick]

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.

[awholenumber]

Thanks a lot ,
Found a good resource online for differential equations

http://ncert.nic.in/textbook/textbook.htm?lemh2=3-6