I First order differential equations ?

[awholenumber]

what is a good book to learn first order differential equations ??

 

[BvU]

There's a forum dedicated to this.

 

[awholenumber]

BvU ,

thanks a lot ...

i was getting lost in the classifications and complexities of these differential equations ...

 

[BvU]

Take it easy: all beginnings are somewhat bewildering...

 

[awholenumber]

BvU ,

thanks ...

i saw this image while i was googling for first order differential equations ...

does all these belong to only first order differential equations ??

separable equations
homogeneous equations
linear equations
exact equations

Differential equations with only first derivatives

or is it like ...

separable equations with only first derivatives
homogeneous equations with only first derivatives
linear equations with only first derivatives
exact equations with only first derivatives

??

 

[BvU]

The latter. The order of the equation is simply the highest number of differentiations appeaaring.

 

[awholenumber]

BvU ,

thanks for the replies ...

i am trying to find at least one example for each of these ...separable equations with only first derivatives
homogeneous equations with only first derivatives
linear equations with only first derivatives
exact equations with only first derivatives

let me see what i can do ...

 

[awholenumber]

i read a little bit more ... and made few more notes ...

An equation containing the derivatives of one or more dependent variables, with respect to one or more independent variables, is said to be a differential equation

they are mainly classified into two ..
ordinary differential equation
partial differential equation ..

then comes first order differential equations to nth order differential equations ...

order is the highest number of the differentiations appearing
degree is the power of the highest order derivative in the equation ...

then there are types of differential equations , depending on their order

separable equations
homogeneous equations
linear equations
exact equationswhat is after this ??

partial differential equations ??

 

[BvU]

Work through a lot of exercises

"Classification is the enemy of understanding" is the signature of an esteemed colleague here on PF...

 

[awholenumber]

BvU ,

i had to play around a lot of pictures to understand the different types of differential equations depending on their order ...
exactly , the classification was very confusing ...

somehow , i managed to make up definitions like this ...

then there are types of differential equations , depending on their order

separable equations
homogeneous equations
linear equations
exact equations

from there , i have been reading on partial differential equation ... seem to be an extremely difficult thing to understand properly ...

A partial differential equation is an equation involving functions and their partial derivatives ...

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constanti was wondering if i could understand this in terms of a Vibrating string and a Vibrating membrane mentioned in wikipedia ..

Vibrating string

If the string is stretched between two points where x=0 and x=L and u denotes the amplitude of the displacement of the string, then u satisfies the one-dimensional wave equation in the region where 0 < x < L and t is unlimited. Since the string is tied down at the ends, u must also satisfy the boundary conditions<Mod note: text and image deleted>



i don't really understand all that "Vibrating string" equation ...

but i don't know what else to look for to learn a partial differential equation??

a note to moderators : can i please keep this picture ??
Mod note: No.
if the picture is inappropriate , feel free to delete it ...
Mod note: The image contained multiple copies of exactly the same thing.
Before asking questions about partial differential equations, you need to get some understanding of how to solve ordinary differential equations, preferably by working through the problems in a textbook on ordinary differential equations.

 

[rahul_26]

An equation that contains independent variable(usually 'x') some function of 'x',dependent variable(usually'y') some function of 'y' and at least one derivative term of 'y' with respect to 'x' is called a differential equation.
The order of differential equations is the order of the highest order derative that occurs in the equations.
In first order differential equation,the order of the derative is one .
for example-$$x^3\frac{dy}{dx}+logx=5$$ is first order differential equation.

 

[awholenumber]

rahul_26,

thanks a lot for the replies ...