few basic questions about differential equations ??

[rosekidcute]

i have a few questions to ask about differential equations ...
how many types of differential equations are there ... ?


sometimes i like to make up themes for my studies ...
few funny things went through my head ...when i saw a thread like this ,How is it that mathematics describe reality so well?

i also happened to read this ...

The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is also often called the Schrödinger wave equation, and is a partial differential equation that describes how the wavefunction of a physical system evolves over time.

i was also wondering that if you learn enough differential equation , you might be able to understand things like " The Schrödinger equation " , the nature of reality ... and in the end how mathematics can describe reality so well ....

i am also looking for some advice on how to start learning differential equation properly ...??

 

[rosekidcute]

anyway i also happened to read this website ... and i don't know if its the complete list ... of the types of differential equations ...??

http://www.dummies.com/how-to/content/differential-equations-for-dummies-cheat-sheet.html


To confidently solve differential equations, you need to understand how the equations are classified by order, how to distinguish between linear, separable, and exact equations, and how to identify homogenous and nonhomogeneous differential equations. Learn the method of undetermined coefficients to work out nonhomogeneous differential equations

are there more types of differential equations ??

 

[stapel]

how many types of differential equations are there ... ?

The number will probably vary with the classification types used. (here) For further information, you might want to enroll in an introductory differential-equations course, followed by whichever other courses are offered by your institution.

when i saw a thread like this....

I'll guess you're referring to the partial sentences and cryptic images. Lacking clear information, I'm afraid it will be difficult to respond.

How is it that mathematics describe reality so well?

This question would be like asking, "How is it that the alphabet describes reality so well?" It isn't the alphabet that does the describing, but the scientists who use the alphabet to use the language to describe what has been observed and tested. In a similar manner, mathematical models can describe, to varying degrees of accuracy, what is observed and tested "in real life". But mathematics, itself, is just a set of tools or a vocabulary.

 

[rosekidcute]

thanks for the answers ...
i have been putting some effort to narrow it down and to find a little bit more order ...

i think it goes a bit like this ...

first order differential equations, second order differential equations , higher order differential equations ...

then there is the linear differential equations ,separable differential equations ,exact differential equations ,homogeneous differential equations ,non homogeneous differential equations, using the method of undetermined coefficients ...

i have ideas about these ...

first order differential equations, second order differential equations , higher order differential equations ...

but not much about these ...

linear differential equations ,separable differential equations ,exact differential equations ,homogeneous differential equations ,non homogeneous differential equations, using the method of undetermined coefficients ...

that is not all , that list is missing ...

partial differential equations ...