Differential equations (1 Viewer)

[Drsoccerball]

Is there a way to solve a differential equation (which there obviously is...) or do we just figure it out by subbing random functions into the equation ?

 

[InteGrand]

Is there a way to solve a differential equation (which there obviously is...) or do we just figure it out by subbing random functions into the equation ?

Certain differential equations have standard methods for solving them (e.g. linear first order differential equations, second order differential equations with constant coefficients, exact differential equations, etc.). Other ones have no known methods of analytic solution or can't be solved analytically with elementary functions; this is a major field of mathematical research. There was a thread about this before with some good discussion:

http://community.boredofstudies.org/238/extracurricular-topics/338784/differential-equations.html.

(Also you probably solved some differential equations for 4U Mechanics without just subbing in given functions.)

 

[Silly Sausage]

Technically, you do solve them in HS.

A very simple example is:

Given , find given when .

 

[anomalousdecay]

As an aside, there are many different techniques to solving differential equations and there are also different sets of tools for it as well.

One could use the s-plane if they wanted.

There are also ways of using differential equations for expressing system inputs and outputs, where solving the differential equations is not required!

There's a lot that can be done with differential equations