which method of the three for solving differential equations is superior?

[PG1995]

Hi

So, I have come across three methods of solving first order differential equations, namely: separation of variables, homogeneous equation solving, and exact equation solving method. In math one method might have wider sphere of application than the other. Which method of the three is 'more' generally applicable than the others? Suppose, the method we use to solve to exact differential equation could also be used to solve separable differential equation, then we might say 'exact equation solving method' is superior and more general than the others. Do you get my what I'm trying to say? Please help me with it. Thank you.

Regards
PG

 

[squishy36]

Yeah, everyone learns those techniques. Out in the real world, at least in my experience, I never needed to solve DEs all that often, but when I did, I just went straight to numerical solution methods on the computers (at least over the last 35 years or so). The real world is often nonlinear and those traditional methods lose steam mighty quick.

 

[MrAl]

Hi,

I have had the similar experience to squishy where most of the time we end up going to numerical solutions using a computer to do the calculations.
I also realize however that the study of low order systems like we're talking about here (2nd order or less) gives us a feel for what other systems might do too, so it's good to study this stuff a little anyway.

From the given list, separation of variables is the least applicable because often the variables are not separable.
One of my old favorite methods that works well for electronics is the "integrating factor" solution. It's worth looking that up and seeing how it works.
Another thing in a lot of electronic work the independent variable is often time t. For example:
dy(t)/dt=E/RC-y(t)/RC