why is it good a linear over non linear differential equation?

Answer 1

huh ?
What do you mean ?

Linear dv are easier to solve , at least numerical.

Answer 2

The simple answer is that linear D.Es are usually much easier to solve than non-linear D.E.s. When students write exams, they all hope for linear D.E.s.

Note that solving D.E.s is more an 'art' than it is a 'science'. Why? Well, there is no general method to solve all types of D.E.s. So what we end up with are many recipes for solving the different types. The only general method for solving is usually a numeric technique. However, even numeric techniques do not work well on all types of D.Es (example, stiff DEs like Van Der Pol's require special numeric techniques). I generally do not recommend Wikipedia as a resource for mathematics, but for this subject, the following link is about as good as it gets:

http://en.wikipedia.org/wiki/Ordinary_differential_equation

At the end of the day, those who are good at solving DEs have generally learned to recognize the types and apply the correct 'recipe'. In my opinion, we are still so backward in this field of mathematics and there is far more method than understanding. I have met no one who has been able to answer certain questions I've had on DEs. Partial differential equations are a completely different kettle of fish...

Answer 3

These links might be helpful...
http://ltcconline.net/greenl/courses/204/firstOrder/linearVsNonlinear.htm
http://en.wikipedia.org/wiki/Differential_equation
http://en.wikipedia.org/wiki/Linear_differential_equation

Answer 4

because of its simplicity.