In differential equation, there are two types of solutions that is, quantitative solution and qualitative solution.
1. What is quantitative solution of DE?
2. What is qualitative solution of DE?
3. Why we mostly give important to qualitative study of DE?
4. What are the drawbacks of quantitative solution of DE?
5. What are the types of qualitative solution of DE?
A simple google could have given you the results. Read page 1-3 of the link mentioned below.
For more information, read chapter 1 and 2 of book
Differential Equations: Graphics, Models, Data by David O. Lomen, David Lovelock
http://www.tesisenred.net/bitstream/handle/10803/134677/jdgs1de1.pdf?sequence=1
Mainly because that most of DEs are not solvable an too complicated. The second fact is more than important - in many cases we need to know the general system behavior this DE describes, not taking into account the concrete and not essential model values, like those: will be the behavior regular and stable, or not, will it be predictable, or chaotic, willthis comet fall down on the Earth on the whole, or not and so on...
Regards!
Saying roughly,
quantitative goal is to find a solution in closed form or by an approximation process:
qualitative goal is to provide a qualitative description of the solution's behavior (as Anatolij mentioned - more important)
Greetings, Tadeusz
All that was said up to now is right,
I'd just like to put my 2 cents in: since a big number of DEs are nowadays solved analytically by asymptotics, knowing the behaviour of the solution in certain ranges may provide very close approximation also for quantitative solutions.
All the best,
Gennaro
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