can any one answer to this question what are the methods for solving ordinary differential equation?

Answer 1

Well, there are quantitative techniques and qualitative
techniques. Quantitative techniques are analytical (mostly algebraic) manipulations to find exact solutions.
Qualitative methods are more concerned with describing
the general behavior of a solution and geometric analysis
(with the use of some linear algebra)is usually employed.

There are many (quantitative)analytical techniques to solve differential equations that are in a "special" form.

This website as some of techniques

http://www.sosmath.com/diffeq/diffeq.html

Answer 2

if i bear in mind from my undergraduate days, one way you cam discover the suggestions to ODEs is observed as the substitution technique. if i bear in mind properly it is going some thing like this: become conscious of what form of equation you're dealing with. become conscious of the boundary circumstances (BC's) of the DE. seem up a table of suggestions to discover the respond which corresponds with the form of equation you have. i'll call it the table answer. differentiate the table answer as quickly as then differentiate returned, so which you wind up with a collection of equations that sounds like table answer y = ? 1st derivative y' = ?? 2nd derivative y'' = ??? say the DE your attempting to remedy is in the kind y'' + y = some thing or 2y" + y' = some thing you purely exchange the derivatives of the table answer into the LHS of your DE. you could now desire to discover the unknown coefficients. you could the two try this by skill of evaluating the derivates promptly at the same time with your ODE, or by skill of substituting the BC's into the differentiated table suggestions and then simplifying to discover the coefficients. (the two way you will could desire to apply the BC's) as quickly as you hit upon the coefficients making use of the assessment technique, exchange them returned into the uncomplicated form of the table answer to offer the entire equation. in case you chosen your answer kind properly and substituted your BCs in suited, the answer could come out, yet that could additionally matter on the complexity of your ODE. this is slightly obscure, sorry. i've got faith Kreyszig grants some everyday suggestions for 2nd Order ODEs that are purely solved by skill of substitution, there are others which i ought to furnish to you later in case you touch me. or you need to look up frequently happening suggestions on the internet.

Answer 3

There are 3 methods;
a) We have the xdx = ydy form. so, we can simply integrate both sides.
b) We have the substitution form where, we take y = vx or x=vy depending on the type of question.
c) We use the e^integration of P(x) form.

Which method are you referring to?

Answer 4

ha ha ha...
ordinary methods...