The discussion revolves around finding specific and general solutions for ordinary differential equations (ODEs), particularly focusing on first-order ODEs. Participants are seeking examples of equations that can be solved using multiple methods, as well as those that lack general solutions.
Participants generally agree on the existence of multiple methods for solving ODEs and the distinction between closed-form solutions and numerical approximations. However, there is no consensus on specific examples or the exact nature of equations that lack general solutions.
Some participants express uncertainty about the specific requirements of the original poster's request, indicating a need for clarification on whether they seek learning materials or specific examples. Additionally, the discussion touches on the limitations of providing direct answers due to forum policies.
Students studying differential equations, educators looking for discussion points on ODE methods, and individuals interested in the nuances of solving first-order ODEs.
jarednjames said:Hello there young_eng,
To start, I would request the use of proper English as per PF guidelines.
I'm not entirely sure what you're asking here, do you just want the materials to learn or are you looking for specific examples?
As JDoolin points out, your textbooks will have many examples of each. If you could clarify the above, I will try to help a bit more.
As a start, here are some of the resources I use as reference:
http://www.efunda.com/math/ode/ode.cfm
The materials within should help, and hopefully will be roughly what you're looking for.
Jared
jarednjames said:Im not at home right now, it's 10pm on a friday night here. I will give more help once I am at my computer.
Jared
young_eng said:yes , i need First Order ODE specific examples . it is a report requir from us in our college
we finshed First Order ODE but i can't solve an eq with 5 methods, but i found some eq that's have no answer but i don't know why ?
sorry 4 my delay replay
JDoolin said:By the way, Physics Forums Policy is that we're not allowed to give answers to homework problems, and technically, this should be in the homework help forum.
As far as five methods, I can think of linear ODE's, exact ODE's, and separable ODE's. I'm sure those are among the five methods; but I don't know what the other two are. Some equations can be solved by more than one method.
When you say "no answer," I'm pretty sure you mean "closed-form solution."
They still have "an answer," but you have to approximate it with numerical methods such as Euler's method, or the Runge-Kutta method.