My Math Forum  

Go Back   My Math Forum > College Math Forum > Differential Equations

Differential Equations Ordinary and Partial Differential Equations Math Forum


Reply
 
LinkBack Thread Tools Display Modes
August 26th, 2016, 05:12 AM   #1
Nid
Newbie
 
Joined: Aug 2016
From: Russia

Posts: 2
Thanks: 0

Linear first ODE with variable coefficients

Hi!

I used to go about solving linear ODEs with constant and variable coefficients. Upon my knowledge all the times the ones with variable coefficients, the coefficients would be dependent on the one independent variable 'x' say.

For example, consider the following ODE:

q(x)= A(y) . dy/dx + k . y(x)

Where:
'q(x)' is the input and is of 'x',
'A' is the variable coefficient and changes with the change of 'y' and not with the change of 'x'.
and Assuming k is a constant.

Which method should one use for solving this equation if any. Another interesting question, to what class does this equation belong ?

Thank you!
Nid is offline  
 
August 26th, 2016, 10:22 AM   #2
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,674
Thanks: 2654

Math Focus: Mainly analysis and algebra
Non-linear ordinary differential equations like this (non-linear because of the function $A(y)$) are not in general solvable. Some classes of such equations are solvable, but the method varies depending on the specific form of the equation.

Last edited by skipjack; August 31st, 2016 at 05:02 AM.
v8archie is offline  
August 30th, 2016, 07:25 AM   #3
Nid
Newbie
 
Joined: Aug 2016
From: Russia

Posts: 2
Thanks: 0

Non linear

Thank you Archie for the concise answer,
Nid is offline  
Reply

  My Math Forum > College Math Forum > Differential Equations

Tags
coefficients, linear, ode, variable



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Nonlinear change of variables w/ variable coefficients WWRtelescoping Differential Equations 0 September 22nd, 2014 11:48 PM
Homogeneous linear ODEs with Constant Coefficients oasi Calculus 2 March 14th, 2012 01:50 PM
DE - linear homogeneous w/ constant coefficients mbradar2 Calculus 7 October 23rd, 2010 08:56 PM
A brief LDE with variable coefficients chengfw Applied Math 0 January 6th, 2010 07:35 PM
Linear Coefficients clatham Advanced Statistics 1 November 9th, 2009 05:36 PM





Copyright © 2019 My Math Forum. All rights reserved.