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August 26th, 2016, 05:12 AM  #1 
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! 
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 
Nonlinear ordinary differential equations like this (nonlinear 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. 
August 30th, 2016, 07:25 AM  #3 
Newbie Joined: Aug 2016 From: Russia Posts: 2 Thanks: 0  Non linear
Thank you Archie for the concise answer,


Tags 
coefficients, linear, ode, variable 
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