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August 26th, 2016, 05:12 AM   #1
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Linear first ODE with variable coefficients


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)

'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
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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.
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August 30th, 2016, 07:25 AM   #3
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Non linear

Thank you Archie for the concise answer,
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