My Math Forum How to solve an ODE to find its solution

 Differential Equations Ordinary and Partial Differential Equations Math Forum

 December 1st, 2018, 07:25 PM #1 Newbie   Joined: Dec 2018 From: Colombia Posts: 6 Thanks: 0 How to solve an ODE to find its solution Salutations, I have a problem when I approach this ODE: $$\left(\frac{y}{y'}\right)^2+y^2=b^2\left(x-\frac{y}{y'}\right)^2$$ I have done a series of steps as I show in this document: https://drive.google.com/file/d/1Ht4...ew?usp=sharing But I'm not convinced that those were the correct steps neither solutions were adequated, and my question is: How would be the mathematical steps to apply to find the correct solution of the ODE? So, I would like any guidance or starting steps or explanations to find the solution of this interesting problem. Thanks for your attention.
 December 2nd, 2018, 10:52 AM #2 Senior Member   Joined: Dec 2015 From: somewhere Posts: 603 Thanks: 88 Most useful step is substitution , example : y=ux I checked your document and steps are correct as i see Thanks from ht1204
 December 2nd, 2018, 11:09 AM #3 Newbie   Joined: Dec 2018 From: Colombia Posts: 6 Thanks: 0 Thanks for your commentary, but I have proven y=kx in both sides and there is no equality, that's the reason why I require help to find a correct procedure. Thanks for your attention.
December 2nd, 2018, 11:21 AM   #4
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Quote:
 Originally Posted by ht1204 I have done a series of steps . . .
Why did you use "-" instead of "+"?

 December 15th, 2018, 08:17 PM #5 Newbie   Joined: Dec 2018 From: Colombia Posts: 6 Thanks: 0 Hi, thanks for your commentary and observation, I didn't realize I had made a mistake with the sign and a I think I could solve it. I share my procedure in this link. https://drive.google.com/file/d/13kI...ew?usp=sharing Thanks for your attention.

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