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December 1st, 2018, 08:25 PM   #1
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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.
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December 2nd, 2018, 11:52 AM   #2
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Most useful step is substitution , example : y=ux
I checked your document and steps are correct as i see
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December 2nd, 2018, 12:09 PM   #3
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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.
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December 2nd, 2018, 12:21 PM   #4
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Quote:
Originally Posted by ht1204 View Post
I have done a series of steps . . .
Why did you use "-" instead of "+"?
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December 15th, 2018, 09:17 PM   #5
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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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