Solving the differential equation of planetary motion

AI Thread Summary
The discussion focuses on a user's attempt to solve the differential equation of planetary motion, noting that their solution does not align with the general solution. They express confusion over why differentiating their result twice does not yield the original equation. The user is familiar with solving methods involving the Complementary Function (CF) and Particular Integral (PI) but seeks clarification on the errors in their approach. Other participants indicate difficulty in understanding the user's equations and suggest a simpler solution might be beneficial. The conversation emphasizes the need for clearer communication and understanding of the differential equation methods used.
RpWinter
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Hey, this is how i tried solving the differential equation
1Dhki.png

The solution however does not match the general solution of the equation. Also differentiating it twice does not give me the previous equation. Please tell me if i did some mistake while solving.
I already know how to solve by finding CF and PI. I want to know what's wrong with this method.
 

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dRic2 said:
http://gsjournal.net/Science-Journals/Research Papers-Astrophysics/Download/3763
I have already seen this derivation. Here the differential equation is solved by finding Central function and Particular Integral of the Differential equation. I want to know what's wrong with the method that i have used. Both of them are not giving the same result.
 
Sorry I don't understand your equations or where they came from. I thought you were looking for a simpler solution
 

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