I Solving the differential equation of planetary motion

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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 whats wrong with this method.
 

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dRic2

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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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