Solving the differential equation of planetary motion

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SUMMARY

The discussion focuses on the challenges faced in solving the differential equation of planetary motion using the methods of Complementary Function (CF) and Particular Integral (PI). The user reports discrepancies between their solution and the general solution of the equation, specifically noting that differentiating their result twice does not yield the original equation. The conversation emphasizes the need for clarity in the derivation process and highlights potential errors in the application of these methods.

PREREQUISITES
  • Understanding of differential equations, specifically in the context of planetary motion.
  • Familiarity with the methods of Complementary Function (CF) and Particular Integral (PI).
  • Basic knowledge of calculus, particularly differentiation.
  • Experience with mathematical derivations and their applications in physics.
NEXT STEPS
  • Review the derivation of the general solution for planetary motion differential equations.
  • Study the application of Complementary Function (CF) and Particular Integral (PI) in solving differential equations.
  • Learn about common pitfalls in solving differential equations and how to avoid them.
  • Explore alternative methods for solving differential equations, such as numerical methods or Laplace transforms.
USEFUL FOR

Students and researchers in physics and mathematics, particularly those focusing on celestial mechanics and differential equations related to planetary motion.

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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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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