# Solving the differential equation of planetary motion

• RpWinter
In summary, the individual is seeking assistance with solving a differential equation and is questioning the accuracy of their method. They have already tried solving the equation using the method of finding central function and particular integral, but the solution does not match the general solution and differentiating twice does not give the previous equation. They have also come across a different method through a research paper, but are unsure of its accuracy. They apologize for any confusion and clarify that they are looking for a simpler solution.
RpWinter
Hey, this is how i tried solving the differential equation

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:
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

## What is a differential equation?

A differential equation is a mathematical equation that describes how a function changes over time, based on its current value and the rate at which it is changing. In simpler terms, it shows the relationship between a function and its derivatives.

## How is a differential equation used to solve planetary motion?

A differential equation can be used to describe the motion of a planet by showing how its position and velocity change over time. By solving the differential equation, we can determine the exact path of the planet and predict its future motion.

## What are the main challenges in solving the differential equation of planetary motion?

One of the main challenges is accurately accounting for all the forces acting on the planet, such as gravity and other celestial bodies. Another challenge is finding an analytical solution to the differential equation, as it can be complex and involve multiple variables.

## What are some techniques used to solve the differential equation of planetary motion?

The most common technique is numerical integration, where the differential equation is approximated using small time steps. Other techniques include Laplace transforms, perturbation methods, and series solutions.

## How important is solving the differential equation of planetary motion in understanding our universe?

Solving the differential equation of planetary motion is crucial in understanding the behavior of celestial bodies and the dynamics of our solar system. It allows us to make accurate predictions and gain insight into the fundamental laws of nature.

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