I've been searching for exact solution of d(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}y/dx^{2}= C/y, where C is some constant, such equation take place when deriving equation of motion in gravitationnal field, I'm more interested in how to solve it, yet I only managed to express it as power series using taylor's theorem at x = 0, just pick y(0) = c1, y'(0) = c2, so y''= C/c1, y'''(x) = C*c2/c1^{2}and so on, until y ≈ c1 + c2*x + C/2c1 * x^{2}+ C*c2/6c1^{2}*x^{3}+ ......., Is there's any special function that solves the equation or any other approximisation ?, I want to hear some thoughts !,

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# 2nd Order Elliptic Equation

Loading...

Similar Threads - Order Elliptic Equation | Date |
---|---|

I A common 2nd order ODE from dynamics but... | Feb 28, 2018 |

A Solve a non-linear ODE of third order | Feb 20, 2018 |

A Numerical solution techniques for 6th order PDE's | Feb 3, 2018 |

A Numerical solution for a two dimensional 3rd order nonlinear diff. eq. | Jan 17, 2018 |

A Solution of a weakly formulated pde involving p-Laplacian | Aug 3, 2017 |

**Physics Forums - The Fusion of Science and Community**