(adsbygoogle = window.adsbygoogle || []).push({}); 2nd Order Homogenous ODE (Two solutions??)

Alright.

I understand that if we have a differential equation of the form

[itex]A\cdot\frac{d^{2}y}{dt}+B\cdot\frac{dy}{dt}+C\cdot y = 0[/itex]

and it has the solution y_{1}(t), and y_{2}is also a solution. Then any combination of the two

y_{H}=C_{1}y_{1}(t)+C_{2}y_{2}(t) is also a solution.

But, mathmatically speaking, so would a combination with a third "possible" solution y_{3}.

Now I know there must be some theorem stating that there will only be two solutions for this type of ODE, but can anyone tell me where I can find these?

ALSO,

If there are two solutions, why do we always use the combination of the two? Why not just pick one of the solutions and use it? Why "overcomplicate" it and use the combination of the two solutions as the general solution?

I know there must be a good reason, but I havent found it, and I need someone to point it out to me, or tell me where I can read about it.

Thank you in advance,

Rune

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

Dismiss Notice

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 Homogenous ODE (Two solutions?)

Loading...

Similar Threads for Order Homogenous solutions | Date |
---|---|

I Constructing a 2nd order homogenous DE given fundamental solution | May 13, 2017 |

Why 2nd order differential equation has two solutions | Jan 20, 2016 |

Why does the 2nd order homogeneous linear ODE have 2 general solutions? | Dec 11, 2014 |

Solutions to Homogeneous 2nd-order Linear D.E.s | May 7, 2008 |

General Solutions of 2nd Order Linear Homogeneous Ordinary D.E.s | Oct 17, 2004 |

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