Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I noticed that the solution of a homogeneous linear second order DE can be interpreted as the kernel of a linear transformation.

It can also be easily shown that the general solution, Ygeneral, of a nonhomogenous DE is given by:

Ygeneral = Yhomogeneous + Yparticular

My question:Is it possible to arrive at the above result by using arguments involving the relationship between the kernel, column space, row space, etc of the linear differential operator of a DE?

My current attempt:The solution space of a non-homogeneous DE is isomorphic to the solution space (kernel) of the corresponding homogeneous DE, and is "displaced" from the kernel by the vector, Yparticular. Hence Ygeneral could be constructing by adding any Yparticular back to the Yparticular.

My solution is probably pretty flawed, and I have no idea how I can justify it. Could someone please enlighten me (or tell me that my question is dumb)? :D

Thanks in advance!

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

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

# Derive gen sol of non-homogeneous DEs through linear algebra

Tags:

Loading...

Similar Threads - Derive homogeneous through | Date |
---|---|

A How to simplify the solution of the following linear homogeneous ODE? | Feb 18, 2018 |

I Partial Vector Derivative | Oct 15, 2017 |

I What is the Result of this Partial Derivative | Jun 21, 2017 |

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