It says on Wikipedia in the article on differential equations that:(adsbygoogle = window.adsbygoogle || []).push({}); 'a differential equation is linear if the unknown function and its derivatives appear to the power 1 (products are not allowed) and nonlinear otherwise'

Are these products between any of the variables that appear? So, are products between derivatives, the unknown function AND the independent variable not allowed or is it just between the derivatives and unknown functions?

In a book on ODEs I found in the library, it says:

..the general form linear ordinary differential equation of order n is

[tex]a_0(x)y^{(n)}+a_1(x)y^{(n-1)}+...}a_n(x)y=g(x)[/tex]

[tex]a_n(x)[/tex] are coefficients which are functions of x...so can these be any random function of x that doesn't really relate to the unknown function we're trying to find? Are they usually constants?

And what is the g(x) on the RHS?

Thanks

**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!

# Question about linear ODEs

Loading...

Similar Threads - Question linear ODEs | Date |
---|---|

I Question about second order linear differential equations | Aug 21, 2017 |

Question about linear ODEs | Feb 26, 2013 |

Question about 2nd order linear ODEs series solutions | May 12, 2012 |

Question about linear second order ODE solution coefficients | Feb 16, 2012 |

Non-Linear ODE Question | Jan 23, 2009 |

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