An ODE of second order with constants coefficients, linear and homogeneous: [tex] Af''(x) + Bf'(x) +Cf(x) = 0 [/tex] has how caractherisc equation this equation here: [tex] Ax^2 + Bx +C = 0 [/tex] and has how solution this equation here: [tex] f(x) = a \exp(u x) + b \exp(v x)[/tex] where u and v are the solutions (roots) of the characteristic equation and a and b are arbitrary constants.(adsbygoogle = window.adsbygoogle || []).push({});

Very well, until here, no problems!

But, in domain of discrete math, exist an analog equation for each equation above.

Solution equation: [tex] f(n) = a u^n + b v^n[/tex] Caractherisc equation: [tex] Ax^2 + Bx +C = 0 [/tex] Differential equation:????

I don't know what's the "differential" equation in discrete domain whose solution and characteristic equation are the two equations above. This my question!

Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

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

# Characteristic equation for recurrence equation

**Physics Forums | Science Articles, Homework Help, Discussion**