- #1
Bruno Tolentino
- 97
- 0
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.
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!
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!