Second, it is generally only useful for constant coefficient differential equations.
Nonhomogeneous linear equation with constant coefficients: L[y] = ay + by + cy = g(t). Aim: Find a particular solution Y to the equation. Table of possible guess: ...
Solve a nonhomogeneous differential equation by the method of undetermined coefficients.
In the following table, Pn(t) is a polynomial of degree n: Pn(t) = antn + an−1tn−1 + ··· + a1t + a0. g(t)
- equations-fall-2011/unit-ii-second-order-constant-coefficient-linear-equations/
The homogeneous equation d2ydx2 − y = 0 has a general solution y = Aex + Be−x ... of the type d2ydx2 + pdydx + qy = f(x) where f(x) is a polynomial of degree n, our guess ...
This fact and the second equation imply that B=-1/2. If the nonhomogeneous term is a polynomial of degree n, then an initial guess for the particular
our guess for the particular solution should be a polynomial of the same degree, and it
Of course, its an educated guess, there's a lot of maths behind why we make the
As (tn)′ = n tn−1, we would like to guess that there is a particular solution of the form A ...