In a homogeneous
, linear differential equation
with constant coefficient
s, this is the equation you arrive at when you let y=emx
. It is also known as the characteristic equation
. For example...
y'' + 2y' - 3y = 0
m2emx + 2memx - 3emx = 0
Divide by emx (since it cannot equal 0)
m2 + 2m - 3 = 0 <-----auxiliary equation
general equation : y=c1e-3x+c2ex
The problems don't always end up with such a simple general equation for y, but the auxiliary equation is obtained just the same way. It's then factored to solve for m, which in turn solves the differential equation.