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Linear Second order ordinary Differential equation
ay''+by'+cy = g(t)

ay''+by'+cy = 0
 is a constant constant coefficent
 a,b,c are real numbers not variables

The equation is called homogeneous when g(t)
If g(t) =0

The equation is called inhomogeneous when g(t)
if g(t) != 0

y'' + ry' = 0
u' + ru = 0
 y = ce^{rt}
 y' =  re^{rt}
 y'' = r^{2}e^{rt}
How do we check
plug and check
 (y'') + r(y') = 0
 (r^{2}e^{rt}) + r(re^{rt}) = 0

ay''+by'+cy = g(t)
(ar^{2}+br+c)e^{rt}

