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OSU Math 256
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conjecture
A guess
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 = y'
u' = y''
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}
Author
Rayen
ID
46555
Card Set
OSU Math 256
Description
For the 2nd midterm
Updated
2010-11-01T21:31:42Z
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