OSU Math 256

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'' = -r²e^-rt
How do we check

plug and check
- (y'') + r(y') = 0
- (-r²e^-rt) + r(-re^-rt) = 0
ay''+by'+cy = g(t)

(ar²+br+c)e^-rt

Author

Rayen

46555

Card Set

OSU Math 256

Description

For the 2nd midterm

Updated

2010-11-01T21:31:42Z

Show Answers