Transcript Section 18.1 Second-Order Linear Differential Equations

Section 18.2.1
Nonhomogeneous Linear
Equations (Undetermined
Coefficients Method)
Differential Equations
Berkley High School
March 31, 2010
What is a second-order linear
differential equation?

It is in the general form…
P  x  y  Q  x  y  R  x  y  G  x 
It is a second-order equation because it
contains a second derivative, but none
higher.
 It is called nonhomogeneous if…

G  x  0
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The form of the nonhomogeneous
solution
The general solution of the nonhomogeneous
differential equation can be written as
y  x   yh  x   y p  x 
where yh is called the homogeneous solution
and where y p is called the particular solution.
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What is a solution to y  y  2 y  x ?
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y  4 y  e3 x
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y  y  2 y  sin x
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y  y  sin x
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Exercises
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Section 18.2: 1-10 all
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