Topics For Midterm II
3.1 Homogeneous Equations with Constant Coefficients
•
Characteristic Equation to find general solutions, solutions to IVPs.
(This works only for
linear homogeneous ODEs with constant coefficients, although it can be used as a step in
solving linear nonhomogeneous ODEs with constant coefficients.)
•
Equations of the form
y
00
=
f
(
t, y
0
). (Let
u
=
y
0
to reduce to first order. 3.1.283.1.33)
•
Equations with no independent variable. (Let
u
=
y
0
. Use chain rule to transform into the
form
u
(
du/dy
) =
f
(
y, u
), solve this 1st order equation, integrate to find
y
. 3.1.343.1.43)
3.2 Fundamental Solutions of Linear Homogeneous Equations
•
Existence and uniqueness. (Theorem 3.2.1)
•
Superposition Principle. (A linear combination of solutions to a homogeneous linear ODE is
a solution.)
•
Determinant definition of the Wronskian. (Calculate Wronskians, given the Wronskian and
a function find the other, etc . . . ).
•
Fundamental solution set.
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 Fall '07
 COSTIN
 Differential Equations, Equations, Taylor Series, Vector Space, Complex number, linear homogeneous equations

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