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ZixuanZhang
ZixuanZhang
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Constant-Coefficient Homogeneous Solutions

Solutions of linear homogeneous ODEs with constant coefficients are of the form .

Proposition 4.11
Solutions of linear homogeneous ODEs with constant coefficients (for any order) are of the form

Example

Example 4.12

Consider the equation

We should try . Then

Which leads to (given that )

So .

This is the general solution, as it contains an arbitrary constant .

Related

Stated in

  • Proposition 4.11§4.2.1 Homogeneous Linear ODEs with Constant Coefficients
  • Example 4.12§4.2.1 Homogeneous Linear ODEs with Constant Coefficients