# User:Twine

From Drorbn

Week 6, Lecture 3

Constant Coefficient Homogeneous High Order ODEs

Ex **Failed to parse (lexing error): L(y) = ay" + by' +cy = 0, a, b, c \in \mathbb{R}**

Or generally

**Failed to parse (syntax error): L:{functions on \mathbb{R} \rightarrow {functions on \mathbb{R}**

is a linear transformation ("linear operator").

What do we expect from ? We expect an n-dimensional vector space.

Take **Failed to parse (lexing error): y"+y'-6y = 0**
, guess **Failed to parse (lexing error): y = c, y' = \alpha e^{\alpha x}, y" = \alpha^2e^{\alpha x}**

So we have as the general solution.

Say we have complex . Then what?