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Section 9.6 Theorems about Linear ODEs

In this section, we will give, without proof, several important theorems about linear differential equations. But before we get to the theorems, you will need to understand what is meant by the word linear, see Section 9.5 and Section 4.3. so that you can understand the content of these theorems. Before you read this section, you should also make sure you know the definitions and notation in Section 9.1.

The first two theorems tell us the general form for solutions for homogeneous and inhomogeneous linear differential equations and describe the free parameters that exist in each solution. The third theorem describes what kind of initial conditions are necessary to remove this freedom and specify a unique solution.