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Equations of the form

where *y*, the *a*´s and the *b* are functions of *x*, and *n*>0 are called linear differential equations. The term linear comes from that the whole expression is a linear combination of derivatives, for a given *x* at least.

We will here look at some special cases. To start with, what can we solve more or less directly? Say we have

This can be directly rewritten as

that can then be solved directly by *n* integrations (if possible).

So if we have

then we can separate the variables to get

that also can then be solved directly by integration (if possible).

In the next few pages, we will look at a few more special cases.

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