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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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