**Made a slip somewhere in the tutorial and rather looking for it I said I’d put it up here — the point is that the term disappears so we have a differential equation in and — in other words a function and it’s derivative. This can then be integrated in the usual way.**

*Verify that is a solution to the second order ODE*

* (*)*

**Solution**

We have that and . Hence

as required. That is is a solution.

*Find the general solution by trying a solution of the form *

Let . Hence

.

Substituting into the left-hand side of (*):

Grouping into and :

A bit of factorisation:

Now let and note :

.

,

That is

,

for a general solution:

.

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