Exact Linear Second-Order Equations

1. Oct 9, 2015

2. Oct 9, 2015

Jack Davies

I think that it's just saying that, with that special condition on $a_i(x)$, the differential equation becomes:

$$a_0 y'' -a_0 '' y+a_1 y' + a_1 ' y =0$$

Which we can write as:

$$\frac{d}{dx}(a_0 y' -a_0' y) + \frac{d}{dx} (a_1 y) = 0$$

So with that very useful condition we can write it as a total derivative and then integrate up to a first order problem.