# How to solve DE with irreducible quadratic

1. Sep 29, 2008

### TOD

I'm fine solving DE with a reducible quadratic, but what happens when the quadratic is irreducible, how would I go about solving the DE? So for example,
$$\frac{dP}{dt}=-P^{2}+10P-26$$
Thanks in advance.

2. Sep 29, 2008

### rock.freak667

Try writing your DE as

$$\frac{1}{-P^{2}+10P-26} \frac{dP}{dt}=1$$

then complete the square for $-P^{2}+10P-26$, and try a trig substitution.

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