# A simple Riccati equation

The Riccati equation is $$-\dot p=1-p^2(1-\gamma^{-2}), \quad p(T)=\delta,$$ where $\gamma$ is just a constant. I tried the two methods given in wikipedia. The first one is to transform it into a second order linear ODE. But then I don't have enough initial conditions. The second is to first find a particular solution and then transform it into a Bernoulli equation. However I failed to identify a particular solution. Could anyone help me?

• This is not, strictly speaking, a Ricatti equation. This equation is separable and can be easily integrated. – Artem Apr 14 '13 at 19:55

To continue my comment: $$\dot p=Ap^2-1\implies \\ \frac{dp}{Ap^2-1}=dt\implies\\ \ldots$$