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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?

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    $\begingroup$ This is not, strictly speaking, a Ricatti equation. This equation is separable and can be easily integrated. $\endgroup$ – Artem Apr 14 '13 at 19:55
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To continue my comment: $$ \dot p=Ap^2-1\implies \\ \frac{dp}{Ap^2-1}=dt\implies\\ \ldots $$

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