Riccati equation

In mathematics, a Riccati equation in the narrowest sense is any first-order ordinary differential equation that is quadratic in the unknown function. In other words, it is an equation of the form

where ${\displaystyle q_{0}(x)\neq 0}$ and ${\displaystyle q_{2}(x)\neq 0}$. If ${\displaystyle q_{0}(x)=0}$ the equation reduces to a Bernoulli equation, while if ${\displaystyle q_{2}(x)=0}$ the equation becomes a first order linear ordinary differential equation.

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