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 y ′ ( x ) = q 0 ( x ) + q 1 ( x ) y ( x ) + q 2 ( x ) y 2 ( x ) {\displaystyle y'(x)=q_{0}(x)+q_{1}(x)\,y(x)+q_{2}(x)\,y^{2}(x)} where q 0 ( x ) ≠ 0 {\displaystyle q_{0}(x)\neq 0} and q 2 ( x ) ≠ 0 {\displaystyle q_{2}(x)\neq 0} .
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 y ′ ( x ) = q 0 ( x ) + q 1 ( x ) y ( x ) + q 2 ( x ) y 2 ( x ) {\displaystyle y'(x)=q_{0}(x)+q_{1}(x)\,y(x)+q_{2}(x)\,y^{2}(x)} where q 0 ( x ) ≠ 0 {\displaystyle q_{0}(x)\neq 0} and q 2 ( x ) ≠ 0 {\displaystyle q_{2}(x)\neq 0} .
Source: Wikipedia "Riccati equation" · CC BY-SA 4.0
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