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Riccati equation of a special type, the general form y '= f (x) y2 + g (x) y + h (x).

Lecture



Special type Riccati equation, general view


y '= f (x) y 2 + g (x) y + h (x). Special type Riccati equation.

1. For a given particular solution, y 0 = y 0 (x), the general solution can be written as

Riccati equation of a special type, the general form y = f (x) y2 + g (x) y + h (x).

where C is some constant. The private solution y 0 = y 0 (x) corresponds to the infinite C.
3. Replacement

Riccati equation of a special type, the general form y = f (x) y2 + g (x) y + h (x).

reduces the general Riccati equation to a second order linear equation:

Riccati equation of a special type, the general form y = f (x) y2 + g (x) y + h (x).

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