Riccati Differential Equation - Differential Equations

In this video we will learn how to solve Riccati Differential Equation.
The general form of a Riccati Equation is:
y' = a(x) y + b(x) y^2 + c(x)

The equation is named after Jacopo Riccati (1676–1754).

More generally, the term Riccati equation is used to refer to matrix equations with an analogous quadratic term, which occur in both continuous-time and discrete-time linear-quadratic-Gaussian control. The steady-state (non-dynamic) version of these is referred to as the algebraic Riccati equation.

[abdulhusseinalsultani]

Hello sir
Please I put a new D.E to solve riccati equation simply
dy/dx +(2Ay1+B)y=_A (Alsultani D.E 2)
y^'=Ay^2+ By+C
For this example
y^'=y^2 _2xy+x^2+1
Solution
A=1 , B=_2x C=1+x^2
dy/dx +(2x_2x)y=_1
dy/dx = _1
dy= _dx
y=_x+c
1/y= 1/(c_x)
y2=y1+1/y
y2= x+ 1/(c_x)
Thank you very much

[jubilantchikukwa]

this video is so helpful thank you so much

[yarenkaya]

What if we are not given the solution namely y1? How to guess it?
Thank you

[abdulrahmanhassan]

i think u messed up of the value of v coz u suppossed to intergrate -1 and not -x