🔵17 - Ricatti Differential Equation 1 - (dy/dx + p(x)y = r(x)y^2 + q(x))

In this video, we shall learn how to solve a Ricatti differential equations.
A Ricatti Differential Equation is a non linear differential equation of the form
dy/dx + p(x)y = r(x)y^2 + q(x), where both p, r and q are all functions of x.
To solve a ricatti differential equation, a particular solution is either given or obtain by inspection.
To solve a ricatti differential equation, you need to reduce the R.D.E to either
1. a Linear first order differential equation by making the substitution
y = y1 + 1/z.
or
2. a Bernoulli differential equation by making the substitution
y = y1 + z.

3. solve the general soultion.

00:00 - Ricatti Differential Equation
04:03 - Ex 1

Playlists on various Course
1. Applied Electricity

2. Linear Algebra / Math 151

3. Basic Mechanics

4. Calculus with Analysis / Calculus 1 / Math 152

5. Differential Equations / Math 251

6. Electric Circuit Theory / Circuit Design

Make sure to watch till the end.
Like, share, and subscribe.
Thank you.

[mentality]

Thank you sir! May I just clarify something, in the particular solution part, can I also use the bernoulli one to solve the problem?

[meaahhaidee]

How to know it needs to subs y=y1+1/z?

[yourloner_Keys]

where did the Z^2 go? how does 3Z^2 on the left cancel out the 2Z^2 + 2Z^2 on the right?

[evwerenisaacoghenenyerhovw]

Sir I need a video on how to reduce from Ricatti to Bernoulli's sir

[mentality]

What if y1 is not given? How can we solve that?

[iurgdgchsbgfej]

Please sir I have a question on riccati I have tried my best but it not go please help me out