Special type Riccati equation

Lecture

y '= ay ² + bx ⁿ . Special type Riccati equation.

1. Solution for n ≠ -2:

where k = (n + 2) / 2; J _m (z) and Y _m (z) are Bessel functions: C ₁ and C ₂ are some constants.

2. Solution for n = -2:

Special type Riccati equation

where λ is the root of the quadratic equation aλ ² + λ + b = 0.

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Lectures and tutorial on "HANDBOOK ON MATHEMATICS, SCHOOL MATHEMATICS, HIGHER MATHEMATICS"

Terms: HANDBOOK ON MATHEMATICS, SCHOOL MATHEMATICS, HIGHER MATHEMATICS

Math Handbook

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Return (algebraic) equation

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Special type Riccati equation

Special type Riccati equation, case 1

A special type of Riccati equation, case 2 y '= f (x) y2 + ay - ab - b2f (x).

Riccati equation of a special type, case 3 y '= y2 + xf (x) y + f (x).

Special type Riccati equation, case 4 y '= f (x) y2 - axnf (x) y + anxn-1

Special Riccati equation, case 5 y '= f (x) y2 + anxn-1 - a2x2nf (x).

Riccati equation of special type, case 6 y '= - (n + 1) xny2 + xn + 1f (x) y - f (x).

A special type of Riccati equation, case 7 xy '= f (x) y2 + ny + ax2nf (x).

Special Riccati equation, case 8 xy '= x2nf (x) y2 + [axnf (x) - n] y + bf (x).

Riccati equation of a special type, case 9 y '= f (x) y2 + g (x) y - a2f (x) - ag (x).

Special Riccati equation, case 10 y '= f (x) y2 + g (x) y + anxn-1 λ a2x2nf (x) λ axng (x).

A special type of Riccati equation, case 11 y '= aeλxy2 + aeλxf (x) y + λf (x).

Special Riccati equation, case 12 y '= f (x) y2 - aeλxf (x) y + aλeλx.

Riccati equation of special type, case 13 y '= f (x) y2 + aλeλx - a2e2λxf (x).

Special type Riccati equation, case 14 y '= f (x) y2 + λy + ae2λxf (x)

Riccati equation of special type, case 15 y '= y2 - f2 (x) + f' (x).

Special type Riccati equation, case 16 y '= f (x) y2 - f (x) g (x) y + g' (x)

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

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