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Return (algebraic) equation

Lecture



Algebraic equation of the form: Return (algebraic) equation is called returnable if its coefficients, which are located at symmetrical relative to the middle positions, are equal, that is, if Return (algebraic) equation , with k = 0, 1, ..., n. Sometimes such equations are called symmetric or symmetric .

a o x 2n + a 1 x 2n-1 + a 2 x 2n-2 + ... + a 2 x 2 + a 1 x + a 0 = 0. - Returnable (algebraic) equation. (a 0 ≠ 0)

Replacing y = x + 1 / x brings the equation to the nth power.

Return (algebraic) equation

created: 2014-10-05
updated: 2026-03-09
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Terms: HANDBOOK ON MATHEMATICS, SCHOOL MATHEMATICS, HIGHER MATHEMATICS

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Return (algebraic) equation
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Return (algebraic) equation
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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).
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