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Special case of equation 1. y '= f (y). Autonomous equation
2. y '= f (x) g (y). Equation with separable variables.
3. g (x) y '; = f
1 (x) y + f
0 (x). Linear equation
4. g (x) y '= f
1 (x) y + f
n (x) y
n . Bernoulli equation.
5. y '= f (y / x). Homogeneous equation.
6. y '= ay
2 + bx
n . Ricatti equation of special type.
7. y '= y
2 + f (x) y - a
2 - af (x). Ricatti equation of a special type, case 1.
8. y '= f (x) y
2 + ay - ab - b
2 f (x). Ricatti equation of a special type, case 2.
9. y '= y
2 + xf (x) y + f (x). Ricatti equation of a special type, case 3.
10. y '= f (x) y
2 - ax
n f (x) y + anx
n-1 . Riccati equation of special type, case 4.
11. y '= f (x) y
2 + anx
n-1 - a
2 x
2n f (x). Ricatti equation of special type, case 5.
12. y '= - (n + 1) x
n y
2 + x
n + 1 f (x) y - f (x). Riccati equation of special type, case 6.
13. xy '= f (x) y
2 + ny + ax
2n f (x). Riccati equation of special type, case 7.
14. xy '= x
2n f (x) y
2 + [ax
n f (x) - n] y + bf (x). Special type Riccati equation, case 8.
15. y '= f (x) y
2 + g (x) y - a
2 f (x) - ag (x). Ricatti equation of special type, case 9.
16. y '= f (x) y
2 + g (x) y + anx
n-1 λ a
2 x
2n f (x) λ ax
n g (x). Riccati equation of a special type, case 10.
17. y '= ae
λx y
2 + ae
λx f (x) y + λf (x). Special type Riccati equation, case 11.
18. y '= f (x) y
2 - ae
λx f (x) y + aλe
λx . Ricatti equation of a special type, case 12.
19. y '= f (x) y
2 + aλe
λx - a
2 e
2λx f (x). Riccati equation of special type, case 13.
20. y '= f (x) y
2 + λy + ae
2λx f (x). Riccati equation of special type, case 14.
21. y '= y
2 - f
2 (x) + f' (x). Riccati equation of special type, case 15.
22. y '= f (x) y
2 - f (x) g (x) y + g' (x). A special type of Ricatti equation, case 16.
23. y '= f (x) y
2 + g (x) y + h (x). Ricatti's general equation.
24. yy '= y + f (x). The Abel equation of the second kind in canonical form.
25. yy '= f (x) y + g (x). The Abel equation of the second kind.
26. yy '= f (x) y
2 + g (x) y + h (x). The Abel equation of the second kind.
27. y '= f (ax + by + c).
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HANDBOOK ON MATHEMATICS, SCHOOL MATHEMATICS, HIGHER MATHEMATICS
Terms: HANDBOOK ON MATHEMATICS, SCHOOL MATHEMATICS, HIGHER MATHEMATICS