Ordinary differential equations of the first order

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).