пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ > пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ > пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ

PDF пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅ.

2. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ

2.1. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ

1. y′′ + ay = 0.    пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ.
2. y′′ − axⁿy = 0.
3. y′′ + ay′ + by = 0.    пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ.
4. y′′ + ay′ + (bx + c)y = 0.
5. y′′ + (ax+ b)y′ + (αx² + βx + σ)y = 0.
6. xy′′ + ay′ + by = 0.
7. xy′′ + ay′ + bxy = 0.
8. xy′′ + ny′ + bx^{1 − 2n}y = 0.
9. xy′′ + ay′ + bxⁿy = 0.
10. xy′′ + (b − x)y′ − ay = 0.    пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ.
11. (a₂x + b₂)y′′ + (a₁x + b₁)y′ + (a₀x + b₀)y = 0.
12. x²y′′ + axy′ + by = 0.    пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ.
13. x²y′′ + xy′ + (x² − ν²)y = 0.    пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ.
14. x²y′′ + xy′ − (x² + ν²)y = 0.    пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ.
15. x²y′′ + axy′ + (bxⁿ + c)y = 0.
16. x²y′′ + axy′ + xⁿ(bxⁿ + c)y = 0.
17. x²y′′ + (ax + b)y′ + cy = 0.
18. (1 − x²)y′′ − 2xy′ + n(n + 1)y = 0,   n = 0, 1, 2, ...    пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ.
19. (1 − x²)y′′ − 2xy′ + ν(ν + 1)y = 0.    пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ.
20. (ax² + b)y′′ + axy′ + cy = 0.
21. (1 − x²)y′′ + (ax + b)y′ + cy = 0.
22. x(x − 1)y′′ + [(α + β + 1)x − γ]xy′ + αβy = 0.    пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ.
23. (1 − x²)²y′′ − 2x(1 − x²)y′ + [ν(ν + 1)(1 − x²) − μ²]y = 0.    пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ.
24. (x − a)²(x − b)²y′′ − cy = 0.
25. (ax² + bx + c)²y′′ + Ay = 0.
26. x²(axⁿ − 1)y′′ + x(apxⁿ + q)y′ + (arxⁿ + s)y = 0.

2.2. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ

27. y′′ + ae^λxy = 0.
28. y′′ + (ae^x − b)y = 0.
29. y′′ − (ae^2λx + be^λx + c)y = 0.
30. y′′ + ay′ + be^2axy = 0.
31. y′′ − ay′ + be^2axy = 0.
32. y′′ + ay′ + (be^λx + c)y = 0.
33. y′′ − (a − 2q cosh 2x)y = 0.    пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ.
34. y′′ + (a − 2q cos 2x)y = 0.    пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ.
35. y′′ + a tan x y′ + by = 0.

2.3. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ, f=f(x)

36. y′′ + fy′ + a(f − a)y = 0.
37. y′′ + xfy′ − fy = 0.
38. xy′′ + (xf + a)y′ + (a − 1)fy = 0.
39. xy′′ + [(ax + 1)f + ax − 1]y′ + a²xfy = 0.
40. xy′′ + [(ax² + bx)f + 2]y′ + bfy = 0.
41. x²y′′ + xfy′ + a(f − a − 1)y = 0.
42. y′′ + (f + ae^λx)y′ + ae^λx(f + λ)y = 0.
43. y′′ − (f ² + f′)y = 0.
44. y′′ + 2fy′ + (f ² + f′)y = 0.
45. y′′ + (1 − a)fy′ − a(f ² + f′)y = 0.
46. y′′ + fy′ + (fg − g² + g′)y = 0,   g=g(x).
47. fy′′ − af′y′ − bf ^{2a + 1}y = 0.
48. f ²y′′ + f(f′ + a)y′ + by = 0.
49. y′′ − f′y′ + a²e^2fy = 0.
50. y′′ − f′y′ − a²e^2fy = 0.