This document lists 40 differential equations involving variables separated and reducible to variables separated, homogeneous and reducible to homogeneous forms. The equations cover a wide range of standard forms involving trigonometric, exponential, logarithmic and algebraic functions of variables x and y. They also include initial/boundary value problems by specifying known conditions for variables x or y at given values.

1. UNIVERSIDAD SEÑOR DE SIPÁN
FACULTAD DE INGENIERÍA, ARQUITECTURA Y URBANISMO
ESCUELA DE INGENIERÍA INDUSTRIAL
2014-II
MATEMÁTICA II
Mg. Freundt Santimperi Sánchez
ECUACIONES DIFERENCIALES:
 DE VARIABLES SEPARADAS Y REDUCTIBLES A VARIABLES SEPARADAS
 HOMOGÉNEAS Y REDUCTIBLES A HOMOGÉNEAS
1. y’ = Sen(x).(Cos(2y) – Cos2(y))
24. xy + y2
dy
dx
= 6x
2. 2y(x+1)dy = xdx 25. x.Tg(y) = y’Sec(x) = 0
3. Sec2(x)dy + Cosc(y)dx = 0
26. Sec(y).
dy
dx
+ Sen(x - y) = Sen(x + y)
4.
dx 2 2
x y
1 x
dy


27. (1 + x2 + y2 + x2y2)dy = y2dx
5. (ey + 1)2 e-ydx + (ex + 1)3e-xdy = 0 28. 3ex. Tg(y).dx + (1 - ex).Sec2(y)dy = 0
6. (4y + yx2)dy – (2x + xy2)dx = 0 29. y(x3dy + y3dx) = x3dy
7. (y – yx2)y’ = (y + 1)2
30.
dx
dy
= 4(x2 + 1) ;X(/4) = 1
8. (xy + x)dx = (x2y2 + x2 + y2 + 1)dy 31. yLn(x).Ln(y).dx + dy = 0
2 2 32
9. y. 2x  3 .dy – x. 4  y dx = 0
10. Tg(x)Sen2(y)dx+Cos2(x).Cotg(y).dy = 0 33. x2y’ = y – xy ;Y(-1) = -1
11. (1 + Ln(x))dx + (1 + Ln(y))dy = 0 34. ey(1 + x2)dy – 2x(1 + ey)dx = 0
12.
2x
y
1
y
2dy
dx
 
35. y’ = Tg(x + y)
13. (e-y + 1)Sen(x)dx = (1 + Cos(x))dy ; Y(0) = 0 36. y’ = Sen(x + y)
14. xSen(x).e-ydx – ydy = 0 37. y’ = (x – y + 1)2
15. ydy = 4x(y2 + 1)1/2dx ;Y(0) = 1 38. y’ = (x + y + 1)2
16. (x + x )y’ = y + y
39. y’ = (8x + 2y + 1)2
17. ex.y.
dy
dx
1
dy
= e-y + e-2x – y 40. 2
Ln(2x y 3)
dx

 

18.
dy
dy  e
3x  2y 41. 2 y 2x 3
dx
dx
   
19. x 2 1 y dx = dy
42. y’ = Tg2(x + y)
20. (ex + e-x)y’ = y2 43. y’ = (x + y)2
21.
  
xy 3x y 3
 44.
xy 8 2x 4y
dy
dx
  
1
x y 1
dy
dx
 

22. eySen(2x)dx + Cosc(x) . (e2y – y)dy = 0 45. y’ = ex + y – 1 – 1

2. 23. yLnx . x’ =
2
 
1 y
x





1. (yCos(y/x) + xSen(y/x))dx = xCos(y/x)dy
21. y
dx
dy
= x + 4ye-2x/y
2. (2xTg(y/x) + y)dx = xdy 22. (y2 + 3xy)dx = (4x2 + xy)dy
3.
xy
 23. xy2
2 2 x xy y
dy
dx
 
dy
dx
= y3 – x3 ; Y(1) = 2
4. xCos(y/x).dy/dx = yCos(y/x) – x
24. (x + xy y 2  )y’ = y
5.
dy
) xy x(  + x – y = x-1/2.y3/2 ;Y(1) = 1 25.
dx
xy
2 2 x xy y
dy
dx
 

6. xCos(y/x)(ydx + xdy) = ySen(y/x)(xdy - ydx) 26. (x + y -1)dy = (x – y – 3)dx
7. xdy – ydx = 2 2 x  y dx
27. (2x – y + 2)dx + (4x – 2y – 1)dy = 0
8. y’ =
( x x y ) 2 2   
y
28. (2x – 2y)dx + (y – x + 1)dy = 0
9. y’ = ey/x + y/x 29. (2x + y + 7)dx + (x – 3y)dy = 0
10. 2x3ydx + (x4 + y4)dy = 0 30. (x + 2y – 1)dx – (2x + y – 5)dy = 0
11. (y + xCotg(y/x))dx – xdy = 0 31. (6x + 4y – 8)dx + (x + y – 1)dy = 0
12. (ySen(y/x) + xCos(y/x))dx – xSen(y/x)dy = 0 32. (2x + 3y)dx + (y + 2)dy = 0
13. (x2 + y2)dx + (x2 - xy)dy = 0 33. (2x – y – 1)dx – (y – 1)dy = 0
14. (y2 + yx)dx – x2dy = 0 34. (x – y - 1)dy – (x + y - 3)dx = 0
2 2 35. (x + 3y – 5)dy = (x – y – 1)dx
15. (x(x2 + y2))dy = y(x2 + y x  y + y2)dx
16. (x2 – y2)y’ = xy 36. (y – 2)dx – (x – y – 1)dy = 0
17.
(
2 2 x  y - yArcsen(y/x))dx + Arcsen(y/x)dy = 0
37. (2x – y + 4)dy + (x – 2y + 5)dx = 0
18. 3x2y’ = 2x2 + y2 38. (2x – y)dx + (4x + y – 6)dy = 0
19. (x2 + xy – y2)dx + xydy = 0 39. (2x + 4y + 3)dy = (2y + x + 1)dx
20.
x
y
y
x
dy
dx
 
40. (3x + 5y + 6)dy = (7y + x+ 2)dx