ID

problem

ODE

8712

1

$y^{\prime }=\frac{\cos \left(y\right)\sec \left(x\right)}{x}$

8713

2

$y^{\prime }=x(\cos \left(y\right)+y)$

8714

3

$y^{\prime }=\frac{\sec \left(x\right)(\sin \left(y\right)+y)}{x}$

8715

4

$y^{\prime }=(5+\frac{\sec \left(x\right)}{x})(\sin \left(y\right)+y)$

8716

5

$y^{\prime }=y+1$

8717

6

$y^{\prime }=1+x$

8718

7

$y^{\prime }=x$

8719

8

$y^{\prime }=y$

8720

9

$y^{\prime }=0$

8721

10

$y^{\prime }=1+\frac{\sec \left(x\right)}{x}$

8722

11

$y^{\prime }=x+\frac{\sec \left(x\right)y}{x}$

8723

12

$y^{\prime }=\frac{2y}{x}$

8724

13

$y^{\prime }=\frac{2y}{x}$

8725

14

$y^{\prime }=\frac{\ln (y^2+1)}{\ln (x^2+1)}$

8726

15

$y^{\prime }=\frac{1}{x}$

8727

16

$y^{\prime }=\frac{-xy-1}{4x^{3}y-2x^2}$

8728

17

$\frac{{y^{\prime }}^2}{4}-x{y}^{\prime }+y=0$

8729

18

$y^{\prime }=\sqrt{\frac{y+1}{y^2}}$

8730

19

$y^{\prime }=\sqrt{1-x^2-y^2}$

8731

20

$y^{\prime }+\frac{y}{3}=\frac{(1-2x)y^4}{3}$

8732

21

$y^{\prime }=\sqrt{y}+x$

8733

23

$x^2{y}^{\prime }+y^2=x{y}^{\prime }y$

8734

24

$y=x{y}^{\prime }+x^2{y^{\prime }}^2$

8735

25

$(x+y)y^{\prime }=0$

8736

26

$x{y}^{\prime }=0$

8737

27

$\frac{y^{\prime }}{x+y}=0$

8738

28

$\frac{y^{\prime }}{x}=0$

8739

29

$y^{\prime }=0$

8740

30

$y=x{y^{\prime }}^2+{y^{\prime }}^2$

8741

31

$y^{\prime }=\frac{5x^2-xy+y^2}{x^2}$

8742

32

$2t+3x+(x+2)x^{\prime }=0$

8743

33

$y^{\prime }=\frac{1}{1-y}$

8744

34

$p^{\prime }=ap-b{p}^2$

8745

35

$y^2+\frac{2}{x}+2x{y}^{\prime }y=0$

8746

36

$f^{\prime }x-f=\frac{{f^{\prime }}^2{(1-{f^{\prime }}^{\lambda })}^2}{{\lambda }^2}$

8747

37

$x{y}^{\prime }-2y+b{y}^2=c{x}^4$

8748

38

$x{y}^{\prime }-y+y^2=x^{2/3}$

8749

39

$u^{\prime }+u^2=\frac{1}{x^{4/5}}$

8750

40

$y{y}^{\prime }-y=x$

8751

41

$y^{\prime \prime }+2y^{\prime }+y=0$

8752

41

$5y^{\prime \prime }+2y^{\prime }+4y=0$

8753

42

$y^{\prime \prime }+y^{\prime }+4y=1$

8754

43

$y^{\prime \prime }+y^{\prime }+4y=\sin \left(x\right)$

8755

44

$y=x{y^{\prime }}^2$

8756

45

$y{y}^{\prime }=1-x{y^{\prime }}^3$

8757

46

$f^{\prime }=\frac{1}{f}$

8758

47

$t{y}^{\prime \prime }+4y^{\prime }=t^2$

8759

48

$(t^2+9)y^{\prime \prime }+2y^{\prime }t=0$

8760

49

$t^2{y}^{\prime \prime }-3y^{\prime }t+5y=0$

8761

50

$t{y}^{\prime \prime }+y^{\prime }=0$

8762

51

$t^2{y}^{\prime \prime }-2y^{\prime }=0$

8763

52

$y^{\prime \prime }+\frac{(t^2-1)y^{\prime }}{t}+\frac{t^{2}y}{{(1+{\mathrm{e}}^{\frac{t^2}{2}})}^2}=0$

8764

53

$t{y}^{\prime \prime }-y^{\prime }+4t^{3}y=0$

8765

54

$y^{\prime \prime }=0$

8766

55

$y^{\prime \prime }=1$

8767

56

$y^{\prime \prime }=f\left(t\right)$

8768

57

$y^{\prime \prime }=k$

8769

58

$y^{\prime }=-4\sin (x-y)-4$

8770

59

$y^{\prime }+\sin (x-y)=0$

8771

60

$y^{\prime \prime }=4\sin \left(x\right)-4$

8772

61

$y{y}^{\prime \prime }=0$

8773

62

$y{y}^{\prime \prime }=1$

8774

63

$y{y}^{\prime \prime }=x$

8775

64

$y^2{y}^{\prime \prime }=x$

8776

65

$y^2{y}^{\prime \prime }=0$

8777

66

$3y{y}^{\prime \prime }=\sin \left(x\right)$

8778

67

$3y{y}^{\prime \prime }+y=5$

8779

68

$ay{y}^{\prime \prime }+by=c$

8780

69

$a{y}^2{y}^{\prime \prime }+b{y}^2=c$

8781

70

$ay{y}^{\prime \prime }+by=0$

8782

71

$[x^{\prime }\left(t\right)=9x\left(t\right)+4y\left(t\right),y^{\prime }\left(t\right)=-6x\left(t\right)-y\left(t\right),z^{\prime }\left(t\right)=6x\left(t\right)+4y\left(t\right)+3z\left(t\right)]$

8783

72

$[x^{\prime }\left(t\right)=x\left(t\right)-3y\left(t\right),y^{\prime }\left(t\right)=3x\left(t\right)+7y\left(t\right)]$

8784

73

$[x^{\prime }\left(t\right)=x\left(t\right)-2y\left(t\right),y^{\prime }\left(t\right)=2x\left(t\right)+5y\left(t\right)]$

8785

74

$[x^{\prime }\left(t\right)=7x\left(t\right)+y\left(t\right),y^{\prime }\left(t\right)=-4x\left(t\right)+3y\left(t\right)]$

8786

75

$[x^{\prime }\left(t\right)=x\left(t\right)+y\left(t\right),y^{\prime }\left(t\right)=y\left(t\right),z^{\prime }\left(t\right)=z\left(t\right)]$

8787

76

$[x^{\prime }\left(t\right)=2x\left(t\right)+y\left(t\right)-z\left(t\right),y^{\prime }\left(t\right)=-x\left(t\right)+2z\left(t\right),z^{\prime }\left(t\right)=-x\left(t\right)-2y\left(t\right)+4z\left(t\right)]$

8788

77

$x^{\prime }=4Ak{\left(\frac{x}{A}\right)}^{3/4}-3kx$

8789

78

$\frac{y^{\prime }y}{1+\frac{\sqrt{1+{y^{\prime }}^2}}{2}}=-x$

8790

78

$\frac{y^{\prime }y}{1+\frac{\sqrt{1+{y^{\prime }}^2}}{2}}=-x$

8791

79

$y^{\prime }=\frac{y(1+\frac{a^{2}x}{\sqrt{a^2(x^2+1)}})}{\sqrt{a^2(x^2+1)}}$

8792

80

$y^{\prime }=x^2+y^2$

8793

81

$y^{\prime }=2\sqrt{y}$

8794

82

$z^{\prime \prime }+3z^{\prime }+2z=24{\mathrm{e}}^{-3t}-24{\mathrm{e}}^{-4t}$

8795

83

$y^{\prime }=\sqrt{1-y^2}$

8796

84

$y^{\prime }=x^2+y^2-1$

8797

85

$y^{\prime }=2y(x\sqrt{y}-1)$

8798

86

$y^{\prime \prime }=\frac{1}{y}-\frac{x{y}^{\prime }}{y^2}$

8799

87

$y^{\prime \prime }+y^{\prime }+y=0$

8800

88

$y^{\prime \prime }+y^{\prime }+y=0$

8801

88

$y^{\prime \prime }+y^{\prime }+y=0$

8802

89

$y^{\prime \prime }-y{y}^{\prime }=2x$

8803

90

$y^{\prime }-y^2-x-x^2=0$

ID

problem

ODE

8804

1

$y^{\prime \prime }-x{y}^{\prime }-xy-x=0$

8805

2

$y^{\prime \prime }-x{y}^{\prime }-xy-2x=0$

8806

3

$y^{\prime \prime }-x{y}^{\prime }-xy-3x=0$

8807

4

$y^{\prime \prime }-x{y}^{\prime }-xy-x^2-x=0$

8808

5

$y^{\prime \prime }-x{y}^{\prime }-xy-x^3+2=0$

8809

6

$y^{\prime \prime }-x{y}^{\prime }-xy-x^4-6=0$

8810

7

$y^{\prime \prime }-x{y}^{\prime }-xy-x^5+24=0$

8811

8

$y^{\prime \prime }-x{y}^{\prime }-xy-x=0$

8812

9

$y^{\prime \prime }-x{y}^{\prime }-xy-x^2=0$

8813

10

$y^{\prime \prime }-x{y}^{\prime }-xy-x^3=0$

8814

11

$y^{\prime \prime }-ax{y}^{\prime }-bxy-cx=0$

8815

12

$y^{\prime \prime }-ax{y}^{\prime }-bxy-c{x}^2=0$

8816

13

$y^{\prime \prime }-ax{y}^{\prime }-bxy-c{x}^3=0$

8817

14

$y^{\prime \prime }-y^{\prime }-xy-x=0$

8818

15

$y^{\prime \prime }-y^{\prime }-xy-x^2=0$

8819

16

$y^{\prime \prime }-y^{\prime }-xy-x^2-1=0$

8820

16

$y^{\prime \prime }-y^{\prime }-xy-x^2-1=0$

8821

17

$y^{\prime \prime }-2y^{\prime }-xy-x^2-2=0$

8822

18

$y^{\prime \prime }-4y^{\prime }-xy-x^2-4=0$

8823

19

$y^{\prime \prime }-y^{\prime }-xy-x^3+1=0$

8824

20

$y^{\prime \prime }-2y^{\prime }-xy-x^3-x^2=0$

8825

21

$y^{\prime \prime }-y^{\prime }-xy-x^3+2=0$

8826

22

$y^{\prime \prime }-2y^{\prime }-xy-x^3+2=0$

8827

23

$y^{\prime \prime }-4y^{\prime }-xy-x^3+2=0$

8828

24

$y^{\prime \prime }-6y^{\prime }-xy-x^3+2=0$

8829

25

$y^{\prime \prime }-8y^{\prime }-xy-x^3+2=0$

8830

26

$y^{\prime \prime }-y^{\prime }-xy-x^4+3=0$

8831

27

$y^{\prime \prime }-y^{\prime }-xy-x^3=0$

8832

28

$y^{\prime \prime }-xy-x^3+2=0$

8833

29

$y^{\prime \prime }-xy-x^6+64=0$

8834

30

$y^{\prime \prime }-xy-x=0$

8835

31

$y^{\prime \prime }-xy-x^2=0$

8836

32

$y^{\prime \prime }-xy-x^3=0$

8837

33

$y^{\prime \prime }-xy-x^6-x^3+42=0$

8838

34

$y^{\prime \prime }-x^{2}y-x^2=0$

8839

35

$y^{\prime \prime }-x^{2}y-x^3=0$

8840

36

$y^{\prime \prime }-x^{2}y-x^4=0$

8841

37

$y^{\prime \prime }-x^{2}y-x^4+2=0$

8842

38

$y^{\prime \prime }-2x^{2}y-x^4+1=0$

8843

39

$y^{\prime \prime }-x^{3}y-x^3=0$

8844

40

$y^{\prime \prime }-x^{3}y-x^4=0$

8845

41

$y^{\prime \prime }-x^2{y}^{\prime }-x^{2}y-x^2=0$

8846

42

$y^{\prime \prime }-x^3{y}^{\prime }-x^{3}y-x^3=0$

8847

43

$y^{\prime \prime }-x{y}^{\prime }-xy-x=0$

8848

44

$y^{\prime \prime }-x^2{y}^{\prime }-xy-x^2=0$

8849

45

$y^{\prime \prime }-x^2{y}^{\prime }-x^{2}y-x^3-x^2=0$

8850

46

$y^{\prime \prime }-x^2{y}^{\prime }-x^{3}y-x^4-x^2=0$

8851

47

$y^{\prime \prime }-\frac{y^{\prime }}{x}-xy-x^2-\frac{1}{x}=0$

8852

48

$y^{\prime \prime }-\frac{y^{\prime }}{x}-x^{2}y-x^3-\frac{1}{x}=0$

8853

49

$y^{\prime \prime }-\frac{y^{\prime }}{x}-x^{3}y-x^4-\frac{1}{x}=0$

8854

50

$y^{\prime \prime }-x^3{y}^{\prime }-xy-x^3-x^2=0$

8855

51

$y^{\prime \prime }-x^3{y}^{\prime }-x^{2}y-x^3=0$

8856

52

$y^{\prime \prime }-x^3{y}^{\prime }-x^{3}y-x^4-x^3=0$

8857

50

$y^{\prime \prime \prime }-x^3{y}^{\prime }-x^{2}y-x^3=0$

ID

problem

ODE

8858

1

$y^{\prime \prime }+c{y}^{\prime }+ky=0$

8859

2

$w^{\prime }=-\frac{1}{2}-\frac{\sqrt{1-12w}}{2}$

8860

3

$y^{\prime \prime }+y=\sin \left(x\right)$

8861

4

$y^{\prime \prime }+y=\sin \left(x\right)$

8862

5

$y^{\prime \prime }+y=\sin \left(x\right)$

8863

6

$y^{\prime \prime }+y=\sin \left(x\right)$

8864

7

$y^{\prime \prime }+y=\sin \left(x\right)$

8865

8

$y^{\prime \prime }+y=\sin \left(x\right)$

8866

9

$y^{\prime \prime }+y=\sin \left(x\right)$

8867

10

$y^{\prime \prime }+y=\sin \left(x\right)$

8868

11

$y^{\prime \prime }+y^{\prime }+y=\sin \left(x\right)$

8869

12

$y^{\prime \prime }+y^{\prime }+y=\sin \left(x\right)$

8870

13

$y^{\prime \prime }+y^{\prime }+y=\sin \left(x\right)$

8871

14

$y^{\prime \prime \prime }+y^{\prime }+y=x$

8872

15

$x^4{y}^{\prime \prime }+x^3{y}^{\prime }-4x^{2}y=1$

8873

16

$x^4{y}^{\prime \prime }+x^3{y}^{\prime }-4x^{2}y=x$

8874

17

$x^2{y}^{\prime \prime }+x{y}^{\prime }-4y=x$

8875

18

$x^4{y}^{\prime \prime \prime }+x^3{y}^{\prime \prime }+x^2{y}^{\prime }+xy=0$

8876

19

$x^4{y}^{\prime \prime \prime }+x^3{y}^{\prime \prime }+x^2{y}^{\prime }+xy=x$

8877

20

$5x^5{y}^{\prime \prime \prime \prime }+4x^4{y}^{\prime \prime \prime }+x^2{y}^{\prime }+xy=0$

8878

21

$(x^2+1)y^{\prime \prime }+1+{y^{\prime }}^2=0$

8879

22

$(x^2+1)y^{\prime \prime }+1+{y^{\prime }}^2=x$

8880

23

$(x^2+1)y^{\prime \prime }+1+x{y^{\prime }}^2=1$

8881

24

$(x^2+1)y^{\prime \prime }+y{y^{\prime }}^2=0$

8882

25

$(x^2+1)y^{\prime \prime }+{y^{\prime }}^2=0$

8883

26

$y^{\prime \prime }+\sin \left(y\right){y^{\prime }}^2=0$

8884

27

$(x^2+1)y^{\prime \prime }+{y^{\prime }}^3=0$

8885

28

$y^{\prime }={\mathrm{e}}^{-\frac{y}{x}}$

8886

29

$y^{\prime }=2x^2\sin {\left(\frac{y}{x}\right)}^2+\frac{y}{x}$

8887

30

$4x^2{y}^{\prime \prime }+y=8\sqrt{x}(\ln \left(x\right)+1)$

8888

31

$v{v}^{\prime }=\frac{2v^2}{r^3}+\frac{\lambda r}{3}$

ID

problem

ODE

8889

1

$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=0$

8890

2

$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=1$

8891

3

$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=1+x$

8892

4

$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=x$

8893

5

$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=x^2+x+1$

8894

6

$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=x^2$

8895

7

$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=x^2+1$

8896

8

$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=x^4$

8897

9

$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=\sin \left(x\right)$

8898

10

$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=1+\sin \left(x\right)$

8899

11

$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=x\sin \left(x\right)$

8900

12

$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=\cos \left(x\right)+\sin \left(x\right)$

8901

13

$x^2{y}^{\prime \prime }+(\cos \left(x\right)-1)y^{\prime }+y{\mathrm{e}}^x=0$

8902

14

$(x-2)y^{\prime \prime }+\frac{y^{\prime }}{x}+(1+x)y=0$

8903

15

$(x-2)y^{\prime \prime }+\frac{y^{\prime }}{x}+(1+x)y=0$

8904

16

$(1+x)(3x-1)y^{\prime \prime }+y^{\prime }\cos \left(x\right)-3xy=0$

8905

17

$x{y}^{\prime \prime }+2y^{\prime }+xy=0$

8906

18

$2x^2{y}^{\prime \prime }+3x{y}^{\prime }-xy=x^2+2x$

8907

19

$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=1$

8908

20

$2x^2{y}^{\prime \prime }+2x{y}^{\prime }-xy=1$

8909

21

$y^{\prime \prime }+(x-6)y=0$

8910

22

$x^2{y}^{\prime \prime }+(3x^2+2x)y^{\prime }-2y=0$

8911

23

$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=x^2+\cos \left(x\right)$

8912

24

$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=\cos \left(x\right)$

8913

24

$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=x^3+\cos \left(x\right)$

8914

24

$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=x^3\cos \left(x\right)$

8915

24

$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=x^3\cos \left(x\right)+\sin {\left(x\right)}^2$

8916

24

$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=\ln \left(x\right)$

8917

25

$2x^2(x^2+x+1)y^{\prime \prime }+x(11x^2+11x+9)y^{\prime }+(7x^2+10x+6)y=0$