ID |
problem |
ODE |
1 |
\(\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\) |
|
2 |
\(\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y = 0\) |
|
3 |
\(\left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y = 0\) |
|
4 |
\(\left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y = 0\) |
|
5 |
\(3 y^{\prime \prime }+y^{\prime } x -4 y = 0\) |
|
6 |
\(5 y^{\prime \prime }-2 y^{\prime } x +10 y = 0\) |
|
7 |
\(y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0\) |
|
8 |
\(\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0\) |
|
9 |
\(y^{\prime \prime }+y^{\prime } x -2 y = 0\) |
|
10 |
\(\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0\) |
|
11 |
\(\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0\) |
|
12 |
\(t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{2} y = 0\) |
|
13 |
\(t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0\) |
|
14 |
\(t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0\) |
|
15 |
\(\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 0\) |
|
16 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
17 |
\(t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0\) |
|
18 |
\(\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 0\) |
|
19 |
\(y^{\prime \prime }+y^{\prime } x +2 y = 0\) |
|
20 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y = 0\) |
|
21 |
\(\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = 0\) |
|
22 |
\(2 y^{\prime \prime }+y^{\prime } x +3 y = 0\) |
|
23 |
\(y^{\prime \prime }+y^{\prime } x +2 y = 0\) |
|
24 |
\(\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = 0\) |
|
25 |
\(y^{\prime \prime }+y^{\prime } x +2 y = 0\) |
|
26 |
\(\left (-x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x +2 y = 0\) |
|
27 |
\(4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y = 0\) |
|
28 |
\(\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\) |
|
29 |
\(x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0\) |
|
31 |
\(\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0\) |
|
32 |
\(4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0\) |
|
33 |
\(y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0\) |
|
34 |
\(\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = 0\) |
|
35 |
\(x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 0\) |
|
36 |
\(x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0\) |
|
38 |
\(4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y = 0\) |
|
39 |
\(4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y = 0\) |
|
40 |
\(x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}-2\right ) y = 0\) |
|
41 |
\(x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0\) |
|
42 |
\(x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y = 0\) |
|
43 |
\(x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y = 0\) |
|
44 |
\(\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\) |
|
45 |
\(4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y = 0\) |
|
46 |
\(\left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }-\left (6 x -8\right ) y = 0\) |
|
47 |
\(\left (x +2\right ) y^{\prime \prime }+y^{\prime } x +3 y = 0\) |
|
48 |
\(x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (4+x \right ) y^{\prime }+\left (2-x \right ) y = 0\) |
|
49 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (4+6 x \right ) y = 0\) |
|
50 |
\(x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y = 0\) |
|
51 |
\(x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y = 0\) |
|
52 |
\(\left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +6 y = 0\) |
|
53 |
\(\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0\) |
|
54 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x +20 y = 0\) |
|
55 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x -12 y = 0\) |
|
56 |
\(\left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y = 0\) |
|
57 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x -4 y = 0\) |
|
58 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x +28 y = 0\) |
|
59 |
\(y^{\prime \prime }+y^{\prime } x +2 y = 0\) |
|
60 |
\(\left (2 x^{2}+1\right ) y^{\prime \prime }-9 y^{\prime } x -6 y = 0\) |
|
61 |
\(\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y = 0\) |
|
62 |
\(y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y = 0\) |
|
63 |
\(\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0\) |
|
64 |
\(\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y = 0\) |
|
65 |
\(\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y = 0\) |
|
66 |
\(\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0\) |
|
67 |
\(y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0\) |
|
68 |
\(\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0\) |
|
69 |
\(y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y = 0\) |
|
70 |
\(\left (3 x +1\right ) y^{\prime \prime }+y^{\prime } x +2 y = 0\) |
|
71 |
\(\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0\) |
|
72 |
\(\left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y = 0\) |
|
73 |
\(\left (4+x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y = 0\) |
|
74 |
\(\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y = 0\) |
|
75 |
\(x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y = 0\) |
|
76 |
\(\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y = 0\) |
|
77 |
\(\left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (2-x \right ) y = 0\) |
|
78 |
\(y^{\prime \prime }+3 y^{\prime } x +\left (2 x^{2}+4\right ) y = 0\) |
|
79 |
\(\left (2+4 x \right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y = 0\) |
|
80 |
\(y^{\prime \prime }-3 y^{\prime } x +\left (2 x^{2}+5\right ) y = 0\) |
|
81 |
\(2 y^{\prime \prime }+5 y^{\prime } x +\left (2 x^{2}+4\right ) y = 0\) |
|
82 |
\(y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0\) |
|
83 |
\(y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0\) |
|
84 |
\(2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0\) |
|
85 |
\(3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y = 0\) |
|
86 |
\(12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y = 0\) |
|
87 |
\(x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y = 0\) |
|
88 |
\(18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y = 0\) |
|
89 |
\(2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y = 0\) |
|
90 |
\(2 x^{2} y^{\prime \prime }+x \left (x +5\right ) y^{\prime }-\left (2-3 x \right ) y = 0\) |
|
91 |
\(3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y = 0\) |
|
92 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (1-2 x \right ) y = 0\) |
|
93 |
\(3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (3 x +1\right ) y = 0\) |
|
94 |
\(2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (x +1\right ) y = 0\) |
|
95 |
\(x^{2} \left (4+x \right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0\) |
|
96 |
\(2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y = 0\) |
|
97 |
\(6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (x +2\right ) y = 0\) |
|
98 |
\(x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (3+4 x \right ) y = 0\) |
|
99 |
\(2 x^{2} \left (2+3 x \right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y = 0\) |
|
100 |
\(x^{2} \left (x +2\right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y = 0\) |
|
101 |
\(8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0\) |
|
102 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y = 0\) |
|
103 |
\(x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 x y = 0\) |
|
104 |
\(4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y = 0\) |
|
105 |
\(3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y = 0\) |
|
106 |
\(2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y = 0\) |
|
107 |
\(2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y = 0\) |
|
108 |
\(2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y = 0\) |
|
109 |
\(x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 x y = 0\) |
|
110 |
\(2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y = 0\) |
|
111 |
\(9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y = 0\) |
|
112 |
\(6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y = 0\) |
|
113 |
\(9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0\) |
|
114 |
\(4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0\) |
|
115 |
\(8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y = 0\) |
|
116 |
\(2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0\) |
|
117 |
\(6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y = 0\) |
|
118 |
\(28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y = 0\) |
|
119 |
\(8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y = 0\) |
|
120 |
\(4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y = 0\) |
|
121 |
\(3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0\) |
|
122 |
\(4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y = 0\) |
|
123 |
\(x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4+x \right ) y = 0\) |
|
124 |
\(2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0\) |
|
125 |
\(x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0\) |
|
126 |
\(x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y = 0\) |
|
127 |
\(4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y = 0\) |
|
128 |
\(x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y = 0\) |
|
129 |
\(9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y = 0\) |
|
130 |
\(x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y = 0\) |
|
131 |
\(16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y = 0\) |
|
132 |
\(9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y = 0\) |
|
133 |
\(36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y = 0\) |
|
134 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3-x \right ) y^{\prime }+4 y = 0\) |
|
135 |
\(x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y = 0\) |
|
136 |
\(2 x^{2} \left (x +2\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y = 0\) |
|
137 |
\(2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y = 0\) |
|
138 |
\(x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y = 0\) |
|
139 |
\(x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0\) |
|
140 |
\(x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y = 0\) |
|
141 |
\(x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0\) |
|
142 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y = 0\) |
|
143 |
\(4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0\) |
|
144 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y = 0\) |
|
145 |
\(2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0\) |
|
146 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y = 0\) |
|
147 |
\(4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0\) |
|
148 |
\(3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0\) |
|
149 |
\(9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y = 0\) |
|
150 |
\(x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0\) |
|
151 |
\(x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (1+4 x \right ) y = 0\) |
|
152 |
\(x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0\) |
|
153 |
\(x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y = 0\) |
|
154 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y = 0\) |
|
155 |
\(9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0\) |
|
156 |
\(x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 x y = 0\) |
|
157 |
\(4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0\) |
|
158 |
\(4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y = 0\) |
|
159 |
\(9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (3+4 x \right ) y = 0\) |
|
160 |
\(x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y = 0\) |
|
161 |
\(16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y = 0\) |
|
162 |
\(x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (4-3 x \right ) y^{\prime }+4 y = 0\) |
|
163 |
\(4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y = 0\) |
|
164 |
\(x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0\) |
|
165 |
\(9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y = 0\) |
|
166 |
\(2 x^{2} \left (x +2\right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y = 0\) |
|
167 |
\(x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0\) |
|
168 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y = 0\) |
|
169 |
\(x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 y x^{2} = 0\) |
|
170 |
\(4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (3 x +1\right ) y = 0\) |
|
171 |
\(2 x^{2} \left (2+3 x \right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y = 0\) |
|
172 |
\(x^{2} y^{\prime \prime }+x \left (x +2\right ) y^{\prime }-\left (2-3 x \right ) y = 0\) |
|
173 |
\(4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y = 0\) |
|
174 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 x y = 0\) |
|
175 |
\(x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y = 0\) |
|
176 |
\(x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y = 0\) |
|
177 |
\(4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y = 0\) |
|
178 |
\(3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y = 0\) |
|
179 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y = 0\) |
|
180 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y = 0\) |
|
181 |
\(x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y = 0\) |
|
182 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y = 0\) |
|
183 |
\(4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y = 0\) |
|
184 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y = 0\) |
|
185 |
\(x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y = 0\) |
|
186 |
\(x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y = 0\) |
|
187 |
\(x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y = 0\) |
|
188 |
\(x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y = 0\) |
|
189 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 y x^{2} = 0\) |
|
190 |
\(4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y = 0\) |
|
191 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y = 0\) |
|
192 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y = 0\) |
|
193 |
\(4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y = 0\) |
|
194 |
\(y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0\) |
|
195 |
\(y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0\) |
|
196 |
\(\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0\) |
|
197 |
\(\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0\) |
|
198 |
\(\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0\) |
|
199 |
\(\left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0\) |
|
200 |
\(t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0\) |
|
201 |
\(y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = 0\) |
|
202 |
\(y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y = 0\) |
|
204 |
\(2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y = 0\) |
|
205 |
\(2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y = 0\) |
|
206 |
\(2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y = 0\) |
|
207 |
\(2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y = 0\) |
|
208 |
\(t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y = 0\) |
|
209 |
\(t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y = 0\) |
|
210 |
\(t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y = 0\) |
|
211 |
\(t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y = 0\) |
|
212 |
\(t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0\) |
|
213 |
\(t y^{\prime \prime }+t y^{\prime }+2 y = 0\) |
|
214 |
\(t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0\) |
|
215 |
\(t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y = 0\) |
|
216 |
\(y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+6\right ) y = 0\) |
|
217 |
\(\left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+\lambda y = 0\) |
|
218 |
\(4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y = 0\) |
|
219 |
\(f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f = 0\) |
|
220 |
\(z y^{\prime \prime }-2 y^{\prime }+y z = 0\) |
|
221 |
\(z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z} = 0\) |
|
222 |
\(y^{\prime \prime }+2 y^{\prime } x +4 y = 0\) |
|
223 |
\(y^{\prime \prime }+y^{\prime } x +3 y = 0\) |
|
224 |
\(y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0\) |
|
225 |
\(\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 y^{\prime } x -16 y = 0\) |
|
226 |
\(\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y = 0\) |
|
227 |
\(y^{\prime \prime }+y^{\prime } x +\left (x +2\right ) y = 0\) |
|
228 |
\(\left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y = 0\) |
|
229 |
\(4 y^{\prime \prime }+y^{\prime } x +4 y = 0\) |
|
230 |
\(y^{\prime \prime }+y^{\prime } x -4 y = 0\) |
|
231 |
\(4 x y^{\prime \prime }-y^{\prime } x +2 y = 0\) |
|
232 |
\(6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y = 0\) |
|
233 |
\(3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y = 0\) |
|
234 |
\(2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y = 0\) |
|
235 |
\(4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y = 0\) |
|
236 |
\(x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y = 0\) |
|
237 |
\(x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y = 0\) |
|
238 |
\(x^{2} y^{\prime \prime }+x \left (3-x \right ) y^{\prime }+y = 0\) |
|
239 |
\(x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0\) |
|
240 |
\(x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y = 0\) |
|
241 |
\(x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y = 0\) |
|
242 |
\(x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y = 0\) |
|
243 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0\) |
|
244 |
\(x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y = 0\) |
|
245 |
\(x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0\) |
|
246 |
\(x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y = 0\) |
|
247 |
\(x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y = 0\) |
|
248 |
\(x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (2+3 x \right ) y = 0\) |
|
249 |
\(x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y = 0\) |
|
250 |
\(4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y = 0\) |
|
251 |
\(x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (x +1\right ) y = 0\) |
|
252 |
\(x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y = 0\) |
|
253 |
\(4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y = 0\) |
|
254 |
\(x^{2} y^{\prime \prime }+x \left (4+x \right ) y^{\prime }+\left (x +2\right ) y = 0\) |
|
255 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y = 0\) |
|
256 |
\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\) |
|
257 |
\(2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0\) |
|
258 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
259 |
\(x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y = 0\) |
|
260 |
\(x^{4} y^{\prime \prime }+y^{\prime } x +y = 0\) |
|
261 |
\(x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y = 0\) |
|
262 |
\(\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y = 0\) |
|
263 |
\(x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y = 0\) |
|
264 |
\(x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y = 0\) |
|
265 |
\(x^{2} \left (1-4 x \right ) y^{\prime \prime }-\frac {y^{\prime } x}{2}-\frac {3 x y}{4} = 0\) |
|
266 |
\(x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y = 0\) |
|
267 |
\(x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y = 0\) |
|
268 |
\(x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y = 0\) |
|
269 |
\(2 x^{2} y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x} = 0\) |
|
270 |
\(x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4} = 0\) |
|
271 |
\(2 x \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = 0\) |
|
272 |
\(2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y = 0\) |
|
273 |
\(x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9} = 0\) |
|
274 |
\(4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}} = 0\) |
|
275 |
\(u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0\) |
|
276 |
\(u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0\) |
|
277 |
\(u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0\) |
|
278 |
\(u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0\) |
|
279 |
\(u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0\) |
|
280 |
\(y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}}\) |
|
281 |
\(y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}}\) |
|
282 |
\(x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+\frac {1}{4}\right ) y = 0\) |
|
283 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0\) |
|
284 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {25}{4}\right ) y = 0\) |
|
285 |
\(y^{\prime \prime }+q y^{\prime } = \frac {2 y}{x^{2}}\) |
|
286 |
\(x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0\) |
|
287 |
\(\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0\) |
|
288 |
\(\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0\) |
|
289 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\) |
|
290 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\) |
|
291 |
\(y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0\) |
|
292 |
\(y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0\) |
|
293 |
\(\left (2 x -3\right ) y^{\prime \prime }-y^{\prime } x +y = 0\) |
|
294 |
\(y^{\prime \prime }-y^{\prime } x -3 y = 0\) |
|
295 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\) |
|
296 |
\(y^{\prime \prime }-y^{\prime } x +2 y = 0\) |
|
297 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = 0\) |
|
298 |
\(x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (x -1\right ) y = 0\) |
|
299 |
\(2 x y^{\prime \prime }-y^{\prime }+2 y = 0\) |
|
300 |
\(x y^{\prime \prime }+y^{\prime } x -2 y = 0\) |
|
301 |
\(x \left (x -1\right )^{2} y^{\prime \prime }-2 y = 0\) |
|
302 |
\(y^{\prime \prime }-2 y^{\prime } x +y x^{2} = 0\) |
|
303 |
\(x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right ) = 0\) |
|
304 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+y^{\prime } x \right ) = 0\) |
|
305 |
\(2 \left (2-x \right ) x^{2} y^{\prime \prime }-x \left (4-x \right ) y^{\prime }+\left (3-x \right ) y = 0\) |
|
306 |
\(x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0\) |
|
307 |
\(x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0\) |
|
309 |
\(y^{\prime \prime }-2 y^{\prime } x +8 y = 0\) |
|
310 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y = 0\) |
|
311 |
\(x \left (x +2\right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y = 0\) |
|
313 |
\(x \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y = 0\) |
|
314 |
\(\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\) |
|
315 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\) |
|
316 |
\(\left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y = 0\) |
|
317 |
\(\left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y = 0\) |
|
318 |
\(y^{\prime \prime }-y^{\prime } x +2 y = 0\) |
|
319 |
\(\left (x +2\right ) y^{\prime \prime }+y^{\prime } x -y = 0\) |
|
320 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0\) |
|
321 |
\(\left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y = 0\) |
|
322 |
\(\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\) |
|
325 |
\(x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0\) |
|
326 |
\(2 x y^{\prime \prime }-y^{\prime }+2 y = 0\) |
|
327 |
\(2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0\) |
|
328 |
\(2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y = 0\) |
|
329 |
\(x y^{\prime \prime }+2 y^{\prime }-x y = 0\) |
|
330 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
331 |
\(x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0\) |
|
332 |
\(x^{4} y^{\prime \prime }+\lambda y = 0\) |
|
333 |
\(4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y = 0\) |
|
334 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y = 0\) |
|
335 |
\(x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0\) |
|
336 |
\(x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0\) |
|
337 |
\(x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y = 0\) |
|
338 |
\(16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y = 0\) |
|
339 |
\(y^{\prime \prime }-x^{2} y^{\prime }+x y = 0\) |
|
340 |
\(x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0\) |
|
341 |
\(y^{\prime \prime }+y^{\prime } x +2 y = 0\) |
|
342 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\) |
|
343 |
\(y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0\) |
|
344 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y = 0\) |
|
345 |
\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\) |
|
346 |
\(x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0\) |
|
347 |
\(2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0\) |
|
348 |
\(x y^{\prime \prime }+2 y^{\prime }+4 x y = 0\) |
|
349 |
\(x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (x -2\right ) y = 0\) |
|
350 |
\(x^{2} y^{\prime \prime }+6 y^{\prime } x +\left (4 x^{2}+6\right ) y = 0\) |
|
351 |
\(x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0\) |
|
352 |
\(x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y = 0\) |
|
353 |
\(4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y = 0\) |
|
354 |
\(2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (-3+2 t \right ) y^{\prime }-8 y = 0\) |
|
355 |
\(3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0\) |
|
356 |
\(x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0\) |
|
357 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (x^{2}-1\right ) y}{4} = 0\) |
|
358 |
\(x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0\) |
|
359 |
\(x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0\) |
|
360 |
\(x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0\) |
|
361 |
\(x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0\) |
|
362 |
\(2 x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-y = 0\) |
|
363 |
\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\) |
|
364 |
\(y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y = 0\) |
|
365 |
\(u^{\prime \prime }+\frac {u}{x^{2}} = 0\) |
|
366 |
\(u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u = 0\) |
|
367 |
\(y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0\) |
|
368 |
\(x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0\) |
|
369 |
\(y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}} = 0\) |
|
370 |
\(y^{\prime \prime }+\frac {y}{2 x^{4}} = 0\) |
|
371 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
372 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
373 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
374 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
375 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
376 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
377 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
378 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
379 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
380 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
381 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
382 |
\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\) |
|
383 |
\(2 x^{2} y^{\prime \prime }+3 y^{\prime } x -x y = 0\) |
|
384 |
\(x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0\) |
|
385 |
\(2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0\) |
|
388 |
\(x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y = 0\) |
|
389 |
\(x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4+x \right ) y = 0\) |
|
390 |
\(2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0\) |
|
391 |
\(x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y = 0\) |
|
392 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
394 |
\(x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y = 0\) |
|
395 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
396 |
\(x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y = 0\) |
|
398 |
\(y^{\prime \prime } = \left (x^{2}+3\right ) y\) |
|
399 |
\(y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}+1\right ) y = 0\) |
|
400 |
\(x^{3} y^{\prime \prime }+y^{\prime }-\frac {y}{x} = 0\) |
|
401 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
402 |
\(4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0\) |
|
404 |
\(y^{\prime \prime }-y^{\prime }+y = 0\) |
|
405 |
\(\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\) |
|
406 |
\(x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0\) |
|
407 |
\(\left (x +1\right ) y^{\prime \prime }-\left (x +2\right ) y^{\prime }+y = 0\) |
|
408 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0\) |
|
409 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\) |
|
410 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
411 |
\(\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y = 0\) |
|
412 |
\(\left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y = 0\) |
|
413 |
\(\left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y = 0\) |
|
414 |
\(3 y^{\prime \prime }+y^{\prime } x -4 y = 0\) |
|
415 |
\(5 y^{\prime \prime }-2 y^{\prime } x +10 y = 0\) |
|
416 |
\(y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0\) |
|
417 |
\(\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0\) |
|
418 |
\(y^{\prime \prime }+y^{\prime } x -2 y = 0\) |
|
419 |
\(\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0\) |
|
420 |
\(\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0\) |
|
421 |
\(t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y = 0\) |
|
422 |
\(t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0\) |
|
423 |
\(\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\) |
|
424 |
\(x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0\) |
|
425 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
426 |
\(t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0\) |
|
427 |
\(t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0\) |
|
428 |
\(\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 0\) |
|
429 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
430 |
\(t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0\) |
|
431 |
\(\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 0\) |
|
432 |
\(y^{\prime \prime }+y^{\prime } x +2 y = 0\) |
|
433 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y = 0\) |
|
434 |
\(\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = 0\) |
|
435 |
\(2 y^{\prime \prime }+y^{\prime } x +3 y = 0\) |
|
436 |
\(y^{\prime \prime }+y^{\prime } x +2 y = 0\) |
|
437 |
\(\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = 0\) |
|
438 |
\(y^{\prime \prime }+y^{\prime } x +2 y = 0\) |
|
439 |
\(\left (-x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x +2 y = 0\) |
|
440 |
\(4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y = 0\) |
|
441 |
\(\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\) |
|
442 |
\(x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0\) |
|
444 |
\(\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0\) |
|
445 |
\(\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = 0\) |
|
446 |
\(4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0\) |
|
447 |
\(y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0\) |
|
448 |
\(x^{2} y^{\prime \prime }+2 x \left (x -1\right ) y^{\prime }+\left (x^{2}-2 x +2\right ) y = 0\) |
|
449 |
\(x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y = 0\) |
|
450 |
\(\left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y = 0\) |
|
451 |
\(2 x y^{\prime \prime }+\left (1+4 x \right ) y^{\prime }+\left (2 x +1\right ) y = 0\) |
|
452 |
\(x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0\) |
|
453 |
\(4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y = 0\) |
|
454 |
\(x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (x -2\right ) y = 0\) |
|
455 |
\(x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0\) |
|
456 |
\(x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 0\) |
|
457 |
\(x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0\) |
|
458 |
\(x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (2+4 x \right ) y = 0\) |
|
460 |
\(4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y = 0\) |
|
461 |
\(\left (2 x +1\right ) x y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (x +1\right ) y = 0\) |
|
462 |
\(\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0\) |
|
463 |
\(x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (2+4 x \right ) y = 0\) |
|
464 |
\(\left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }-\left (6 x -8\right ) y = 0\) |
|
465 |
\(\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y = 0\) |
|
466 |
\(4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0\) |
|
467 |
\(y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0\) |
|
468 |
\(\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = 0\) |
|
469 |
\(x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 0\) |
|
470 |
\(x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0\) |
|
472 |
\(4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y = 0\) |
|
473 |
\(4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y = 0\) |
|
474 |
\(x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}-2\right ) y = 0\) |
|
475 |
\(x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0\) |
|
476 |
\(x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y = 0\) |
|
477 |
\(x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y = 0\) |
|
478 |
\(\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\) |
|
479 |
\(4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y = 0\) |
|
480 |
\(\left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }-\left (6 x -8\right ) y = 0\) |
|
481 |
\(\left (x +2\right ) y^{\prime \prime }+y^{\prime } x +3 y = 0\) |
|
482 |
\(x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (4+x \right ) y^{\prime }+\left (2-x \right ) y = 0\) |
|
483 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (4+6 x \right ) y = 0\) |
|
484 |
\(x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y = 0\) |
|
485 |
\(x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y = 0\) |
|
486 |
\(\left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +6 y = 0\) |
|
487 |
\(\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0\) |
|
488 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x +20 y = 0\) |
|
489 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x -12 y = 0\) |
|
490 |
\(\left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y = 0\) |
|
491 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x -4 y = 0\) |
|
492 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x +28 y = 0\) |
|
493 |
\(y^{\prime \prime }+y^{\prime } x +2 y = 0\) |
|
495 |
\(\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y = 0\) |
|
496 |
\(y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y = 0\) |
|
497 |
\(\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0\) |
|
498 |
\(\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y = 0\) |
|
499 |
\(\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y = 0\) |
|
500 |
\(\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0\) |
|
501 |
\(y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0\) |
|
502 |
\(\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0\) |
|
503 |
\(y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y = 0\) |
|
504 |
\(\left (3 x +1\right ) y^{\prime \prime }+y^{\prime } x +2 y = 0\) |
|
505 |
\(\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0\) |
|
506 |
\(\left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y = 0\) |
|
507 |
\(\left (4+x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y = 0\) |
|
508 |
\(\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y = 0\) |
|
509 |
\(x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y = 0\) |
|
510 |
\(\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y = 0\) |
|
511 |
\(\left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (2-x \right ) y = 0\) |
|
512 |
\(y^{\prime \prime }+3 y^{\prime } x +\left (2 x^{2}+4\right ) y = 0\) |
|
513 |
\(\left (2+4 x \right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y = 0\) |
|
514 |
\(y^{\prime \prime }-3 y^{\prime } x +\left (2 x^{2}+5\right ) y = 0\) |
|
515 |
\(2 y^{\prime \prime }+5 y^{\prime } x +\left (2 x^{2}+4\right ) y = 0\) |
|
516 |
\(y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0\) |
|
517 |
\(y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0\) |
|
518 |
\(2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0\) |
|
519 |
\(3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y = 0\) |
|
520 |
\(12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y = 0\) |
|
521 |
\(y^{\prime \prime }+3 y^{\prime }+4 y = 0\) |
|
522 |
\(18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y = 0\) |
|
523 |
\(2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y = 0\) |
|
524 |
\(2 x^{2} y^{\prime \prime }+x \left (x +5\right ) y^{\prime }-\left (2-3 x \right ) y = 0\) |
|
525 |
\(3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y = 0\) |
|
526 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (1-2 x \right ) y = 0\) |
|
527 |
\(3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (3 x +1\right ) y = 0\) |
|
528 |
\(2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (x +1\right ) y = 0\) |
|
529 |
\(x^{2} \left (4+x \right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0\) |
|
530 |
\(2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y = 0\) |
|
531 |
\(6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (x +2\right ) y = 0\) |
|
532 |
\(x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (3+4 x \right ) y = 0\) |
|
533 |
\(2 x^{2} \left (2+3 x \right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y = 0\) |
|
534 |
\(x^{2} \left (x +2\right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y = 0\) |
|
535 |
\(8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0\) |
|
536 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y = 0\) |
|
537 |
\(x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 x y = 0\) |
|
538 |
\(4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y = 0\) |
|
539 |
\(3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y = 0\) |
|
540 |
\(2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y = 0\) |
|
541 |
\(2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y = 0\) |
|
542 |
\(2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y = 0\) |
|
543 |
\(x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 x y = 0\) |
|
544 |
\(2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y = 0\) |
|
545 |
\(9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y = 0\) |
|
546 |
\(6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y = 0\) |
|
547 |
\(9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0\) |
|
548 |
\(4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0\) |
|
549 |
\(8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y = 0\) |
|
550 |
\(2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0\) |
|
551 |
\(6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y = 0\) |
|
552 |
\(28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y = 0\) |
|
553 |
\(8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y = 0\) |
|
554 |
\(4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y = 0\) |
|
555 |
\(3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0\) |
|
556 |
\(4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y = 0\) |
|
557 |
\(x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4+x \right ) y = 0\) |
|
558 |
\(2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0\) |
|
559 |
\(x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0\) |
|
560 |
\(x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y = 0\) |
|
561 |
\(4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y = 0\) |
|
562 |
\(x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y = 0\) |
|
563 |
\(9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y = 0\) |
|
564 |
\(x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y = 0\) |
|
565 |
\(16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y = 0\) |
|
566 |
\(9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y = 0\) |
|
567 |
\(36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y = 0\) |
|
568 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3-x \right ) y^{\prime }+4 y = 0\) |
|
569 |
\(x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y = 0\) |
|
570 |
\(2 x^{2} \left (x +2\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y = 0\) |
|
571 |
\(2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y = 0\) |
|
572 |
\(x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y = 0\) |
|
573 |
\(x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0\) |
|
574 |
\(x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y = 0\) |
|
575 |
\(x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0\) |
|
576 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y = 0\) |
|
577 |
\(4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0\) |
|
578 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y = 0\) |
|
579 |
\(2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0\) |
|
580 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y = 0\) |
|
581 |
\(4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0\) |
|
582 |
\(3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0\) |
|
583 |
\(9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y = 0\) |
|
584 |
\(x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0\) |
|
585 |
\(x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (1+4 x \right ) y = 0\) |
|
586 |
\(x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0\) |
|
587 |
\(x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y = 0\) |
|
588 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y = 0\) |
|
589 |
\(9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0\) |
|
590 |
\(x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 x y = 0\) |
|
591 |
\(4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0\) |
|
592 |
\(4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y = 0\) |
|
593 |
\(9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (3+4 x \right ) y = 0\) |
|
594 |
\(x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y = 0\) |
|
595 |
\(16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y = 0\) |
|
596 |
\(x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (4-3 x \right ) y^{\prime }+4 y = 0\) |
|
597 |
\(4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y = 0\) |
|
598 |
\(x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0\) |
|
599 |
\(9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y = 0\) |
|
600 |
\(2 x^{2} \left (x +2\right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y = 0\) |
|
601 |
\(x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0\) |
|
602 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y = 0\) |
|
603 |
\(x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 y x^{2} = 0\) |
|
604 |
\(4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (3 x +1\right ) y = 0\) |
|
605 |
\(2 x^{2} \left (2+3 x \right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y = 0\) |
|
606 |
\(x^{2} y^{\prime \prime }+x \left (x +2\right ) y^{\prime }-\left (2-3 x \right ) y = 0\) |
|
607 |
\(4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y = 0\) |
|
608 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 x y = 0\) |
|
609 |
\(x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y = 0\) |
|
610 |
\(x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y = 0\) |
|
611 |
\(4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y = 0\) |
|
612 |
\(3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y = 0\) |
|
613 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y = 0\) |
|
614 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y = 0\) |
|
615 |
\(x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y = 0\) |
|
616 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y = 0\) |
|
617 |
\(4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y = 0\) |
|
618 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y = 0\) |
|
619 |
\(x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y = 0\) |
|
620 |
\(x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y = 0\) |
|
621 |
\(x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y = 0\) |
|
622 |
\(x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y = 0\) |
|
623 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 y x^{2} = 0\) |
|
624 |
\(4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y = 0\) |
|
625 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y = 0\) |
|
626 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y = 0\) |
|
627 |
\(4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y = 0\) |
|
628 |
\(y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0\) |
|
629 |
\(y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0\) |
|
630 |
\(\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0\) |
|
631 |
\(\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0\) |
|
632 |
\(\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0\) |
|
633 |
\(\left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0\) |
|
634 |
\(t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0\) |
|
635 |
\(y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = 0\) |
|
636 |
\(y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y = 0\) |
|
638 |
\(2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y = 0\) |
|
639 |
\(2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y = 0\) |
|
640 |
\(2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y = 0\) |
|
641 |
\(2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y = 0\) |
|
642 |
\(t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y = 0\) |
|
643 |
\(t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y = 0\) |
|
644 |
\(t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y = 0\) |
|
645 |
\(t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y = 0\) |
|
646 |
\(t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0\) |
|
647 |
\(t y^{\prime \prime }+t y^{\prime }+2 y = 0\) |
|
648 |
\(t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0\) |
|
649 |
\(t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y = 0\) |
|
650 |
\(y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+6\right ) y = 0\) |
|
651 |
\(\left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+y = 0\) |
|
652 |
\(4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y = 0\) |
|
653 |
\(f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f = 0\) |
|
654 |
\(z y^{\prime \prime }-2 y^{\prime }+y z = 0\) |
|
655 |
\(z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z} = 0\) |
|
656 |
\(x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0\) |
|
657 |
\(x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0\) |
|
658 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\) |
|
659 |
\(4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-1\right ) y = 0\) |
|
660 |
\(x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y = 0\) |
|
661 |
\(y^{\prime \prime }+2 y^{\prime } x +4 y = 0\) |
|
662 |
\(y^{\prime \prime }+y^{\prime } x +3 y = 0\) |
|
663 |
\(y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0\) |
|
664 |
\(\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 y^{\prime } x -16 y = 0\) |
|
665 |
\(\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y = 0\) |
|
666 |
\(y^{\prime \prime }+y^{\prime } x +\left (x +2\right ) y = 0\) |
|
667 |
\(\left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y = 0\) |
|
668 |
\(4 y^{\prime \prime }+y^{\prime } x +4 y = 0\) |
|
669 |
\(y^{\prime \prime }+y^{\prime } x -4 y = 0\) |
|
670 |
\(4 x y^{\prime \prime }-y^{\prime } x +2 y = 0\) |
|
671 |
\(6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y = 0\) |
|
672 |
\(3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y = 0\) |
|
673 |
\(2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y = 0\) |
|
674 |
\(4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y = 0\) |
|
675 |
\(x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y = 0\) |
|
676 |
\(x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y = 0\) |
|
677 |
\(x^{2} y^{\prime \prime }+x \left (3-x \right ) y^{\prime }+y = 0\) |
|
678 |
\(x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0\) |
|
679 |
\(x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y = 0\) |
|
680 |
\(x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y = 0\) |
|
681 |
\(x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y = 0\) |
|
682 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0\) |
|
683 |
\(x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y = 0\) |
|
684 |
\(x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0\) |
|
685 |
\(x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y = 0\) |
|
686 |
\(x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y = 0\) |
|
687 |
\(x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (2+3 x \right ) y = 0\) |
|
688 |
\(x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y = 0\) |
|
689 |
\(4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y = 0\) |
|
690 |
\(x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (x +1\right ) y = 0\) |
|
691 |
\(x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y = 0\) |
|
692 |
\(4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y = 0\) |
|
693 |
\(x^{2} y^{\prime \prime }+x \left (4+x \right ) y^{\prime }+\left (x +2\right ) y = 0\) |
|
694 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y = 0\) |
|
695 |
\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\) |
|
696 |
\(2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0\) |
|
697 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
698 |
\(x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y = 0\) |
|
699 |
\(x^{4} y^{\prime \prime }+y^{\prime } x +y = 0\) |
|
700 |
\(x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y = 0\) |
|
701 |
\(\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y = 0\) |
|
702 |
\(x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y = 0\) |
|
703 |
\(x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y = 0\) |
|
704 |
\(x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (-\frac {1}{4} x -x^{2}\right ) y^{\prime }-\frac {5 x y}{16} = 0\) |
|
705 |
\(x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y = 0\) |
|
706 |
\(x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y = 0\) |
|
707 |
\(x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y = 0\) |
|
708 |
\(2 x^{2} y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x} = 0\) |
|
709 |
\(x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4} = 0\) |
|
710 |
\(2 x \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = 0\) |
|
711 |
\(2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y = 0\) |
|
712 |
\(x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9} = 0\) |
|
713 |
\(4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}} = 0\) |
|
714 |
\(u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0\) |
|
715 |
\(u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0\) |
|
716 |
\(u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0\) |
|
717 |
\(u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0\) |
|
718 |
\(u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0\) |
|
719 |
\(y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}}\) |
|
720 |
\(y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}}\) |
|
721 |
\(x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+\frac {1}{4}\right ) y = 0\) |
|
722 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0\) |
|
723 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {25}{4}\right ) y = 0\) |
|
724 |
\(y^{\prime \prime }+q y^{\prime } = \frac {2 y}{x^{2}}\) |
|
725 |
\(x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0\) |
|
726 |
\(\left (2-x \right ) x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y = 0\) |
|
727 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\) |
|
728 |
\(x y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+\left (x +2\right ) y = 0\) |
|
729 |
\(3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y = 0\) |
|
730 |
\(x \left (x +1\right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y = 0\) |
|
731 |
\(\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0\) |
|
732 |
\(\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0\) |
|
733 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\) |
|
734 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\) |
|
735 |
\(y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0\) |
|
736 |
\(y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0\) |
|
737 |
\(\left (2 x -3\right ) y^{\prime \prime }-y^{\prime } x +y = 0\) |
|
738 |
\(y^{\prime \prime }-y^{\prime } x -3 y = 0\) |
|
739 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\) |
|
740 |
\(y^{\prime \prime }-y^{\prime } x +2 y = 0\) |
|
741 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = 0\) |
|
742 |
\(x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (x -1\right ) y = 0\) |
|
743 |
\(2 x y^{\prime \prime }-y^{\prime }+2 y = 0\) |
|
744 |
\(x y^{\prime \prime }+y^{\prime } x -2 y = 0\) |
|
745 |
\(x \left (x -1\right )^{2} y^{\prime \prime }-2 y = 0\) |
|
746 |
\(y^{\prime \prime }-2 y^{\prime } x +y x^{2} = 0\) |
|
747 |
\(x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right ) = 0\) |
|
748 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+y^{\prime } x \right ) = 0\) |
|
749 |
\(2 \left (2-x \right ) x^{2} y^{\prime \prime }-x \left (4-x \right ) y^{\prime }+\left (3-x \right ) y = 0\) |
|
750 |
\(x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0\) |
|
751 |
\(x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0\) |
|
754 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y = 0\) |
|
755 |
\(x \left (x +2\right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y = 0\) |
|
757 |
\(x \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y = 0\) |
|
758 |
\(\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\) |
|
759 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\) |
|
760 |
\(\left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y = 0\) |
|
761 |
\(\left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y = 0\) |
|
762 |
\(y^{\prime \prime }-y^{\prime } x +2 y = 0\) |
|
763 |
\(\left (x +2\right ) y^{\prime \prime }+y^{\prime } x -y = 0\) |
|
764 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0\) |
|
765 |
\(\left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y = 0\) |
|
766 |
\(\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\) |
|
769 |
\(x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0\) |
|
770 |
\(2 x y^{\prime \prime }-y^{\prime }+2 y = 0\) |
|
771 |
\(2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0\) |
|
772 |
\(2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y = 0\) |
|
773 |
\(x y^{\prime \prime }+2 y^{\prime }-x y = 0\) |
|
774 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
775 |
\(x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0\) |
|
776 |
\(x^{4} y^{\prime \prime }+\lambda y = 0\) |
|
777 |
\(4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y = 0\) |
|
778 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y = 0\) |
|
779 |
\(x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0\) |
|
780 |
\(x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0\) |
|
781 |
\(x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y = 0\) |
|
782 |
\(16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y = 0\) |
|
783 |
\(y^{\prime \prime }-x^{2} y^{\prime }+x y = 0\) |
|
784 |
\(x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0\) |
|
785 |
\(y^{\prime \prime }+y^{\prime } x +2 y = 0\) |
|
786 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\) |
|
787 |
\(y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0\) |
|
788 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y = 0\) |
|
789 |
\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\) |
|
790 |
\(x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0\) |
|
791 |
\(2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0\) |
|
792 |
\(x y^{\prime \prime }+2 y^{\prime }+4 x y = 0\) |
|
793 |
\(x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (x -2\right ) y = 0\) |
|
794 |
\(x^{2} y^{\prime \prime }+6 y^{\prime } x +\left (4 x^{2}+6\right ) y = 0\) |
|
795 |
\(x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0\) |
|
796 |
\(x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y = 0\) |
|
797 |
\(4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y = 0\) |
|
798 |
\(2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (-3+2 t \right ) y^{\prime }-8 y = 0\) |
|
799 |
\(3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0\) |
|
800 |
\(x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0\) |
|
801 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (x^{2}-1\right ) y}{4} = 0\) |
|
802 |
\(x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0\) |
|
803 |
\(x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0\) |
|
804 |
\(x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0\) |
|
805 |
\(x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0\) |
|
806 |
\(2 x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-y = 0\) |
|
807 |
\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\) |
|
808 |
\(y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y = 0\) |
|
809 |
\(u^{\prime \prime }+2 u^{\prime }+u = 0\) |
|
810 |
\(u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u = 0\) |
|
811 |
\(y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0\) |
|
812 |
\(x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0\) |
|
813 |
\(y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}} = 0\) |
|
815 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
816 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
817 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
818 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
819 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
820 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
821 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
822 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
823 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
824 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
825 |
\(y^{\prime \prime }-y^{\prime } x -x y = 0\) |
|
826 |
\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\) |
|
827 |
\(2 x^{2} y^{\prime \prime }+3 y^{\prime } x -x y = 0\) |
|
828 |
\(x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0\) |
|
829 |
\(2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0\) |
|
830 |
\(x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y = 0\) |
|
831 |
\(x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4+x \right ) y = 0\) |
|
832 |
\(2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0\) |
|
833 |
\(x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y = 0\) |
|
834 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
835 |
\(x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y = 0\) |
|
836 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
837 |
\(x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y = 0\) |
|
838 |
\(y^{\prime \prime } = \left (x^{2}+3\right ) y\) |
|
839 |
\(y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}+1\right ) y = 0\) |
|
840 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
841 |
\(4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0\) |
|
843 |
\(y^{\prime \prime } = 0\) |
|
844 |
\(y^{\prime \prime } = \frac {2 y}{x^{2}}\) |
|
845 |
\(y^{\prime \prime } = \frac {6 y}{x^{2}}\) |
|