|
ID |
problem |
ODE |
|
1 |
\(\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0\) |
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2 |
\(\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0\) |
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3 |
\(\left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y = 0\) |
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4 |
\(\left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0\) |
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5 |
\(3 y^{\prime \prime }+x y^{\prime }-4 y = 0\) |
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6 |
\(5 y^{\prime \prime }-2 x y^{\prime }+10 y = 0\) |
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7 |
\(y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0\) |
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8 |
\(\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0\) |
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9 |
\(y^{\prime \prime }+x y^{\prime }-2 y = 0\) |
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10 |
\(\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0\) |
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11 |
\(\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0\) |
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12 |
\(t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{2} y = 0\) |
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13 |
\(t^{2} y^{\prime \prime }-t \left (2+t \right ) y^{\prime }+\left (2+t \right ) y = 0\) |
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14 |
\(t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0\) |
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15 |
\(\left (-t +1\right ) y^{\prime \prime }+y^{\prime } t -y = 0\) |
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16 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
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17 |
\(t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0\) |
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18 |
\(\left (-t +1\right ) y^{\prime \prime }+y^{\prime } t -y = 0\) |
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19 |
\(y^{\prime \prime }+x y^{\prime }+2 y = 0\) |
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20 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y = 0\) |
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21 |
\(\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0\) |
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22 |
\(2 y^{\prime \prime }+x y^{\prime }+3 y = 0\) |
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23 |
\(y^{\prime \prime }+x y^{\prime }+2 y = 0\) |
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24 |
\(\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0\) |
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25 |
\(y^{\prime \prime }+x y^{\prime }+2 y = 0\) |
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26 |
\(\left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0\) |
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27 |
\(4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0\) |
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28 |
\(\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0\) |
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29 |
\(x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0\) |
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31 |
\(\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0\) |
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32 |
\(4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0\) |
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33 |
\(y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0\) |
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34 |
\(\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = 0\) |
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35 |
\(x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 0\) |
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36 |
\(x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0\) |
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38 |
\(4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0\) |
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39 |
\(4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y = 0\) |
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40 |
\(x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y = 0\) |
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41 |
\(x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0\) |
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42 |
\(x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y = 0\) |
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43 |
\(x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = 0\) |
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44 |
\(\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0\) |
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45 |
\(4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y = 0\) |
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46 |
\(\left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }-\left (6 x -8\right ) y = 0\) |
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47 |
\(\left (x +2\right ) y^{\prime \prime }+x y^{\prime }+3 y = 0\) |
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48 |
\(x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2-x \right ) y = 0\) |
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49 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (4+6 x \right ) y = 0\) |
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50 |
\(x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y = 0\) |
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51 |
\(x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y = 0\) |
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52 |
\(\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+6 y = 0\) |
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53 |
\(\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0\) |
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54 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y = 0\) |
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55 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y = 0\) |
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56 |
\(\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0\) |
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57 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }-4 y = 0\) |
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58 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y = 0\) |
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59 |
\(y^{\prime \prime }+x y^{\prime }+2 y = 0\) |
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60 |
\(\left (2 x^{2}+1\right ) y^{\prime \prime }-9 x y^{\prime }-6 y = 0\) |
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61 |
\(\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y = 0\) |
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62 |
\(y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y = 0\) |
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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 |
\(\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0\) |
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|
67 |
\(y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0\) |
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|
68 |
\(\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0\) |
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|
69 |
\(y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y = 0\) |
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|
70 |
\(\left (3 x +1\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0\) |
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71 |
\(\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0\) |
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|
72 |
\(\left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y = 0\) |
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73 |
\(\left (x +4\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y = 0\) |
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|
74 |
\(\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y = 0\) |
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|
75 |
\(x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y = 0\) |
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76 |
\(\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y = 0\) |
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77 |
\(\left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (2-x \right ) y = 0\) |
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|
78 |
\(y^{\prime \prime }+3 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0\) |
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|
79 |
\(\left (2+4 x \right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y = 0\) |
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80 |
\(y^{\prime \prime }-3 x y^{\prime }+\left (2 x^{2}+5\right ) y = 0\) |
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81 |
\(2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0\) |
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82 |
\(y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0\) |
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83 |
\(y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0\) |
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84 |
\(2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0\) |
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85 |
\(3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y = 0\) |
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86 |
\(12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y = 0\) |
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|
87 |
\(x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y = 0\) |
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|
88 |
\(18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y = 0\) |
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89 |
\(2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y = 0\) |
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90 |
\(2 x^{2} y^{\prime \prime }+x \left (x +5\right ) y^{\prime }-\left (2-3 x \right ) y = 0\) |
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91 |
\(3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y = 0\) |
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92 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-2 x +1\right ) y = 0\) |
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93 |
\(3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (3 x +1\right ) y = 0\) |
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94 |
\(2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (x +1\right ) y = 0\) |
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95 |
\(x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0\) |
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96 |
\(2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (x +1\right ) y = 0\) |
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97 |
\(6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (x +2\right ) y = 0\) |
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98 |
\(x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (3+4 x \right ) y = 0\) |
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99 |
\(2 x^{2} \left (2+3 x \right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y = 0\) |
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100 |
\(x^{2} \left (x +2\right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y = 0\) |
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101 |
\(8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0\) |
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102 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y = 0\) |
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103 |
\(x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 x y = 0\) |
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104 |
\(4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y = 0\) |
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105 |
\(3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y = 0\) |
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106 |
\(2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y = 0\) |
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107 |
\(2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y = 0\) |
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108 |
\(2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y = 0\) |
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109 |
\(x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 x y = 0\) |
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110 |
\(2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y = 0\) |
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111 |
\(9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y = 0\) |
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112 |
\(6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y = 0\) |
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113 |
\(9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0\) |
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114 |
\(4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0\) |
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115 |
\(8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y = 0\) |
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116 |
\(2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0\) |
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117 |
\(6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y = 0\) |
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118 |
\(28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y = 0\) |
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119 |
\(8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y = 0\) |
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120 |
\(4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y = 0\) |
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121 |
\(3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0\) |
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122 |
\(4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y = 0\) |
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123 |
\(x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0\) |
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124 |
\(2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0\) |
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125 |
\(x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0\) |
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126 |
\(x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y = 0\) |
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127 |
\(4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y = 0\) |
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128 |
\(x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y = 0\) |
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129 |
\(9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y = 0\) |
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130 |
\(x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y = 0\) |
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131 |
\(16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y = 0\) |
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132 |
\(9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y = 0\) |
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133 |
\(36 x^{2} \left (-2 x +1\right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y = 0\) |
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134 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3-x \right ) y^{\prime }+4 y = 0\) |
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135 |
\(x^{2} \left (-2 x +1\right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y = 0\) |
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136 |
\(2 x^{2} \left (x +2\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y = 0\) |
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137 |
\(2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y = 0\) |
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138 |
\(x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y = 0\) |
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139 |
\(x^{2} \left (-2 x +1\right ) y^{\prime \prime }-x \left (4 x +5\right ) y^{\prime }+\left (9+4 x \right ) y = 0\) |
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140 |
\(x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y = 0\) |
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141 |
\(x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0\) |
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142 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y = 0\) |
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143 |
\(4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0\) |
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144 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y = 0\) |
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145 |
\(2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0\) |
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146 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y = 0\) |
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147 |
\(4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0\) |
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148 |
\(3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0\) |
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149 |
\(9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y = 0\) |
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150 |
\(x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0\) |
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151 |
\(x^{2} \left (-2 x +1\right ) y^{\prime \prime }+3 x y^{\prime }+\left (4 x +1\right ) y = 0\) |
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152 |
\(x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0\) |
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|
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 |
\(x^{2} \left (-2 x +1\right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0\) |
|
|
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 |
\(x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y = 0\) |
|
|
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 |
\(4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (4 x +1\right ) y^{\prime }-\left (49+27 x \right ) y = 0\) |
|
|
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 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y = 0\) |
|
|
190 |
\(4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y = 0\) |
|
|
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 |
\(y^{\prime \prime }-4 y^{\prime } t +\left (4 t^{2}-2\right ) y = 0\) |
|
|
196 |
\(\left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y = 0\) |
|
|
197 |
\(\left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y = 0\) |
|
|
198 |
\(\left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +6 y = 0\) |
|
|
199 |
\(\left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0\) |
|
|
200 |
\(t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-\frac {1}{4}\right ) y = 0\) |
|
|
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 |
\(2 t^{2} y^{\prime \prime }-y^{\prime } t +\left (t +1\right ) y = 0\) |
|
|
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 |
\(t y^{\prime \prime }-\left (4+t \right ) y^{\prime }+2 y = 0\) |
|
|
212 |
\(t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0\) |
|
|
213 |
\(t y^{\prime \prime }+y^{\prime } t +2 y = 0\) |
|
|
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 |
\(y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0\) |
|
|
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 |
\(y^{\prime \prime }+2 x y^{\prime }+4 y = 0\) |
|
|
223 |
\(y^{\prime \prime }+x y^{\prime }+3 y = 0\) |
|
|
224 |
\(y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0\) |
|
|
225 |
\(\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y = 0\) |
|
|
226 |
\(\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0\) |
|
|
227 |
\(y^{\prime \prime }+x y^{\prime }+\left (x +2\right ) y = 0\) |
|
|
228 |
\(\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0\) |
|
|
229 |
\(4 y^{\prime \prime }+x y^{\prime }+4 y = 0\) |
|
|
230 |
\(y^{\prime \prime }+x y^{\prime }-4 y = 0\) |
|
|
231 |
\(4 x y^{\prime \prime }-x y^{\prime }+2 y = 0\) |
|
|
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 |
\(x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (-2 x +1\right ) y = 0\) |
|
|
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 |
\(x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (x +2\right ) y = 0\) |
|
|
255 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y = 0\) |
|
|
256 |
\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\) |
|
|
257 |
\(2 x y^{\prime \prime }+5 \left (-2 x +1\right ) y^{\prime }-5 y = 0\) |
|
|
258 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
|
259 |
\(x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y = 0\) |
|
|
260 |
\(x^{4} y^{\prime \prime }+x y^{\prime }+y = 0\) |
|
|
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 |
\(x^{2} \left (1-4 x \right ) y^{\prime \prime }-\frac {x y^{\prime }}{2}-\frac {3 x y}{4} = 0\) |
|
|
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 |
\(2 x \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0\) |
|
|
272 |
\(2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y = 0\) |
|
|
273 |
\(x \left (1-x \right ) y^{\prime \prime }+\frac {\left (-2 x +1\right ) y^{\prime }}{3}+\frac {20 y}{9} = 0\) |
|
|
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 |
\(x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y = 0\) |
|
|
283 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0\) |
|
|
284 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0\) |
|
|
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 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0\) |
|
|
290 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0\) |
|
|
291 |
\(y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0\) |
|
|
292 |
\(y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0\) |
|
|
293 |
\(\left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y = 0\) |
|
|
294 |
\(y^{\prime \prime }-x y^{\prime }-3 y = 0\) |
|
|
295 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0\) |
|
|
296 |
\(y^{\prime \prime }-x y^{\prime }+2 y = 0\) |
|
|
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 |
\(x y^{\prime \prime }+x y^{\prime }-2 y = 0\) |
|
|
301 |
\(x \left (x -1\right )^{2} y^{\prime \prime }-2 y = 0\) |
|
|
302 |
\(y^{\prime \prime }-2 x y^{\prime }+x^{2} y = 0\) |
|
|
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 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+x y^{\prime }\right ) = 0\) |
|
|
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 |
\(y^{\prime \prime }-2 x y^{\prime }+8 y = 0\) |
|
|
310 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0\) |
|
|
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 |
\(\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0\) |
|
|
315 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0\) |
|
|
316 |
\(\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0\) |
|
|
317 |
\(\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0\) |
|
|
318 |
\(y^{\prime \prime }-x y^{\prime }+2 y = 0\) |
|
|
319 |
\(\left (x +2\right ) y^{\prime \prime }+x y^{\prime }-y = 0\) |
|
|
320 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0\) |
|
|
321 |
\(\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y = 0\) |
|
|
322 |
\(\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0\) |
|
|
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 |
\(2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y = 0\) |
|
|
329 |
\(x y^{\prime \prime }+2 y^{\prime }-x y = 0\) |
|
|
330 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
|
331 |
\(x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0\) |
|
|
332 |
\(x^{4} y^{\prime \prime }+\lambda y = 0\) |
|
|
333 |
\(4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0\) |
|
|
334 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0\) |
|
|
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 |
\(x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0\) |
|
|
338 |
\(16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0\) |
|
|
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 |
\(y^{\prime \prime }+x y^{\prime }+2 y = 0\) |
|
|
342 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0\) |
|
|
343 |
\(y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0\) |
|
|
344 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0\) |
|
|
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 |
\(x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0\) |
|
|
351 |
\(x y^{\prime \prime }+\left (-2 x +1\right ) y^{\prime }+\left (x -1\right ) y = 0\) |
|
|
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 |
\(2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0\) |
|
|
355 |
\(3 t \left (t +1\right ) y^{\prime \prime }+y^{\prime } t -y = 0\) |
|
|
356 |
\(x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0\) |
|
|
357 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4} = 0\) |
|
|
358 |
\(x y^{\prime \prime }+\left (-2 x +1\right ) y^{\prime }+\left (x -1\right ) y = 0\) |
|
|
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 |
\(x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0\) |
|
|
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 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
372 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
373 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
374 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
375 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
376 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
377 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
378 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
379 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
380 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
381 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
382 |
\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\) |
|
|
383 |
\(2 x^{2} y^{\prime \prime }+3 x y^{\prime }-x y = 0\) |
|
|
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 |
\(x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0\) |
|
|
390 |
\(2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0\) |
|
|
391 |
\(x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0\) |
|
|
392 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
|
394 |
\(x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y = 0\) |
|
|
395 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
|
396 |
\(x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y = 0\) |
|
|
398 |
\(y^{\prime \prime } = \left (x^{2}+3\right ) y\) |
|
|
399 |
\(y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0\) |
|
|
400 |
\(x^{3} y^{\prime \prime }+y^{\prime }-\frac {y}{x} = 0\) |
|
|
401 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
|
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 |
\(\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0\) |
|
|
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 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0\) |
|
|
409 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0\) |
|
|
410 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
|
411 |
\(\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0\) |
|
|
412 |
\(\left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y = 0\) |
|
|
413 |
\(\left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0\) |
|
|
414 |
\(3 y^{\prime \prime }+x y^{\prime }-4 y = 0\) |
|
|
415 |
\(5 y^{\prime \prime }-2 x y^{\prime }+10 y = 0\) |
|
|
416 |
\(y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0\) |
|
|
417 |
\(\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0\) |
|
|
418 |
\(y^{\prime \prime }+x y^{\prime }-2 y = 0\) |
|
|
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 |
\(t^{2} y^{\prime \prime }-t \left (2+t \right ) y^{\prime }+\left (2+t \right ) y = 0\) |
|
|
423 |
\(\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0\) |
|
|
424 |
\(x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0\) |
|
|
425 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
|
426 |
\(t^{2} y^{\prime \prime }-t \left (2+t \right ) y^{\prime }+\left (2+t \right ) y = 0\) |
|
|
427 |
\(t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0\) |
|
|
428 |
\(\left (-t +1\right ) y^{\prime \prime }+y^{\prime } t -y = 0\) |
|
|
429 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
|
430 |
\(t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0\) |
|
|
431 |
\(\left (-t +1\right ) y^{\prime \prime }+y^{\prime } t -y = 0\) |
|
|
432 |
\(y^{\prime \prime }+x y^{\prime }+2 y = 0\) |
|
|
433 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y = 0\) |
|
|
434 |
\(\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0\) |
|
|
435 |
\(2 y^{\prime \prime }+x y^{\prime }+3 y = 0\) |
|
|
436 |
\(y^{\prime \prime }+x y^{\prime }+2 y = 0\) |
|
|
437 |
\(\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0\) |
|
|
438 |
\(y^{\prime \prime }+x y^{\prime }+2 y = 0\) |
|
|
439 |
\(\left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0\) |
|
|
440 |
\(4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0\) |
|
|
441 |
\(\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0\) |
|
|
442 |
\(x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0\) |
|
|
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 |
\(y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0\) |
|
|
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 |
\(\left (-2 x +1\right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y = 0\) |
|
|
451 |
\(2 x y^{\prime \prime }+\left (4 x +1\right ) y^{\prime }+\left (2 x +1\right ) y = 0\) |
|
|
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 |
\(x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0\) |
|
|
456 |
\(x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 0\) |
|
|
457 |
\(x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0\) |
|
|
458 |
\(x y^{\prime \prime }-\left (4 x +1\right ) y^{\prime }+\left (2+4 x \right ) y = 0\) |
|
|
460 |
\(4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0\) |
|
|
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 |
\(x y^{\prime \prime }-\left (4 x +1\right ) y^{\prime }+\left (2+4 x \right ) y = 0\) |
|
|
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 |
\(y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0\) |
|
|
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 |
\(x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0\) |
|
|
472 |
\(4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0\) |
|
|
473 |
\(4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y = 0\) |
|
|
474 |
\(x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y = 0\) |
|
|
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 |
\(x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = 0\) |
|
|
478 |
\(\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0\) |
|
|
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 |
\(\left (x +2\right ) y^{\prime \prime }+x y^{\prime }+3 y = 0\) |
|
|
482 |
\(x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2-x \right ) y = 0\) |
|
|
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 |
\(\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+6 y = 0\) |
|
|
487 |
\(\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0\) |
|
|
488 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y = 0\) |
|
|
489 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y = 0\) |
|
|
490 |
\(\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0\) |
|
|
491 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }-4 y = 0\) |
|
|
492 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y = 0\) |
|
|
493 |
\(y^{\prime \prime }+x y^{\prime }+2 y = 0\) |
|
|
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 |
\(\left (3 x +1\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0\) |
|
|
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 |
\(\left (x +4\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y = 0\) |
|
|
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 |
\(y^{\prime \prime }+3 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0\) |
|
|
513 |
\(\left (2+4 x \right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y = 0\) |
|
|
514 |
\(y^{\prime \prime }-3 x y^{\prime }+\left (2 x^{2}+5\right ) y = 0\) |
|
|
515 |
\(2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0\) |
|
|
516 |
\(y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0\) |
|
|
517 |
\(y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0\) |
|
|
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 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-2 x +1\right ) y = 0\) |
|
|
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 |
\(x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0\) |
|
|
530 |
\(2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (x +1\right ) y = 0\) |
|
|
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 |
\(x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0\) |
|
|
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 |
\(36 x^{2} \left (-2 x +1\right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y = 0\) |
|
|
568 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3-x \right ) y^{\prime }+4 y = 0\) |
|
|
569 |
\(x^{2} \left (-2 x +1\right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y = 0\) |
|
|
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 |
\(x^{2} \left (-2 x +1\right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0\) |
|
|
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 |
\(x^{2} \left (-2 x +1\right ) y^{\prime \prime }+3 x y^{\prime }+\left (4 x +1\right ) y = 0\) |
|
|
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 |
\(x^{2} \left (-2 x +1\right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0\) |
|
|
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 |
\(x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y = 0\) |
|
|
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 |
\(4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (4 x +1\right ) y^{\prime }-\left (49+27 x \right ) y = 0\) |
|
|
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 |
\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y = 0\) |
|
|
624 |
\(4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y = 0\) |
|
|
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 |
\(y^{\prime \prime }-4 y^{\prime } t +\left (4 t^{2}-2\right ) y = 0\) |
|
|
630 |
\(\left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y = 0\) |
|
|
631 |
\(\left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y = 0\) |
|
|
632 |
\(\left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +6 y = 0\) |
|
|
633 |
\(\left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0\) |
|
|
634 |
\(t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-\frac {1}{4}\right ) y = 0\) |
|
|
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 |
\(2 t^{2} y^{\prime \prime }-y^{\prime } t +\left (t +1\right ) y = 0\) |
|
|
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 |
\(t y^{\prime \prime }-\left (4+t \right ) y^{\prime }+2 y = 0\) |
|
|
646 |
\(t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0\) |
|
|
647 |
\(t y^{\prime \prime }+y^{\prime } t +2 y = 0\) |
|
|
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 |
\(y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0\) |
|
|
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 |
\(x y^{\prime \prime }+\left (-2 x +1\right ) y^{\prime }+\left (x -1\right ) y = 0\) |
|
|
657 |
\(x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0\) |
|
|
658 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0\) |
|
|
659 |
\(4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y = 0\) |
|
|
660 |
\(x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y = 0\) |
|
|
661 |
\(y^{\prime \prime }+2 x y^{\prime }+4 y = 0\) |
|
|
662 |
\(y^{\prime \prime }+x y^{\prime }+3 y = 0\) |
|
|
663 |
\(y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0\) |
|
|
664 |
\(\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y = 0\) |
|
|
665 |
\(\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0\) |
|
|
666 |
\(y^{\prime \prime }+x y^{\prime }+\left (x +2\right ) y = 0\) |
|
|
667 |
\(\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0\) |
|
|
668 |
\(4 y^{\prime \prime }+x y^{\prime }+4 y = 0\) |
|
|
669 |
\(y^{\prime \prime }+x y^{\prime }-4 y = 0\) |
|
|
670 |
\(4 x y^{\prime \prime }-x y^{\prime }+2 y = 0\) |
|
|
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 |
\(x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (-2 x +1\right ) y = 0\) |
|
|
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 |
\(x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (x +2\right ) y = 0\) |
|
|
694 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y = 0\) |
|
|
695 |
\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\) |
|
|
696 |
\(2 x y^{\prime \prime }+5 \left (-2 x +1\right ) y^{\prime }-5 y = 0\) |
|
|
697 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
|
698 |
\(x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y = 0\) |
|
|
699 |
\(x^{4} y^{\prime \prime }+x y^{\prime }+y = 0\) |
|
|
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 |
\(2 x \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0\) |
|
|
711 |
\(2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y = 0\) |
|
|
712 |
\(x \left (1-x \right ) y^{\prime \prime }+\frac {\left (-2 x +1\right ) y^{\prime }}{3}+\frac {20 y}{9} = 0\) |
|
|
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 |
\(x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y = 0\) |
|
|
722 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0\) |
|
|
723 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0\) |
|
|
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 |
\(x^{2} \left (2-x \right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0\) |
|
|
727 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0\) |
|
|
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 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0\) |
|
|
734 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0\) |
|
|
735 |
\(y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0\) |
|
|
736 |
\(y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0\) |
|
|
737 |
\(\left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y = 0\) |
|
|
738 |
\(y^{\prime \prime }-x y^{\prime }-3 y = 0\) |
|
|
739 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0\) |
|
|
740 |
\(y^{\prime \prime }-x y^{\prime }+2 y = 0\) |
|
|
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 |
\(x y^{\prime \prime }+x y^{\prime }-2 y = 0\) |
|
|
745 |
\(x \left (x -1\right )^{2} y^{\prime \prime }-2 y = 0\) |
|
|
746 |
\(y^{\prime \prime }-2 x y^{\prime }+x^{2} y = 0\) |
|
|
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 |
\(x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+x y^{\prime }\right ) = 0\) |
|
|
749 |
\(2 x^{2} \left (2-x \right ) y^{\prime \prime }-x \left (4-x \right ) y^{\prime }+\left (3-x \right ) y = 0\) |
|
|
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 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0\) |
|
|
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 |
\(\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0\) |
|
|
759 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0\) |
|
|
760 |
\(\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0\) |
|
|
761 |
\(\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0\) |
|
|
762 |
\(y^{\prime \prime }-x y^{\prime }+2 y = 0\) |
|
|
763 |
\(\left (x +2\right ) y^{\prime \prime }+x y^{\prime }-y = 0\) |
|
|
764 |
\(\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0\) |
|
|
765 |
\(\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y = 0\) |
|
|
766 |
\(\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0\) |
|
|
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 |
\(2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y = 0\) |
|
|
773 |
\(x y^{\prime \prime }+2 y^{\prime }-x y = 0\) |
|
|
774 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
|
775 |
\(x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0\) |
|
|
776 |
\(x^{4} y^{\prime \prime }+\lambda y = 0\) |
|
|
777 |
\(4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0\) |
|
|
778 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0\) |
|
|
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 |
\(x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0\) |
|
|
782 |
\(16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0\) |
|
|
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 |
\(y^{\prime \prime }+x y^{\prime }+2 y = 0\) |
|
|
786 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0\) |
|
|
787 |
\(y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0\) |
|
|
788 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0\) |
|
|
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 |
\(x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0\) |
|
|
795 |
\(x y^{\prime \prime }+\left (-2 x +1\right ) y^{\prime }+\left (x -1\right ) y = 0\) |
|
|
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 |
\(2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0\) |
|
|
799 |
\(3 t \left (t +1\right ) y^{\prime \prime }+y^{\prime } t -y = 0\) |
|
|
800 |
\(x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0\) |
|
|
801 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4} = 0\) |
|
|
802 |
\(x y^{\prime \prime }+\left (-2 x +1\right ) y^{\prime }+\left (x -1\right ) y = 0\) |
|
|
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 |
\(x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0\) |
|
|
813 |
\(y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}} = 0\) |
|
|
815 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
816 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
817 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
818 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
819 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
820 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
821 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
822 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
823 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
824 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
825 |
\(y^{\prime \prime }-x y^{\prime }-x y = 0\) |
|
|
826 |
\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\) |
|
|
827 |
\(2 x^{2} y^{\prime \prime }+3 x y^{\prime }-x y = 0\) |
|
|
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 |
\(x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0\) |
|
|
832 |
\(2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0\) |
|
|
833 |
\(x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0\) |
|
|
834 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
|
835 |
\(x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y = 0\) |
|
|
836 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
|
837 |
\(x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y = 0\) |
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838 |
\(y^{\prime \prime } = \left (x^{2}+3\right ) y\) |
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839 |
\(y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0\) |
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840 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
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841 |
\(4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0\) |
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843 |
\(y^{\prime \prime } = 0\) |
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844 |
\(y^{\prime \prime } = \frac {2 y}{x^{2}}\) |
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845 |
\(y^{\prime \prime } = \frac {6 y}{x^{2}}\) |
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ID |
problem |
ODE |
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1 |
\(y^{\prime \prime } = \left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (x -1\right )^{2}}+\frac {3}{16 x \left (x -1\right )}\right ) y\) |
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2 |
\(y^{\prime \prime } = \frac {20 y}{x^{2}}\) |
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3 |
\(y^{\prime \prime } = \frac {12 y}{x^{2}}\) |
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4 |
\(y^{\prime \prime }-\frac {y}{4 x^{2}} = 0\) |
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5 |
\(x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 0\) |
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6 |
\(y^{\prime \prime }+\frac {y}{x^{2}} = 0\) |
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7 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y = 0\) |
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8 |
\(\left (x^{2}-x \right ) y^{\prime \prime }-x y^{\prime }+y = 0\) |
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9 |
\(x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0\) |
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|
ID |
problem |
ODE |
|
Kovacic 1985 paper. page 13. section 3.2, example 1 |
\(y^{\prime \prime } = \frac {\left (4 x^{6}-8 x^{5}+12 x^{4}+4 x^{3}+7 x^{2}-20 x +4\right ) y}{4 x^{4}}\) |
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Kovacic 1985 paper. page 14. section 3.2, example 2 |
\(y^{\prime \prime } = \left (\frac {6}{x^{2}}-1\right ) y\) |
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Kovacic 1985 paper. page 15. Weber equation |
\(y^{\prime \prime } = \left (\frac {x^{2}}{4}-\frac {11}{2}\right ) y\) |
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Kovacic 1985 paper. page 19. section 4.2. Example 1 |
\(y^{\prime \prime } = \left (\frac {1}{x}-\frac {3}{16 x^{2}}\right ) y\) |
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Kovacic 1985 paper. page 23. section 5.2. Example 1 |
\(y^{\prime \prime } = \left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (x -1\right )^{2}}+\frac {3}{16 x \left (x -1\right )}\right ) y\) |
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|
Kovacic 1985 paper. page 25. section 5.2. Example 2 |
\(y^{\prime \prime } = -\frac {\left (5 x^{2}+27\right ) y}{36 \left (x^{2}-1\right )^{2}}\) |
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Kovacic 2005 paper. Example 2 |
\(y^{\prime \prime } = -\frac {y}{4 x^{2}}\) |
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David Saunders 1981 paper. Example 1 |
\(y^{\prime \prime } = \left (x^{2}+3\right ) y\) |
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David Saunders 1981 paper. Example 3 |
\(x^{2} y^{\prime \prime } = 2 y\) |
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Carolyn J. Smith 1984 paper. Appendix B examples and tests. Example 1 |
\(y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0\) |
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Carolyn J. Smith 1984 paper. Appendix B examples and tests. Example 2 |
\(x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0\) |
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Carolyn J. Smith 1984 paper. Appendix B examples and tests. Example 3 |
\(\left (x -2\right )^{2} y^{\prime \prime }-\left (x -2\right ) y^{\prime }-3 y = 0\) |
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