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ID |
problem |
ODE |
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1 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = 0\) |
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2 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = 1\) |
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3 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x +1\) |
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4 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x\) |
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5 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{2}+x +1\) |
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6 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{2}\) |
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7 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{2}+1\) |
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8 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{4}\) |
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9 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = \sin \left (x \right )\) |
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10 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = \sin \left (x \right )+1\) |
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11 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x \sin \left (x \right )\) |
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12 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = \cos \left (x \right )+\sin \left (x \right )\) |
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13 |
\(x^{2} y^{\prime \prime }+\left (\cos \left (x \right )-1\right ) y^{\prime }+y \,{\mathrm e}^{x} = 0\) |
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14 |
\(\left (-2+x \right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y = 0\) |
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15 |
\(\left (-2+x \right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y = 0\) |
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16 |
\(\left (x +1\right ) \left (3 x -1\right ) y^{\prime \prime }+\cos \left (x \right ) y^{\prime }-3 x y = 0\) |
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17 |
\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\) |
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18 |
\(2 x^{2} y^{\prime \prime }+3 y^{\prime } x -x y = x^{2}+2 x\) |
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19 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = 1\) |
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20 |
\(2 x^{2} y^{\prime \prime }+2 y^{\prime } x -x y = 1\) |
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21 |
\(y^{\prime \prime }+\left (x -6\right ) y = 0\) |
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22 |
\(x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0\) |
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23 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{2}+\cos \left (x \right )\) |
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24 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = \cos \left (x \right )\) |
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24 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{3}+\cos \left (x \right )\) |
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24 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{3} \cos \left (x \right )\) |
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24 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{3} \cos \left (x \right )+\sin \left (x \right )^{2}\) |
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24 |
\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = \ln \left (x \right )\) |
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25 |
\(2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0\) |
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26 |
\(x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y = 0\) |
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27 |
\(x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0\) |
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28 |
\({y^{\prime }}^{2}+y^{2} = \sec \left (x \right )^{4}\) |
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29 |
\(\left (y-2 y^{\prime } x \right )^{2} = {y^{\prime }}^{3}\) |
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31 |
\(x^{2} y^{\prime \prime }+y = 0\) |
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32 |
\(x y^{\prime \prime }+y^{\prime }-y = 0\) |
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33 |
\(4 x y^{\prime \prime }+2 y^{\prime }+y = 0\) |
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34 |
\(x y^{\prime \prime }+y^{\prime }-y = 0\) |
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35 |
\(x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y = 0\) |
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36 |
\(x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime } x +y = 0\) |
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37 |
\(x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4+x \right ) y = 0\) |
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38 |
\(2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0\) |
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39 |
\(2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -5\right ) y = 0\) |
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40 |
\(2 x^{2} y^{\prime \prime }+2 y^{\prime } x -x y = \sin \left (x \right )\) |
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41 |
\(2 x^{2} y^{\prime \prime }+2 y^{\prime } x -x y = x \sin \left (x \right )\) |
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42 |
\(2 x^{2} y^{\prime \prime }+2 y^{\prime } x -x y = \sin \left (x \right ) \cos \left (x \right )\) |
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43 |
\(2 x^{2} y^{\prime \prime }+2 y^{\prime } x -x y = x^{3}+x \sin \left (x \right )\) |
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44 |
\(\cos \left (x \right ) y^{\prime \prime }+2 y^{\prime } x -x y = 0\) |
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45 |
\(x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y = 0\) |
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46 |
\(x^{2} y^{\prime \prime }+y^{\prime } x -x y = 0\) |
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47 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
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48 |
\(\left (x^{2}-x \right ) y^{\prime \prime }-y^{\prime } x +y = 0\) |
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49 |
\(x^{2} y^{\prime \prime }+\left (x^{2}+6 x \right ) y^{\prime }+x y = 0\) |
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50 |
\(x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}-8\right ) y = 0\) |
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51 |
\(x^{2} y^{\prime \prime }-9 y^{\prime } x +25 y = 0\) |
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52 |
\(x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y = 0\) |
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53 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
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54 |
\(x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0\) |
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55 |
\(2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y = 0\) |
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56 |
\(2 x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = 0\) |
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57 |
\(x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y = 0\) |
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58 |
\(x^{2} y^{\prime \prime }-x y = 0\) |
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59 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y = x \,{\mathrm e}^{x}\) |
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60 |
\(y^{\prime } = y \left (1-y^{2}\right )\) |
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61 |
\(\frac {x y^{\prime \prime }}{1-x}+y = \frac {1}{1-x}\) |
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62 |
\(\frac {x y^{\prime \prime }}{1-x}+x y = 0\) |
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63 |
\(\frac {x y^{\prime \prime }}{1-x}+y = \cos \left (x \right )\) |
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64 |
\(\frac {x y^{\prime \prime }}{-x^{2}+1}+y = 0\) |
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65 |
\(y^{\prime \prime } = \left (x^{2}+3\right ) y\) |
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66 |
\(y^{\prime \prime }+\left (x -1\right ) y = 0\) |
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67 |
\([x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+2 t +1, y^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right )+3 t -1]\) |
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68 |
\(y^{\prime \prime }+20 y^{\prime }+500 y = 100000 \cos \left (100 x \right )\) |
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69 |
\(y^{\prime \prime } \sin \left (2 x \right )^{2}+y^{\prime } \sin \left (4 x \right )-4 y = 0\) |
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