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ID |
problem |
ODE |
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1 |
\(y^{\prime \prime }+y^{\prime } x +y {y^{\prime }}^{2} = 0\) |
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2 |
\(y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y {y^{\prime }}^{2} = 0\) |
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3 |
\(y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y^{2} {y^{\prime }}^{2} = 0\) |
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4 |
\(y^{\prime \prime }+\left (\sin \left (x \right )+2 x \right ) y^{\prime }+\cos \left (y\right ) y {y^{\prime }}^{2} = 0\) |
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5 |
\(y^{\prime \prime } y^{\prime }+y^{2} = 0\) |
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6 |
\(y^{\prime \prime } y^{\prime }+y^{n} = 0\) |
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8 |
\(y^{\prime } = \left (x +y\right )^{4}\) |
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9 |
\(y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (y^{2}+3\right ) {y^{\prime }}^{2} = 0\) |
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10 |
\(y^{\prime \prime }+y^{\prime } x +y {y^{\prime }}^{2} = 0\) |
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11 |
\(y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+{y^{\prime }}^{2} = 0\) |
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12 |
\(3 y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+\sin \left (y\right ) {y^{\prime }}^{2} = 0\) |
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13 |
\(10 y^{\prime \prime }+x^{2} y^{\prime }+\frac {3 {y^{\prime }}^{2}}{y} = 0\) |
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14 |
\(10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )} = 0\) |
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15 |
\(y^{\prime \prime }-\frac {2 y}{x^{2}} = x \,{\mathrm e}^{-\sqrt {x}}\) |
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16 |
\(y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = x\) |
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17 |
\(y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}} = 0\) |
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18 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -c^{2} y = 0\) |
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19 |
\(x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}}\) |
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20 |
\(x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y = 2 x^{3}-x^{2}\) |
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21 |
\(y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+4 y \csc \left (x \right )^{2} = 0\) |
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22 |
\(\left (x^{2}+1\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 4 \cos \left (\ln \left (x +1\right )\right )\) |
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23 |
\(y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cos \left (x \right )^{2} y = 0\) |
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24 |
\(x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 8 x^{3} \sin \left (x \right )^{2}\) |
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25 |
\(x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5}\) |
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25 |
\(\cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 y \cos \left (x \right )^{3} = 2 \cos \left (x \right )^{5}\) |
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26 |
\(y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x} = 4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x}\) |
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27 |
\(y^{\prime \prime }-x^{2} y^{\prime }+x y = x^{m +1}\) |
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28 |
\(y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0\) |
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29 |
\(\cos \left (x \right )^{2} y^{\prime \prime }-2 \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\cos \left (x \right )^{2} y = 0\) |
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30 |
\(y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (x \right )\) |
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31 |
\(y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y = x\) |
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32 |
\(y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-3\right ) y = {\mathrm e}^{x^{2}}\) |
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33 |
\(y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = {\mathrm e}^{x^{2}} \sec \left (x \right )\) |
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34 |
\(x^{2} y^{\prime \prime }-2 y^{\prime } x +2 \left (x^{2}+1\right ) y = 0\) |
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35 |
\(4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y = 0\) |
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36 |
\(x^{2} y^{\prime \prime }+\left (-y+y^{\prime } x \right )^{2} = 0\) |
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37 |
\(x y^{\prime \prime }+2 y^{\prime }-x y = 0\) |
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38 |
\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\) |
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39 |
\(y^{\prime }+y \cot \left (x \right ) = 2 \cos \left (x \right )\) |
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40 |
\(2 y^{2} x -y+\left (y^{2}+x +y\right ) y^{\prime } = 0\) |
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41 |
\(y^{\prime } = x -y^{2}\) |
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42 |
\(y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+5 y^{\prime }-2 y = x \,{\mathrm e}^{x}+3 \,{\mathrm e}^{-2 x}\) |
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43 |
\(x^{2} y^{\prime \prime }-x \left (x +6\right ) y^{\prime }+10 y = 0\) |
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44 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y = 0\) |
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45 |
\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y = 0\) |
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46 |
\(x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0\) |
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47 |
\(y^{\prime \prime \prime }-x y = 0\) |
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48 |
\(y^{\prime } = y^{{1}/{3}}\) |
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49 |
\([x^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )]\) |
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