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Mathematica |
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\]
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\[
{} y y^{\prime \prime } = {y^{\prime }}^{2}+y^{\prime }
\]
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\[
{} y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} 2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} y^{3} y^{\prime \prime } = -1
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} y^{\prime }
\]
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\[
{} y^{\prime \prime } = {\mathrm e}^{2 y}
\]
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\[
{} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2} = 4 y^{2}
\]
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\[
{} y^{\prime \prime \prime } = 3 y y^{\prime }
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }+6 y = 0
\]
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\[
{} x y^{\prime \prime }+y^{\prime } = 0
\]
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\[
{} \left (x +2\right )^{2} y^{\prime \prime }+3 \left (x +2\right ) y^{\prime }-3 y = 0
\]
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\[
{} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }+4 y = 0
\]
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\[
{} x^{2} y^{\prime \prime \prime }-3 x y^{\prime \prime }+3 y^{\prime } = 0
\]
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\[
{} x^{2} y^{\prime \prime \prime } = 2 y^{\prime }
\]
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\[
{} \left (1+x \right )^{2} y^{\prime \prime \prime }-12 y^{\prime } = 0
\]
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\[
{} \left (2 x +1\right )^{2} y^{\prime \prime \prime }+2 \left (2 x +1\right ) y^{\prime \prime }+y^{\prime } = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y = x \left (6-\ln \left (x \right )\right )
\]
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\[
{} x^{2} y^{\prime \prime }-2 y = \sin \left (\ln \left (x \right )\right )
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }-3 y = -\frac {16 \ln \left (x \right )}{x}
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y = x^{2}-2 x +2
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m}
\]
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\[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 \ln \left (x \right )^{2}+12 x
\]
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\[
{} \left (1+x \right )^{3} y^{\prime \prime }+3 \left (1+x \right )^{2} y^{\prime }+\left (1+x \right ) y = 6 \ln \left (1+x \right )
\]
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\[
{} \left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y = x
\]
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\[
{} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0
\]
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\[
{} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y = 0
\]
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\[
{} \left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 \left (1+x \right ) y^{\prime }+6 y = 6
\]
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\[
{} x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }+\left (\tan \left (x \right )-2 \cot \left (x \right )\right ) y^{\prime }+2 \cot \left (x \right )^{2} y = 0
\]
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\[
{} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2} = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y = 1
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }-3 y = 5 x^{4}
\]
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\[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = \left (x -1\right )^{2} {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{-2 x} = {\mathrm e}^{-3 x}
\]
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\[
{} \left (x^{4}-x^{3}\right ) y^{\prime \prime }+\left (2 x^{3}-2 x^{2}-x \right ) y^{\prime }-y = \frac {\left (x -1\right )^{2}}{x}
\]
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\[
{} y^{\prime \prime }-y^{\prime }+y \,{\mathrm e}^{2 x} = x \,{\mathrm e}^{2 x}-1
\]
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\[
{} x \left (x -1\right ) y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+2 y = x^{2} \left (2 x -3\right )
\]
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\[
{} x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime } = 4 x^{3} {\mathrm e}^{x^{2}}
\]
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\[
{} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime } = 1
\]
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\[
{} x \ln \left (x \right ) y^{\prime \prime }-y^{\prime } = \ln \left (x \right )^{2}
\]
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\[
{} x y^{\prime \prime }+\left (2 x -1\right ) y^{\prime } = -4 x^{2}
\]
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\[
{} y^{\prime \prime }+\tan \left (x \right ) y^{\prime } = \cos \left (x \right ) \cot \left (x \right )
\]
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\[
{} 4 x y^{\prime \prime }+2 y^{\prime }+y = 1
\]
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\[
{} 4 x y^{\prime \prime }+2 y^{\prime }+y = \frac {x +6}{x^{2}}
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {1}{x^{2}+1}
\]
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\[
{} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (x -1\right )^{2} {\mathrm e}^{x}
\]
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\[
{} 2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y = \frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}}
\]
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\[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y = 4 \,{\mathrm e}^{x}
\]
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\[
{} x^{3} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-y^{\prime } x^{2}+x y = 2 \ln \left (x \right )
\]
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\[
{} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-2 \left (1-x \right ) y = 2 x -2
\]
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\[
{} x^{\prime \prime }+{x^{\prime }}^{2}+x = 0
\]
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\[
{} x^{\prime \prime }-2 {x^{\prime }}^{2}+x^{\prime }-2 x = 0
\]
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\[
{} x^{\prime \prime }-x \,{\mathrm e}^{x^{\prime }} = 0
\]
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\[
{} x^{\prime \prime }+{\mathrm e}^{-x^{\prime }}-x = 0
\]
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\[
{} x^{\prime \prime }+x {x^{\prime }}^{2} = 0
\]
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\[
{} x^{\prime \prime }+\left (x+2\right ) x^{\prime } = 0
\]
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\[
{} x^{\prime \prime }-x^{\prime }+x-x^{2} = 0
\]
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\[
{} y y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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\[
{} x y^{\prime \prime }+y^{\prime } = 0
\]
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\[
{} x^{2} y^{\prime \prime \prime \prime }+4 x y^{\prime \prime \prime }+2 y^{\prime \prime } = 0
\]
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\[
{} x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime } = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x^{2}-\frac {1}{9}\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{x}+\frac {y}{9} = 0
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{x}+4 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+4 \left (x^{4}-1\right ) y = 0
\]
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\[
{} x y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{4} = 0
\]
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\[
{} y^{\prime \prime }+\frac {5 y^{\prime }}{x}+y = 0
\]
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\[
{} y^{\prime \prime }+\frac {3 y^{\prime }}{x}+4 y = 0
\]
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\[
{} y^{\prime \prime }+t y = 0
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y+y^{3} = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\alpha \left (\alpha +1\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-\nu ^{2}+x^{2}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\mu \left (1-y^{2}\right ) y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }-t y = \frac {1}{\pi }
\]
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\[
{} a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y = d
\]
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\[
{} t y^{\prime \prime }+3 y = t
\]
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\[
{} \left (t -1\right ) y^{\prime \prime }-3 t y^{\prime }+4 y = \sin \left (t \right )
\]
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\[
{} t \left (-4+t \right ) y^{\prime \prime }+3 t y^{\prime }+4 y = 2
\]
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\[
{} y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+3 \ln \left (t \right ) y = 0
\]
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\[
{} \left (x +3\right ) y^{\prime \prime }+x y^{\prime }+y \ln \left (x \right ) = 0
\]
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\[
{} \left (x -2\right ) y^{\prime \prime }+y^{\prime }+\left (x -2\right ) \tan \left (x \right ) y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\frac {\alpha \left (\alpha +1\right ) \mu ^{2} y}{-x^{2}+1} = 0
\]
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\[
{} y^{\prime \prime }-\frac {t}{y} = \frac {1}{\pi }
\]
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\[
{} t^{2} y^{\prime \prime }-2 y = 0
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\]
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\[
{} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\]
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\[
{} \left (1-x \cot \left (x \right )\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0
\]
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\[
{} t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y = 0
\]
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\[
{} t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\]
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\[
{} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0
\]
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\[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\]
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\[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\]
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\[
{} x y^{\prime \prime }-\left (x +n \right ) y^{\prime }+n y = 0
\]
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