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Mathematica |
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\[
{}y^{\prime \prime \prime } = f \left (x \right )
\] |
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\[
{}y^{\prime \prime } = a^{2}+k^{2} {y^{\prime }}^{2}
\] |
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\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = {\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }-x^{2} y^{\prime }+x y = x
\] |
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\[
{}\left (3-x \right ) y^{\prime \prime }-\left (9-4 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
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\[
{}3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+2\right ) y^{\prime }-4 y = 0
\] |
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\[
{}a^{2} {y^{\prime \prime }}^{2} = 1+{y^{\prime }}^{2}
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{1}/{3}}}-\frac {6}{x^{2}}\right ) y = 0
\] |
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\[
{}4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y = 0
\] |
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\[
{}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-2 \left (x^{2}+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}} = 0
\] |
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\[
{}y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+4 \csc \left (x \right )^{2} y = 0
\] |
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\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5}
\] |
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\[
{}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}}
\] |
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\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x} = n^{2} y
\] |
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\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+n^{2} y = 0
\] |
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\[
{}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\left (n^{2}+\frac {2}{x^{2}}\right ) y = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0
\] |
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\[
{}\left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+3 \left (x -2\right ) y = 0
\] |
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\[
{}y^{\prime \prime }-2 b y^{\prime }+b^{2} x^{2} y = 0
\] |
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\[
{}y^{\prime \prime }+4 x y^{\prime }+4 x^{2} y = 0
\] |
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\[
{}x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y = x \left (-x^{2}+1\right )^{{3}/{2}}
\] |
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\[
{}\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
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\[
{}x^{2} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-a^{2} y = 0
\] |
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\[
{}y^{\prime \prime }+x y^{\prime }-y = f \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y = x^{3}
\] |
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\[
{}\left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2} y}{a} = 0
\] |
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\[
{}\left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y = 0
\] |
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\[
{}x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2} = 0
\] |
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\[
{}y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
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\[
{}x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y = 0
\] |
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\[
{}[x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+y \left (t \right ) = 0, y^{\prime }\left (t \right )+5 x \left (t \right )+3 y \left (t \right ) = 0]
\] |
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\[
{}[x^{\prime }\left (t \right )-7 x \left (t \right )+y \left (t \right ) = 0, y^{\prime }\left (t \right )-2 x \left (t \right )-5 y \left (t \right ) = 0]
\] |
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\[
{}[x^{\prime }\left (t \right )+2 x \left (t \right )-3 y \left (t \right ) = t, y^{\prime }\left (t \right )-3 x \left (t \right )+2 y \left (t \right ) = {\mathrm e}^{2 t}]
\] |
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\[
{}[4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+44 x \left (t \right )+49 y \left (t \right ) = t, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+34 x \left (t \right )+38 y \left (t \right ) = {\mathrm e}^{t}]
\] |
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\[
{}[x^{\prime \prime }\left (t \right )-3 x \left (t \right )-4 y \left (t \right ) = 0, y^{\prime \prime }\left (t \right )+x \left (t \right )+y \left (t \right ) = 0]
\] |
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\[
{}[x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-2 x \left (t \right )+2 y \left (t \right ) = 3 \,{\mathrm e}^{t}, 3 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+y \left (t \right ) = 4 \,{\mathrm e}^{2 t}]
\] |
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\[
{}[4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+2 x \left (t \right )+31 y \left (t \right ) = {\mathrm e}^{t}, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+x \left (t \right )+24 y \left (t \right ) = 3]
\] |
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\[
{}[x^{\prime }\left (t \right )+4 x \left (t \right )+3 y \left (t \right ) = t, y^{\prime }\left (t \right )+2 x \left (t \right )+5 y \left (t \right ) = {\mathrm e}^{t}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = n y \left (t \right )-m z \left (t \right ), y^{\prime }\left (t \right ) = L z \left (t \right )-m x \left (t \right ), z^{\prime }\left (t \right ) = m x \left (t \right )-L y \left (t \right )]
\] |
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\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = \frac {1}{x}
\] |
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\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{r} = 0
\] |
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\[
{}y+x +x y^{\prime } = 0
\] |
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\[
{}\left (x y+1\right ) y-x y^{\prime } = 0
\] |
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\[
{}\sin \left (x \right ) y^{\prime }-y \cos \left (x \right )+y^{2} = 0
\] |
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\[
{}\left (x +y\right ) y^{\prime }+y-x = 0
\] |
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\[
{}x +y y^{\prime }+\frac {x y^{\prime }-y}{x^{2}+y^{2}} = 0
\] |
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\[
{}x^{3}+3 x y^{2}+\left (y^{3}+3 x^{2} y\right ) y^{\prime } = 0
\] |
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\[
{}x y^{\prime }+y = y^{2} \ln \left (x \right )
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime }-2 x y = -x^{3}+x
\] |
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\[
{}x y^{\prime }-y-\cos \left (\frac {1}{x}\right ) = 0
\] |
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\[
{}x +y y^{\prime } = m \left (x y^{\prime }-y\right )
\] |
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\[
{}x \cos \left (y\right )^{2} = y \cos \left (x \right )^{2} y^{\prime }
\] |
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\[
{}y^{\prime } = {\mathrm e}^{x -y}+x^{2} {\mathrm e}^{-y}
\] |
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\[
{}x^{2} y^{\prime }+y = 1
\] |
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\[
{}2 y+\left (x^{2}+1\right ) \arctan \left (x \right ) y^{\prime } = 0
\] |
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\[
{}x y^{2}+x +\left (x^{2} y+y\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime } = {\mathrm e}^{x +y}+x^{2} {\mathrm e}^{y}
\] |
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\[
{}\left (3+2 \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime } = 1+2 \sin \left (y\right )+\cos \left (y\right )
\] |
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\[
{}\frac {\cos \left (y\right )^{2} y^{\prime }}{x}+\frac {\cos \left (x \right )^{2}}{y} = 0
\] |
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\[
{}\left (1+{\mathrm e}^{x}\right ) y y^{\prime } = \left (1+y\right ) {\mathrm e}^{x}
\] |
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\[
{}\csc \left (x \right ) \ln \left (y\right ) y^{\prime }+x^{2} y^{2} = 0
\] |
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\[
{}y^{\prime } = \frac {\sin \left (x \right )+x \cos \left (x \right )}{y \left (2 \ln \left (y\right )+1\right )}
\] |
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\[
{}\cos \left (y\right ) \ln \left (\sec \left (x \right )+\tan \left (x \right )\right ) = \cos \left (x \right ) \ln \left (\sec \left (y\right )+\tan \left (y\right )\right ) y^{\prime }
\] |
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\[
{}\left (x^{2}-x^{2} y\right ) y^{\prime }+y^{2}+x y^{2} = 0
\] |
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\[
{}\left (\sin \left (y\right )+y \cos \left (y\right )\right ) y^{\prime }-\left (2 \ln \left (x \right )+1\right ) x = 0
\] |
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\[
{}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
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\[
{}-x y^{\prime }+y = a \left (y^{2}+y^{\prime }\right )
\] |
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\[
{}\left (x +y-1\right ) y^{\prime } = x +y+1
\] |
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\[
{}\left (2 x +2 y+1\right ) y^{\prime } = x +y+1
\] |
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\[
{}\left (2 x +3 y-5\right ) y^{\prime }+2 x +3 y-1 = 0
\] |
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\[
{}\left (x^{2}+y^{2}\right ) y^{\prime } = x y+x^{2}
\] |
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\[
{}\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y-\left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime } = 0
\] |
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\[
{}x^{2}-y^{2}+2 x y y^{\prime } = 0
\] |
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\[
{}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right )
\] |
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\[
{}\left (2 x -2 y+5\right ) y^{\prime }-x +y-3 = 0
\] |
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\[
{}x +y+1-\left (2 x +2 y+1\right ) y^{\prime } = 0
\] |
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\[
{}y^{2} = \left (x y-x^{2}\right ) y^{\prime }
\] |
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\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )-x
\] |
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\[
{}\left (x^{2}+y^{2}\right ) y^{\prime } = x y
\] |
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\[
{}x^{2} y^{\prime }+y \left (x +y\right ) = 0
\] |
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\[
{}2 y^{\prime } = \frac {y}{x}+\frac {y^{2}}{x^{2}}
\] |
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\[
{}\left (6 x -5 y+4\right ) y^{\prime }+y-2 x -1 = 0
\] |
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\[
{}\left (x -3 y+4\right ) y^{\prime }+7 y-5 x = 0
\] |
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\[
{}\left (2 x +4 y+3\right ) y^{\prime } = 2 y+x +1
\] |
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\[
{}x y^{\prime }-y = \sqrt {x^{2}+y^{2}}
\] |
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\[
{}x \left (x^{2}+3 y^{2}\right )+y \left (y^{2}+3 x^{2}\right ) y^{\prime } = 0
\] |
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\[
{}x^{2}+3 y^{2}-2 x y y^{\prime } = 0
\] |
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\[
{}y^{\prime } = \frac {2 x -y+1}{x +2 y-3}
\] |
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\[
{}\left (x -y\right ) y^{\prime } = x +y+1
\] |
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\[
{}x -y-2-\left (2 x -2 y-3\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime }+y \cot \left (x \right ) = 2 \cos \left (x \right )
\] |
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\[
{}\cos \left (x \right )^{2} y^{\prime }+y = \tan \left (x \right )
\] |
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\[
{}x \cos \left (x \right ) y^{\prime }+\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y = 1
\] |
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\[
{}y-\sin \left (x^{2}\right ) x +x y^{\prime } = 0
\] |
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\[
{}x \ln \left (x \right ) y^{\prime }+y = 2 \ln \left (x \right )
\] |
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