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Mathematica |
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\[
{}y^{\prime \prime } x +y^{\prime } = 4 x
\] |
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\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime } = 2
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5}
\] |
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\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{3}
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{4}
\] |
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\[
{}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 8 x^{{4}/{3}}
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = \ln \left (x \right )
\] |
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\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}-1
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5}
\] |
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\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{3}
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{4}
\] |
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\[
{}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 8 x^{{4}/{3}}
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = \ln \left (x \right )
\] |
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\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}-1
\] |
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\[
{}t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1
\] |
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\[
{}t^{2} y^{\prime \prime }-t \left (2+t \right ) y^{\prime }+\left (2+t \right ) y = 2 t^{3}
\] |
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\[
{}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = t^{2} {\mathrm e}^{2 t}
\] |
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\[
{}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right )^{2} {\mathrm e}^{-t}
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \ln \left (x \right ) x^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = g \left (x \right )
\] |
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\[
{}t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 4 t^{2}
\] |
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\[
{}t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t
\] |
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\[
{}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = t^{2} {\mathrm e}^{2 t}
\] |
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\[
{}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right ) {\mathrm e}^{-t}
\] |
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\[
{}\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = \left (2 x +1\right )^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = \frac {4}{x^{2}}
\] |
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\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = x
\] |
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\[
{}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x} \left (4 x +1\right )
\] |
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\[
{}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 8 \,{\mathrm e}^{-x \left (x +2\right )}
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = -6 x -4
\] |
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\[
{}x^{2} y^{\prime \prime }+2 x \left (x -1\right ) y^{\prime }+\left (x^{2}-2 x +2\right ) y = x^{3} {\mathrm e}^{2 x}
\] |
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\[
{}x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y = {\mathrm e}^{x} x^{2}
\] |
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\[
{}\left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y = \left (4 x^{2}-4 x +1\right ) {\mathrm e}^{x}
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 4 x^{4}
\] |
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\[
{}2 y^{\prime \prime } x +\left (4 x +1\right ) y^{\prime }+\left (2 x +1\right ) y = 3 \sqrt {x}\, {\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = -{\mathrm e}^{-x}
\] |
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\[
{}4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y = 4 x^{{5}/{2}} {\mathrm e}^{2 x}
\] |
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\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 4 x^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 4 x^{4}
\] |
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\[
{}\left (1+x \right )^{2} y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y = \left (1+x \right )^{3} {\mathrm e}^{x}
\] |
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\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = x^{2}
\] |
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\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = x +2
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = 2 x^{2}+2
\] |
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\[
{}y^{\prime \prime } x +\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y = {\mathrm e}^{2 x}
\] |
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\[
{}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 4 \,{\mathrm e}^{-x \left (x +2\right )}
\] |
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\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{{5}/{2}}
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 2 x^{4} \sin \left (x \right )
\] |
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\[
{}\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = \left (2 x +1\right )^{2} {\mathrm e}^{-x}
\] |
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\[
{}2 y^{\prime \prime } x +2 y^{\prime }+2 y = \sin \left (\sqrt {x}\right )
\] |
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\[
{}y^{\prime \prime } x -\left (2+2 x \right ) y^{\prime }+\left (x +2\right ) y = 6 \,{\mathrm e}^{x} x^{3}
\] |
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\[
{}x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y = x^{a +1}
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = x^{3} \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime } x -y^{\prime }-4 x^{3} y = 8 x^{5}
\] |
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\[
{}y^{\prime \prime } \sin \left (x \right )+\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime }+\left (\sin \left (x \right )-\cos \left (x \right )\right ) y = {\mathrm e}^{-x}
\] |
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\[
{}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 8 x^{{5}/{2}}
\] |
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\[
{}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y = x^{{7}/{2}}
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y = 3 x^{4}
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = {\mathrm e}^{x} x^{3}
\] |
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\[
{}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = x^{{3}/{2}}
\] |
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\[
{}x^{2} y^{\prime \prime }-x \left (x +4\right ) y^{\prime }+2 \left (x +3\right ) y = {\mathrm e}^{x} x^{4}
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y = 2 x \,{\mathrm e}^{x}
\] |
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\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = x^{4}
\] |
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\[
{}\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 2 \left (x -1\right )^{2} {\mathrm e}^{x}
\] |
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\[
{}4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y = x^{{5}/{2}} {\mathrm e}^{x}
\] |
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\[
{}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = \left (3 x -1\right )^{2} {\mathrm e}^{2 x}
\] |
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\[
{}\left (x -1\right )^{2} y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+2 y = \left (x -1\right )^{2}
\] |
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\[
{}\left (x -1\right )^{2} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+\left (1+x \right ) y = \left (x -1\right )^{3} {\mathrm e}^{x}
\] |
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\[
{}\left (x -1\right )^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 x
\] |
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\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = -2 x^{2}
\] |
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\[
{}\left (1+x \right ) \left (2 x +3\right ) y^{\prime \prime }+2 \left (x +2\right ) y^{\prime }-2 y = \left (2 x +3\right )^{2}
\] |
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\[
{}y^{\prime \prime }+\frac {t^{2} y}{4} = f \cos \left (t \right )
\] |
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\[
{}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = t^{2}+1
\] |
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\[
{}t^{2} y^{\prime \prime }-2 y = t^{2}
\] |
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\[
{}y^{\prime \prime }+p \left (t \right ) y^{\prime }+q \left (t \right ) y = t +1
\] |
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\[
{}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = t^{2}+1
\] |
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\[
{}2 x^{2} y^{\prime \prime }-3 x y^{\prime }-18 y = \ln \left (x \right )
\] |
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\[
{}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = \ln \left (x^{2}\right )
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{3}
\] |
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\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 1-x
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 4 x +\sin \left (\ln \left (x \right )\right )
\] |
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\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = \ln \left (x \right ) x^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+3 y = \left (x -1\right ) \ln \left (x \right )
\] |
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\[
{}y^{\prime \prime } x = x^{2}+1
\] |
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\[
{}y^{\prime \prime } x +x = y^{\prime }
\] |
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\[
{}x^{\prime \prime }+t x^{\prime } = t^{3}
\] |
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\[
{}x^{2} y^{\prime \prime } = x y^{\prime }+1
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime } = 1
\] |
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\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = x
\] |
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\[
{}\left (1+x \right )^{2} y^{\prime \prime }+3 \left (1+x \right ) y^{\prime }+y = x^{2}
\] |
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\[
{}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y = {\mathrm e}^{-x^{2}} \sin \left (2 x \right )
\] |
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\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 9 x^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \sin \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \ln \left (x \right ) x^{2}
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x} = 9 x
\] |
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\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \cos \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 9 \ln \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 8 x \ln \left (x \right )^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \sin \left (x \right )
\] |
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