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Mathematica |
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\[
{}x^{2} y^{\prime \prime }+6 x y^{\prime }+6 y = 4 \,{\mathrm e}^{2 x}
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \frac {x^{2}}{\ln \left (x \right )}
\] |
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\[
{}x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y = x^{m} \ln \left (x \right )^{k}
\] |
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\[
{}y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+2 y = 8 x^{2} {\mathrm e}^{2 x}
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 8 x^{4}
\] |
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\[
{}4 x^{2} y^{\prime \prime }+y = \sqrt {x}\, \ln \left (x \right )
\] |
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\[
{}y^{\prime \prime }+x y = \sin \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}+2
\] |
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\[
{}y^{\prime \prime } x = y^{\prime }+x
\] |
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\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = \ln \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = \frac {5 \ln \left (x \right )}{x^{2}}
\] |
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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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\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = x
\] |
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\[
{}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = x \ln \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = x^{3}
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2} {\mathrm e}^{-x}
\] |
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\[
{}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x}
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime } = 1
\] |
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\[
{}y^{\prime \prime } x -y^{\prime } = x^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime } = 1
\] |
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\[
{}y^{\prime \prime } x -y^{\prime } = x^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 8 x^{4}
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = x -\frac {1}{x}
\] |
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\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 2 x^{3}
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 6 \ln \left (x \right ) x^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }+y = 3 x^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = 2 x
\] |
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\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = x
\] |
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\[
{}y^{\prime \prime } x +y^{\prime } = 4 x
\] |
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\[
{}t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N = t \ln \left (t \right )
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = \ln \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }-x y^{\prime } = {\mathrm e}^{x} x^{3}
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x +\ln \left (x \right ) x^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = \ln \left (x \right )^{2}-\ln \left (x^{2}\right )
\] |
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\[
{}\left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }-y = \ln \left (1+x \right )^{2}+x -1
\] |
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\[
{}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y = 6 x
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 2
\] |
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\[
{}\left (x^{2}+4\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 8
\] |
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\[
{}\left (1+x \right ) y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+\left (x +2\right ) y = \left (x^{2}+2 x +1\right ) {\mathrm e}^{2 x}
\] |
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\[
{}x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+\left (x^{2}+3 x +3\right ) y = \left (-x^{2}+6\right ) {\mathrm e}^{x}
\] |
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\[
{}x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y = \left (x^{2}-x +1\right ) {\mathrm e}^{x}
\] |
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\[
{}x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y = \frac {1+x}{x}
\] |
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\[
{}x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y = \frac {1}{x^{3}}
\] |
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\[
{}\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right ) = x
\] |
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\[
{}y^{\prime \prime } x -3 y^{\prime }+\frac {3 y}{x} = x +2
\] |
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\[
{}\left (1+x \right ) y^{\prime \prime }-\left (3 x +4\right ) y^{\prime }+3 y = \left (3 x +2\right ) {\mathrm e}^{3 x}
\] |
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\[
{}y^{\prime \prime } x +2 y^{\prime }+4 x y = 4
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \frac {-x^{2}+1}{x}
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {2}{x^{3}}
\] |
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\[
{}y^{\prime \prime } x -y^{\prime } = -\frac {2}{x}-\ln \left (x \right )
\] |
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\[
{}\left (1-x \right ) y^{\prime \prime }-4 x y^{\prime }+5 y = \cos \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = \sec \left (\ln \left (x \right )\right )
\] |
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\[
{}y^{\prime \prime }+x y^{\prime }+y = 2 x \,{\mathrm e}^{x}-1
\] |
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\[
{}y^{\prime \prime } x +x y^{\prime }-y = x^{2}+2 x
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x
\] |
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\[
{}x^{3} y^{\prime \prime }+x y^{\prime }-y = \cos \left (\frac {1}{x}\right )
\] |
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\[
{}x \left (1+x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }-y = x +\frac {1}{x}
\] |
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\[
{}2 y^{\prime \prime } x +\left (x -2\right ) y^{\prime }-y = x^{2}-1
\] |
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\[
{}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (4 x +3\right ) y^{\prime }-y = x +\frac {1}{x}
\] |
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\[
{}x^{2} \left (-1+\ln \left (x \right )\right ) y^{\prime \prime }-x y^{\prime }+y = x \left (1-\ln \left (x \right )\right )^{2}
\] |
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\[
{}y^{\prime \prime } x +2 y^{\prime }+x y = \sec \left (x \right )
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\frac {y}{4} = -\frac {x^{2}}{2}+\frac {1}{2}
\] |
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\[
{}\left (\cos \left (x \right )+\sin \left (x \right )\right ) y^{\prime \prime }-2 y^{\prime } \cos \left (x \right )+\left (\cos \left (x \right )-\sin \left (x \right )\right ) y = \left (\cos \left (x \right )+\sin \left (x \right )\right )^{2} {\mathrm e}^{2 x}
\] |
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\[
{}\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }+\left (\cos \left (x \right )+\sin \left (x \right )\right ) y = \left (\cos \left (x \right )-\sin \left (x \right )\right )^{2}
\] |
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\[
{}p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u = f \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = x^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 1
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-4 \pi y = x
\] |
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\[
{}y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } = {\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime } x -2 y^{\prime } = x^{3}
\] |
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\[
{}y^{\prime \prime } x +y^{\prime } = 4 x
\] |
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\[
{}y^{\prime \prime } x -3 y^{\prime } = 5 x
\] |
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\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \left (x^{2}-1\right )^{2}
\] |
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\[
{}\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (x +2\right ) y = x \left (1+x \right )^{2}
\] |
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\[
{}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2}
\] |
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\[
{}y^{\prime \prime } x -\left (1+x \right ) y^{\prime }+y = x^{2} {\mathrm e}^{2 x}
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x \,{\mathrm e}^{-x}
\] |
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\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {2}{x}
\] |
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\[
{}t y^{\prime \prime }-y^{\prime } = 2 t^{2}
\] |
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\[
{}2 y^{\prime \prime }+t y^{\prime }-2 y = 10
\] |
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\[
{}y^{\prime \prime } x = y^{\prime }+x^{5}
\] |
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\[
{}y^{\prime \prime } x +y^{\prime }+x = 0
\] |
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\[
{}x^{3} y^{\prime \prime }-x^{2} y^{\prime } = -x^{2}+3
\] |
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\[
{}t y^{\prime \prime }+4 y^{\prime } = t^{2}
\] |
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\[
{}y^{\prime \prime }-x y^{\prime }-x y-x = 0
\] |
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\[
{}y^{\prime \prime }-x y^{\prime }-x y-2 x = 0
\] |
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\[
{}y^{\prime \prime }-x y^{\prime }-x y-3 x = 0
\] |
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\[
{}y^{\prime \prime }-x y^{\prime }-x y-x^{2}-x = 0
\] |
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\[
{}y^{\prime \prime }-x y^{\prime }-x y-x^{3}+2 = 0
\] |
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\[
{}y^{\prime \prime }-x y^{\prime }-x y-x^{4}-6 = 0
\] |
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\[
{}y^{\prime \prime }-x y^{\prime }-x y-x^{5}+24 = 0
\] |
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\[
{}y^{\prime \prime }-x y^{\prime }-x y-x = 0
\] |
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\[
{}y^{\prime \prime }-x y^{\prime }-x y-x^{2} = 0
\] |
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\[
{}y^{\prime \prime }-x y^{\prime }-x y-x^{3} = 0
\] |
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\[
{}y^{\prime \prime }-a x y^{\prime }-b x y-c x = 0
\] |
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\[
{}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2} = 0
\] |
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\[
{}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3} = 0
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-x y-x = 0
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{2} = 0
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0
\] |
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