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\[
{}x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+y y^{\prime } = 0
\] |
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\[
{}x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime } = 0
\] |
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\[
{}x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (1+y\right ) y^{\prime } = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
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\[
{}\left (1+{y^{\prime }}^{2}\right )^{3} = a^{2} {y^{\prime \prime }}^{2}
\] |
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\[
{}u^{\prime \prime }-\frac {a^{2} u}{x^{{2}/{3}}} = 0
\] |
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\[
{}u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0
\] |
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\[
{}u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0
\] |
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\[
{}u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0
\] |
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\[
{}u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0
\] |
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\[
{}u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0
\] |
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\[
{}y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}}
\] |
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\[
{}y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}}
\] |
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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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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0
\] |
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\[
{}y^{\prime \prime }+q y^{\prime } = \frac {2 y}{x^{2}}
\] |
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\[
{}y^{\prime \prime }+y \,{\mathrm e}^{2 x} = n^{2} y
\] |
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\[
{}y^{\prime \prime }+\frac {y}{4 x} = 0
\] |
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\[
{}x y^{\prime \prime }+y^{\prime }+y = 0
\] |
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\[
{}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime }+9 y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+6 y = 0
\] |
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\[
{}y^{\prime \prime }+16 y = 0
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
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\[
{}y^{\prime \prime }+5 y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = 0
\] |
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\[
{}2 y^{\prime \prime }+y^{\prime }-y = 0
\] |
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\[
{}y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y = 0
\] |
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\[
{}y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y = 0
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime } = 10
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 16
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 24 \,{\mathrm e}^{-3 x}
\] |
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\[
{}y^{\prime \prime }+y = 2 \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 12 \,{\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-2 y = 3 \,{\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }-16 y = 40 \,{\mathrm e}^{4 x}
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 6 \,{\mathrm e}^{3 x}
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = 100 \cos \left (4 x \right )
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+12 y = 80 \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }+8 y^{\prime }+25 y = 120 \sin \left (5 x \right )
\] |
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\[
{}5 y^{\prime \prime }+12 y^{\prime }+20 y = 120 \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+9 y = 30 \sin \left (3 x \right )
\] |
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\[
{}y^{\prime \prime }+16 y = 16 \cos \left (4 x \right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+17 y = 60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right )
\] |
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\[
{}4 y^{\prime \prime }+4 y^{\prime }+5 y = 40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+8 y = 30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right )
\] |
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\[
{}5 y^{\prime \prime }+6 y^{\prime }+2 y = x^{2}+6 x
\] |
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\[
{}2 y^{\prime \prime }+y^{\prime } = 2 x
\] |
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\[
{}y^{\prime \prime }+y = 2 x \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 12 x \,{\mathrm e}^{3 x}
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 16 x^{2} {\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }+y = 8 x \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y = x^{3}-1+2 \cos \left (x \right )+\left (2-4 x \right ) {\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{x}+6 x -5
\] |
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\[
{}y^{\prime \prime }-y = \sinh \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y = 2 \sin \left (x \right )+4 x \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = 4 \,{\mathrm e}^{x}+\left (1-x \right ) \left ({\mathrm e}^{2 x}-1\right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime } = 9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }+2 x y^{\prime } = 0
\] |
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\[
{}2 y y^{\prime \prime } = {y^{\prime }}^{2}
\] |
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\[
{}x y^{\prime \prime } = y^{\prime }+{y^{\prime }}^{3}
\] |
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\[
{}{y^{\prime \prime }}^{2} = k^{2} \left (1+{y^{\prime }}^{2}\right )
\] |
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\[
{}k = \frac {y^{\prime \prime }}{\left (y^{\prime }+1\right )^{{3}/{2}}}
\] |
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\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+6 y = 0
\] |
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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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\[
{}x^{2} \left (2-x \right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
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\[
{}x y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
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\[
{}3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }-y = 0
\] |
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\[
{}x \left (1+x \right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y = 0
\] |
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\[
{}r^{\prime \prime }-6 r^{\prime }+9 r = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 10 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x} \cos \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = x
\] |
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\[
{}x y^{\prime \prime }+y^{\prime } = 4 x
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 26 \,{\mathrm e}^{3 x}
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 2 \,{\mathrm e}^{-2 x} \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 6 \,{\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 5 x +4 \,{\mathrm e}^{x} \left (1+\sin \left (2 x \right )\right )
\] |
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\[
{}x \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right ) = y y^{\prime }
\] |
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