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Mathematica |
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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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\[
{}x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{r} = 0
\] |
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\[
{}y^{\prime \prime }-n^{2} y = 0
\] |
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\[
{}2 x^{\prime \prime }+5 x^{\prime }-12 x = 0
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }-54 y = 0
\] |
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\[
{}9 x^{\prime \prime }+18 x^{\prime }-16 x = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 0
\] |
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\[
{}\left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5+2 x \right ) y^{\prime }+8 y = 0
\] |
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\[
{}x y^{\prime \prime }+2 x y^{\prime }+2 y = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0
\] |
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\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }+2 y = 0
\] |
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\[
{}\left (x^{2}-x \right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }-4 y = 0
\] |
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\[
{}x y y^{\prime \prime }+x {y^{\prime }}^{2}+y y^{\prime } = 0
\] |
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\[
{}\left (-b \,x^{2}+a x \right ) y^{\prime \prime }+2 a y^{\prime }+2 b y = 0
\] |
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\[
{}\sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 y \sin \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime } = y
\] |
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\[
{}y^{\prime \prime }-a^{2} y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {a^{2}}{y} = 0
\] |
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\[
{}y^{\prime \prime } = y^{3}-y
\] |
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\[
{}y^{\prime \prime } = {\mathrm e}^{2 y}
\] |
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\[
{}y^{\prime \prime } = x y^{\prime }
\] |
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\[
{}y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x} = 0
\] |
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\[
{}x y^{\prime \prime }+x {y^{\prime }}^{2}-y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+4 {y^{\prime }}^{2} = 0
\] |
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\[
{}y^{\prime \prime } = a {y^{\prime }}^{2}
\] |
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\[
{}y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} = {y^{\prime }}^{2}
\] |
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\[
{}a y^{\prime \prime } = y^{\prime }
\] |
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\[
{}a y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\] |
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\[
{}y^{\prime } = x y^{\prime \prime }+\sqrt {1+{y^{\prime }}^{2}}
\] |
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\[
{}x y y^{\prime \prime }+x {y^{\prime }}^{2} = 3 y y^{\prime }
\] |
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\[
{}2 x^{2} y y^{\prime \prime }+y^{2} = x^{2} {y^{\prime }}^{2}
\] |
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\[
{}x^{2} y^{\prime \prime } = \sqrt {m \,x^{2} {y^{\prime }}^{3}+y^{2} n}
\] |
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\[
{}x^{4} y^{\prime \prime } = \left (x^{3}+2 x y\right ) y^{\prime }-4 y^{2}
\] |
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\[
{}x^{4} y^{\prime \prime }-x^{3} y^{\prime } = x^{2} {y^{\prime }}^{2}-4 y^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }+4 y^{2}-6 y = x^{4} {y^{\prime }}^{2}
\] |
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\[
{}y^{\prime \prime } = {\mathrm e}^{y}
\] |
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\[
{}y^{\prime \prime }+a^{2} y = 0
\] |
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\[
{}y^{\prime \prime } = \frac {1}{\sqrt {a y}}
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0
\] |
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\[
{}-a y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\] |
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\[
{}\sin \left (y\right )^{3} y^{\prime \prime } = \cos \left (y\right )
\] |
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\[
{}y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} = {y^{\prime }}^{2}
\] |
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\[
{}x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+3 y = 0
\] |
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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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\[
{}y^{\prime \prime }-a x y^{\prime }+a^{2} \left (x -1\right ) y = 0
\] |
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\[
{}\left (2 x^{3}-a \right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 x y = 0
\] |
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\[
{}y^{\prime \prime }+4 x y^{\prime }+4 x^{2} y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+n^{2} y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x} = n^{2} y
\] |
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\[
{}y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y = 0
\] |
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\[
{}4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{3}+6 x^{2}+4\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y = 0
\] |
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\[
{}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-\left (a^{2}+1\right ) y = 0
\] |
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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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\[
{}y^{\prime \prime }+2 n \cot \left (n x \right ) y^{\prime }+\left (m^{2}-n^{2}\right ) y = 0
\] |
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\[
{}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {y \left (-8+\sqrt {x}+x \right )}{4 x^{2}} = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-2 n x y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y = 0
\] |
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\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cos \left (x \right )^{2} y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}} = 0
\] |
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\[
{}\left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+m^{2} y = 0
\] |
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\[
{}y^{\prime \prime }-\cot \left (x \right ) y^{\prime }-\sin \left (x \right )^{2} y = 0
\] |
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\[
{}\sin \left (x \right )^{2} y^{\prime \prime }+\cos \left (x \right ) \sin \left (x \right ) y^{\prime }+y = 0
\] |
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\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime }+\left (\tan \left (x \right )-1\right )^{2} y^{\prime }-n \left (n -1\right ) y \sec \left (x \right )^{4} = 0
\] |
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\[
{}y^{\prime \prime }+\left (3 \sin \left (x \right )-\cot \left (x \right )\right ) y^{\prime }+2 \sin \left (x \right )^{2} y = 0
\] |
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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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\[
{}x y^{\prime }-y = \left (x -1\right ) \left (y^{\prime \prime }-x +1\right )
\] |
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\[
{}x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2} = 0
\] |
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\[
{}\left (x^{2}+a \right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
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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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\[
{}\left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2} y}{a} = 0
\] |
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\[
{}x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\frac {a^{2} y}{-x^{2}+1} = 0
\] |
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\[
{}x \left (-x^{2}+1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) \left (3 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0
\] |
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\[
{}\left (x^{3}-2 x^{2}\right ) y^{\prime \prime }+2 x^{2} y^{\prime }-12 \left (x -2\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-a^{2} y = 0
\] |
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\[
{}x y^{\prime \prime } \left (x \cos \left (x \right )-2 \sin \left (x \right )\right )+\left (x^{2}+2\right ) y^{\prime } \sin \left (x \right )-2 \left (x \sin \left (x \right )+\cos \left (x \right )\right ) y = 0
\] |
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\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime } = m^{2} y
\] |
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\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
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\[
{}2 y^{\prime \prime }+9 y^{\prime }-18 y = 0
\] |
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\[
{}2 x^{2} y y^{\prime \prime }+4 y^{2} = x^{2} {y^{\prime }}^{2}+2 x y y^{\prime }
\] |
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\[
{}x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2}-3 y^{2} = 0
\] |
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\[
{}y+3 x y^{\prime }+2 y {y^{\prime }}^{2}+\left (x^{2}+2 y^{\prime } y^{2}\right ) y^{\prime \prime } = 0
\] |
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\[
{}\left (y^{2}+2 x^{2} y^{\prime }\right ) y^{\prime \prime }+2 \left (x +y\right ) {y^{\prime }}^{2}+x y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+{y^{\prime }}^{3} = 0
\] |
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\[
{}y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} \ln \left (y\right )
\] |
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\[
{}y^{\prime }-y y^{\prime \prime } = n \sqrt {{y^{\prime }}^{2}+a^{2} y^{\prime \prime }}
\] |
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\[
{}x y^{\prime \prime }+y^{\prime } = 0
\] |
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