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ODE |
Mathematica |
Maple |
Sympy |
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\[
{} \left [x^{\prime }\left (t \right ) = \frac {5 x \left (t \right )}{4}+\frac {3 y \left (t \right )}{4}, y^{\prime }\left (t \right ) = \frac {3 x \left (t \right )}{4}+\frac {5 y \left (t \right )}{4}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = -\frac {3 x \left (t \right )}{4}-\frac {7 y \left (t \right )}{4}, y^{\prime }\left (t \right ) = \frac {x \left (t \right )}{4}+\frac {5 y \left (t \right )}{4}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = -\frac {x \left (t \right )}{4}-\frac {3 y \left (t \right )}{4}, y^{\prime }\left (t \right ) = \frac {x \left (t \right )}{2}+y \left (t \right )\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )+4 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+6 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )+4 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = 2 x \left (t \right )-\frac {5 y \left (t \right )}{2}, y^{\prime }\left (t \right ) = \frac {9 x \left (t \right )}{5}-y \left (t \right )\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )-3 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )-y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \frac {3 x \left (t \right )}{4}-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-\frac {5 y \left (t \right )}{4}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = -\frac {4 x \left (t \right )}{5}+2 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+\frac {6 y \left (t \right )}{5}\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = a x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+a y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+a y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = a x \left (t \right )-2 y \left (t \right )]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \frac {5 x \left (t \right )}{4}+\frac {3 y \left (t \right )}{4}, y^{\prime }\left (t \right ) = a x \left (t \right )+\frac {5 y \left (t \right )}{4}\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+a y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+a y \left (t \right ), y^{\prime }\left (t \right ) = -6 x \left (t \right )-4 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = a x \left (t \right )+10 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-4 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+a y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-6 y \left (t \right )]
\]
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\[
{} \left [i^{\prime }\left (t \right ) = \frac {i \left (t \right )}{2}-\frac {v \left (t \right )}{8}, v^{\prime }\left (t \right ) = 2 i \left (t \right )-\frac {v \left (t \right )}{2}\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \frac {5 x \left (t \right )}{4}+\frac {3 y \left (t \right )}{4}, y^{\prime }\left (t \right ) = -\frac {3 x \left (t \right )}{4}-\frac {y \left (t \right )}{4}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = -\frac {3 x \left (t \right )}{2}+y \left (t \right ), y^{\prime }\left (t \right ) = -\frac {x \left (t \right )}{4}-\frac {y \left (t \right )}{2}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = -3 x \left (t \right )+\frac {5 y \left (t \right )}{2}, y^{\prime }\left (t \right ) = -\frac {5 x \left (t \right )}{2}+2 y \left (t \right )\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = -x \left (t \right )-\frac {y \left (t \right )}{2}, y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = 2 x \left (t \right )+\frac {y \left (t \right )}{2}, y^{\prime }\left (t \right ) = -\frac {x \left (t \right )}{2}+y \left (t \right )\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-7 y \left (t \right )]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = -\frac {5 x \left (t \right )}{2}+\frac {3 y \left (t \right )}{2}, y^{\prime }\left (t \right ) = -\frac {3 x \left (t \right )}{2}+\frac {y \left (t \right )}{2}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = 2 x \left (t \right )+\frac {3 y \left (t \right )}{2}, y^{\prime }\left (t \right ) = -\frac {3 x \left (t \right )}{2}-y \left (t \right )\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \frac {5 x \left (t \right )}{4}+\frac {3 y \left (t \right )}{4}, y^{\prime }\left (t \right ) = -\frac {3 x \left (t \right )}{4}-\frac {y \left (t \right )}{4}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = -3 x \left (t \right )+\frac {5 y \left (t \right )}{2}, y^{\prime }\left (t \right ) = -\frac {5 x \left (t \right )}{2}+2 y \left (t \right )\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = 2 x \left (t \right )+\frac {y \left (t \right )}{2}, y^{\prime }\left (t \right ) = -\frac {x \left (t \right )}{2}+y \left (t \right )\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -8 x \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )+x \left (t \right )^{2}, y^{\prime }\left (t \right ) = y \left (t \right )-2 x \left (t \right ) y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )^{2} y \left (t \right )-3 x \left (t \right )^{2}-4 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right ) y \left (t \right )^{2}+6 x \left (t \right ) y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-x \left (t \right )^{2}, y^{\prime }\left (t \right ) = 2 x \left (t \right ) y \left (t \right )-3 y \left (t \right )+2]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )+2 x \left (t \right ) y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2-y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )^{2}]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{2}-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = \frac {y \left (t \right )}{2}-\frac {y \left (t \right )^{2}}{4}-\frac {3 x \left (t \right ) y \left (t \right )}{4}\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = -\left (x \left (t \right )-y \left (t \right )\right ) \left (1-x \left (t \right )-y \left (t \right )\right ), y^{\prime }\left (t \right ) = x \left (t \right ) \left (2+y \left (t \right )\right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right ) \left (2-x \left (t \right )-y \left (t \right )\right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )-2 x \left (t \right ) y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = \left (x \left (t \right )+2\right ) \left (y \left (t \right )-x \left (t \right )\right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )^{2}-y \left (t \right )^{2}]
\]
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\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )^{2}-y \left (t \right )^{2}]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-\frac {x \left (t \right )^{3}}{5}-\frac {y \left (t \right )}{5}\right ]
\]
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\[
{} x^{\prime } = \frac {x \sqrt {6 x-9}}{3}
\]
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\[
{} \left [x^{\prime }\left (t \right ) = x \left (t \right ) \left (1-x \left (t \right )-y \left (t \right )\right ), y^{\prime }\left (t \right ) = y \left (t \right ) \left (\frac {3}{4}-y \left (t \right )-\frac {x \left (t \right )}{2}\right )\right ]
\]
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\[
{} y^{\prime \prime }+t y = 0
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y+y^{3} = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\alpha \left (\alpha +1\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-\nu ^{2}+x^{2}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\mu \left (1-y^{2}\right ) y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }-t y = \frac {1}{\pi }
\]
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\[
{} a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y = d
\]
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\[
{} y^{\prime \prime }+y = 0
\]
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\[
{} y^{\prime \prime }+9 y = 0
\]
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\[
{} y^{\prime \prime }+y^{\prime }+16 y = 0
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }+4 y = 0
\]
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\[
{} t y^{\prime \prime }+3 y = t
\]
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\[
{} \left (t -1\right ) y^{\prime \prime }-3 t y^{\prime }+4 y = \sin \left (t \right )
\]
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\[
{} t \left (t -4\right ) y^{\prime \prime }+3 t y^{\prime }+4 y = 2
\]
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\[
{} y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+3 \ln \left (t \right ) y = 0
\]
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\[
{} \left (x +3\right ) y^{\prime \prime }+x y^{\prime }+y \ln \left (x \right ) = 0
\]
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\[
{} \left (x -2\right ) y^{\prime \prime }+y^{\prime }+\left (x -2\right ) \tan \left (x \right ) y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\frac {\alpha \left (\alpha +1\right ) \mu ^{2} y}{-x^{2}+1} = 0
\]
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\[
{} y^{\prime \prime }-\frac {t}{y} = \frac {1}{\pi }
\]
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\[
{} t^{2} y^{\prime \prime }-2 y = 0
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\]
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\[
{} y^{\prime \prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\]
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\[
{} \left (1-x \cot \left (x \right )\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }-2 y = 0
\]
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\[
{} a y^{\prime \prime }+b y^{\prime }+c y = 0
\]
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✓ |
✓ |
✓ |
|
|
\[
{} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|