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Mathematica |
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\[
{} y^{\prime \prime }-x y^{\prime }-3 y = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }+2 y = 0
\]
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\[
{} x \left (1+x \right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (x -1\right ) y = 0
\]
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\[
{} x y^{\prime \prime }+x y^{\prime }-2 y = 0
\]
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\[
{} x \left (x -1\right )^{2} y^{\prime \prime }-2 y = 0
\]
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\[
{} y^{\prime \prime }-2 x y^{\prime }+x^{2} y = 0
\]
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\[
{} x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right ) = 0
\]
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\[
{} x^{2} \left (1+x \right ) y^{\prime \prime }-\left (2 x +1\right ) \left (x y^{\prime }-y\right ) = 0
\]
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\[
{} 2 x^{2} \left (2-x \right ) y^{\prime \prime }-x \left (4-x \right ) y^{\prime }+\left (3-x \right ) y = 0
\]
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\[
{} x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0
\]
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\[
{} x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0
\]
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\[
{} x \left (x +2\right ) y^{\prime \prime }+2 \left (1+x \right ) y^{\prime }-2 y = 0
\]
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\[
{} x \left (x +2\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }-4 y = 0
\]
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\[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
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\[
{} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0
\]
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\[
{} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }+2 y = 0
\]
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\[
{} \left (x +2\right ) y^{\prime \prime }+x y^{\prime }-y = 0
\]
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\[
{} \left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y = 0
\]
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\[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} 2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0
\]
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\[
{} x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime } x^{2}+x y = 0
\]
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\[
{} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }+x y^{\prime }+2 y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0
\]
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\[
{} x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = 0
\]
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\[
{} 2 x \left (x -1\right ) y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = 0
\]
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\[
{} x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (x -2\right ) y = 0
\]
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\[
{} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0
\]
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\[
{} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y = 0
\]
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\[
{} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0
\]
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\[
{} x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = 0
\]
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\[
{} x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0
\]
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\[
{} 2 x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-y = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime } x^{2}+\left (x^{4}+2 x -1\right ) y = 0
\]
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\[
{} u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (1+x \right )^{2}} = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y = 0
\]
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\[
{} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0
\]
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\[
{} x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+2 y = 0
\]
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\[
{} x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0
\]
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\[
{} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 y^{\prime } x^{2}+\left (1+x \right ) y = 0
\]
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\[
{} y^{\prime \prime } = \left (x^{2}+3\right ) y
\]
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\[
{} y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0
\]
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\[
{} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\]
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\[
{} \left (x^{2}-x \right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0
\]
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\[
{} y^{\prime \prime } = \frac {\left (4 x^{6}-8 x^{5}+12 x^{4}+4 x^{3}+7 x^{2}-20 x +4\right ) y}{4 x^{4}}
\]
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\[
{} y^{\prime \prime } = \left (\frac {x^{2}}{4}-\frac {11}{2}\right ) y
\]
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\[
{} y^{\prime \prime } = \left (x^{2}+3\right ) y
\]
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\[
{} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0
\]
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\[
{} y^{\prime }+y^{2}-a x -b = 0
\]
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\[
{} y^{\prime }+y^{2}+a \,x^{m} = 0
\]
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\[
{} y^{\prime }+y^{2}+\left (x y-1\right ) f \left (x \right ) = 0
\]
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\[
{} y^{\prime }-y^{2}-x y-x +1 = 0
\]
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\[
{} y^{\prime }-y^{2}+\left (x^{2}+1\right ) y-2 x = 0
\]
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\[
{} y^{\prime }-y^{2}+y \sin \left (x \right )-\cos \left (x \right ) = 0
\]
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\[
{} y^{\prime }-y^{2}-y \sin \left (2 x \right )-\cos \left (2 x \right ) = 0
\]
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\[
{} y^{\prime }+a y^{2}-b \,x^{\nu } = 0
\]
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\[
{} y^{\prime }+a y^{2}-b \,x^{2 \nu }-c \,x^{\nu -1} = 0
\]
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\[
{} y^{\prime }+a y \left (y-x \right )-1 = 0
\]
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\[
{} y^{\prime }+x^{-a -1} y^{2}-x^{a} = 0
\]
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\[
{} y^{\prime }+\sin \left (x \right ) y^{2}-\frac {2 \sin \left (x \right )}{\cos \left (x \right )^{2}} = 0
\]
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\[
{} y^{\prime }-\frac {y^{2} f^{\prime }\left (x \right )}{g \left (x \right )}+\frac {g^{\prime }\left (x \right )}{f \left (x \right )} = 0
\]
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\[
{} y^{\prime }+y^{3}+a x y^{2} = 0
\]
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\[
{} y^{\prime }-y^{3}-a \,{\mathrm e}^{x} y^{2} = 0
\]
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\[
{} -a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime } = 0
\]
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\[
{} y^{\prime }+3 a y^{3}+6 a x y^{2} = 0
\]
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\[
{} y^{\prime }-x \left (x +2\right ) y^{3}-\left (x +3\right ) y^{2} = 0
\]
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\[
{} y^{\prime }+\left (4 a^{2} x +3 a \,x^{2}+b \right ) y^{3}+3 x y^{2} = 0
\]
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\[
{} y^{\prime }+2 \left (a^{2} x^{3}-b^{2} x \right ) y^{3}+3 b y^{2} = 0
\]
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\[
{} y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1} = 0
\]
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\[
{} y^{\prime }-a \left (x^{n}-x \right ) y^{3}-y^{2} = 0
\]
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\[
{} y^{\prime }-\left (a \,x^{n}+b x \right ) y^{3}-c y^{2} = 0
\]
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\[
{} y^{\prime }-f_{3} \left (x \right ) y^{3}-f_{2} \left (x \right ) y^{2}-f_{1} \left (x \right ) y-f_{0} \left (x \right ) = 0
\]
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\[
{} y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {a f \left (x \right )+b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )} = 0
\]
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\[
{} y^{\prime }-a y^{n}-b \,x^{\frac {n}{-n +1}} = 0
\]
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\[
{} y^{\prime }-f \left (x \right )^{-n +1} g^{\prime }\left (x \right ) y^{n} \left (a g \left (x \right )+b \right )^{-n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-f \left (x \right ) g^{\prime }\left (x \right ) = 0
\]
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\[
{} y^{\prime }-a^{n} f \left (x \right )^{-n +1} g^{\prime }\left (x \right ) y^{n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-f \left (x \right ) g^{\prime }\left (x \right ) = 0
\]
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\[
{} y^{\prime }-f \left (x \right ) y^{n}-g \left (x \right ) y-h \left (x \right ) = 0
\]
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\[
{} y^{\prime }-f \left (x \right ) y^{a}-g \left (x \right ) y^{b} = 0
\]
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\[
{} y^{\prime }-a \sqrt {y}-b x = 0
\]
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