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Mathematica |
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\[
{}\left (a +\left (x +y\right ) x \right ) y^{\prime } = b \left (x +y\right ) y
\] |
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\[
{}\left (\operatorname {g0} \left (x \right )+y \operatorname {g1} \left (x \right )\right ) y^{\prime } = \operatorname {f0} \left (x \right )+\operatorname {f1} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\operatorname {f3} \left (x \right ) y^{3}
\] |
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\[
{}{y^{\prime }}^{2} = f \left (x \right )^{2} \left (y-u \left (x \right )\right )^{2} \left (y-a \right ) \left (y-b \right )
\] |
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\[
{}x^{2} {y^{\prime }}^{2}+x \left (x^{2}+x y-2 y\right ) y^{\prime }+\left (1-x \right ) \left (x^{2}-y\right ) y = 0
\] |
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\[
{}\left (a^{2}-2 a x y+y^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2} = 0
\] |
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\[
{}{y^{\prime }}^{3}-x y^{\prime }+a y = 0
\] |
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\[
{}{y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\] |
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\[
{}{y^{\prime }}^{3}-2 x y^{\prime }-y = 0
\] |
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\[
{}{y^{\prime }}^{3}+{\mathrm e}^{3 x -2 y} \left (y^{\prime }-1\right ) = 0
\] |
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\[
{}{y^{\prime }}^{3}+{\mathrm e}^{-2 y} \left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x -2 y} = 0
\] |
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\[
{}{y^{\prime }}^{3}+\operatorname {a0} {y^{\prime }}^{2}+\operatorname {a1} y^{\prime }+\operatorname {a2} +\operatorname {a3} y = 0
\] |
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\[
{}2 {y^{\prime }}^{3}+x y^{\prime }-2 y = 0
\] |
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\[
{}2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y = 0
\] |
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\[
{}8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2} = 27 x +27 y
\] |
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\[
{}x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2} x^{2}+x \left (x^{5}+3 y^{2}\right ) y^{\prime }-2 x^{5} y-y^{3} = 0
\] |
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\[
{}x^{6} {y^{\prime }}^{3}-x y^{\prime }-y = 0
\] |
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\[
{}y^{2} {y^{\prime }}^{3}-x y^{\prime }+y = 0
\] |
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\[
{}y^{3} {y^{\prime }}^{3}-\left (1-3 x \right ) y^{2} {y^{\prime }}^{2}+3 x^{2} y y^{\prime }+x^{3}-y^{2} = 0
\] |
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\[
{}{y^{\prime }}^{4}+x y^{\prime }-3 y = 0
\] |
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\[
{}x^{2} \left ({y^{\prime }}^{6}+3 y^{4}+3 y^{2}+1\right ) = a^{2}
\] |
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\[
{}\frac {x^{n} y^{\prime }}{b y^{2}-c \,x^{2 a}}-\frac {a y x^{a -1}}{b y^{2}-c \,x^{2 a}}+x^{a -1} = 0
\] |
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\[
{}x +y+\left (3 x +3 y-4\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
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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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\[
{}s^{2}+s^{\prime } = \frac {s+1}{s t}
\] |
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\[
{}x^{\prime }+t x = {\mathrm e}^{x}
\] |
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\[
{}x x^{\prime }+t^{2} x = \sin \left (t \right )
\] |
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\[
{}{y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y = 0
\] |
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\[
{}x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y = 0
\] |
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\[
{}u^{\prime \prime }+u^{\prime }+u = \cos \left (r +u\right )
\] |
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\[
{}x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x = 0
\] |
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\[
{}\sin \left (x^{\prime }\right )+y^{3} x = \sin \left (y \right )
\] |
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\[
{}y^{\prime \prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime }+4 y = 0
\] |
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\[
{}2 y^{\prime \prime }-3 y^{2} = 0
\] |
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\[
{}y^{\prime } = 6 \sqrt {y}+5 x^{3}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\] |
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\[
{}y^{\prime } = \sqrt {1+y^{2}}\, \sin \left (y\right )^{2}
\] |
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\[
{}y^{\prime } = -\frac {5+8 x}{3 y^{2}+1}
\] |
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\[
{}y^{\prime } = -\frac {5+8 x}{3 y^{2}+1}
\] |
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\[
{}y^{\prime } = -\frac {5+8 x}{3 y^{2}+1}
\] |
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\[
{}y^{\prime } = -\frac {5+8 x}{3 y^{2}+1}
\] |
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\[
{}x y^{\prime }-4 y = x^{6} {\mathrm e}^{x}
\] |
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\[
{}x^{2}+2 x y-y^{2}+\left (y^{2}+2 x y-x^{2}\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime \prime }-2 x y^{\prime \prime }+4 x^{2} y^{\prime }+8 x^{3} y = 0
\] |
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\[
{}y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y \,{\mathrm e}^{x} = 0
\] |
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\[
{}y^{\prime \prime }+\sin \left (y\right ) = 0
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )+x y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{2} \left (x \right )+x^{3} y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 x y_{1} \left (x \right )-y_{2} \left (x \right )+{\mathrm e}^{x} y_{3} \left (x \right )]
\] |
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\[
{}x \ln \left (x \right ) y^{\prime }+y = 3 x^{3}
\] |
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\[
{}2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime }
\] |
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\[
{}y^{\prime \prime } = y^{\prime } {\mathrm e}^{y}
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right )+1, y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = t y \left (t \right )+1, y^{\prime }\left (t \right ) = -t x \left (t \right )+y \left (t \right )]
\] |
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\[
{}y^{\prime } = y+x \,{\mathrm e}^{y}
\] |
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\[
{}y^{\prime \prime }+5 x y^{\prime }+\sqrt {x}\, y = 0
\] |
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\[
{}y = x^{6} {y^{\prime }}^{3}-x y^{\prime }
\] |
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\[
{}2 {y^{\prime }}^{3}+x y^{\prime }-2 y = 0
\] |
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\[
{}{y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\] |
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\[
{}2 y^{\prime \prime } = \sin \left (2 y\right )
\] |
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\[
{}2 y^{\prime \prime } = \sin \left (2 y\right )
\] |
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\[
{}{y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }+x^{2} = 0
\] |
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\[
{}{y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right )
\] |
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\[
{}{y^{\prime }}^{4}+x y^{\prime }-3 y = 0
\] |
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\[
{}{y^{\prime }}^{3}-2 x y^{\prime }-y = 0
\] |
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\[
{}y^{\prime } = \sqrt {-y^{2}-x^{2}+1}
\] |
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\[
{}y^{\prime } = -4 \sin \left (x -y\right )-4
\] |
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\[
{}y y^{\prime \prime } = x
\] |
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\[
{}y^{2} y^{\prime \prime } = x
\] |
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\[
{}3 y y^{\prime \prime } = \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{2} = 0
\] |
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\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{3} = 0
\] |
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\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{3}-x^{2} = 0
\] |
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\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2} = 0
\] |
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\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x y-x^{3}-x^{2} = 0
\] |
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\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{4}-x^{3} = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = x
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y {y^{\prime }}^{2} = 0
\] |
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\[
{}{y^{\prime }}^{2}+y^{2} = \sec \left (x \right )^{4}
\] |
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\[
{}\frac {x y^{\prime \prime }}{-x^{2}+1}+y = 0
\] |
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\[
{}y^{\prime } = \frac {x y+3 x -2 y+6}{x y-3 x -2 y+6}
\] |
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\[
{}y^{\prime } = \cos \left (x \right )+\frac {y^{2}}{x}
\] |
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\[
{}t y^{\prime }+y = t
\] |
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\[
{}t y^{\prime }+y = 0
\] |
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\[
{}{y^{\prime \prime }}^{2}+y^{\prime }+y = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 4 \cos \left (\ln \left (1+x \right )\right )
\] |
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\[
{}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0
\] |
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\[
{}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0
\] |
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\[
{}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0
\] |
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\[
{}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0
\] |
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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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\[
{}y^{\prime }+a \phi ^{\prime }\left (x \right ) y^{3}+6 a \phi \left (x \right ) y^{2}+\frac {\left (2 a +1\right ) y \phi ^{\prime \prime }\left (x \right )}{\phi ^{\prime }\left (x \right )}+2 a +2 = 0
\] |
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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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\[
{}y^{\prime }-f \left (x \right ) y^{n}-g \left (x \right ) y-h \left (x \right ) = 0
\] |
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