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ODE |
Mathematica |
Maple |
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\[
{}\left (\cot \left (x \right )-2 y^{2}\right ) y^{\prime } = y^{3} \csc \left (x \right ) \sec \left (x \right )
\] |
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\[
{}3 y^{\prime } y^{2} = 1+x +a y^{3}
\] |
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\[
{}\left (x^{2}-3 y^{2}\right ) y^{\prime }+1+2 x y = 0
\] |
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\[
{}\left (2 x^{2}+3 y^{2}\right ) y^{\prime }+x \left (3 x +y\right ) = 0
\] |
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\[
{}3 \left (x^{2}-y^{2}\right ) y^{\prime }+3 \,{\mathrm e}^{x}+6 x y \left (1+x \right )-2 y^{3} = 0
\] |
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\[
{}\left (3 x^{2}+2 x y+4 y^{2}\right ) y^{\prime }+2 x^{2}+6 x y+y^{2} = 0
\] |
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\[
{}\left (1-3 x +2 y\right )^{2} y^{\prime } = \left (4+2 x -3 y\right )^{2}
\] |
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\[
{}\left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }+x^{2}-3 x y^{2} = 0
\] |
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\[
{}\left (x -6 y\right )^{2} y^{\prime }+a +2 x y-6 y^{2} = 0
\] |
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\[
{}\left (x^{2}+y^{2} a \right ) y^{\prime } = x y
\] |
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\[
{}\left (x^{2}+x y+y^{2} a \right ) y^{\prime } = a \,x^{2}+x y+y^{2}
\] |
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\[
{}\left (a \,x^{2}+2 x y-y^{2} a \right ) y^{\prime }+x^{2}-2 a x y-y^{2} = 0
\] |
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\[
{}\left (a \,x^{2}+2 b x y+c y^{2}\right ) y^{\prime }+k \,x^{2}+2 a x y+b y^{2} = 0
\] |
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\[
{}x \left (1-y^{2}\right ) y^{\prime } = \left (x^{2}+1\right ) y
\] |
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\[
{}x \left (3 x -y^{2}\right ) y^{\prime }+\left (5 x -2 y^{2}\right ) y = 0
\] |
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\[
{}x \left (x^{2}+y^{2}\right ) y^{\prime } = \left (x^{2}+x^{4}+y^{2}\right ) y
\] |
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\[
{}x \left (1-x^{2}+y^{2}\right ) y^{\prime }+\left (-y^{2}+x^{2}+1\right ) y = 0
\] |
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\[
{}x \left (a -x^{2}-y^{2}\right ) y^{\prime }+\left (a +x^{2}+y^{2}\right ) y = 0
\] |
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\[
{}x \left (2 x^{2}+y^{2}\right ) y^{\prime } = \left (2 x^{2}+3 y^{2}\right ) y
\] |
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\[
{}\left (x \left (a -x^{2}-y^{2}\right )+y\right ) y^{\prime }+x -\left (a -x^{2}-y^{2}\right ) y = 0
\] |
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\[
{}x \left (a +y\right )^{2} y^{\prime } = b y^{2}
\] |
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\[
{}x \left (x^{2}-x y+y^{2}\right ) y^{\prime }+\left (y^{2}+x y+x^{2}\right ) y = 0
\] |
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\[
{}x \left (x^{2}-x y-y^{2}\right ) y^{\prime } = \left (x^{2}+x y-y^{2}\right ) y
\] |
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\[
{}x \left (x^{2}+a x y+y^{2}\right ) y^{\prime } = \left (x^{2}+b x y+y^{2}\right ) y
\] |
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\[
{}x \left (x^{2}-2 y^{2}\right ) y^{\prime } = \left (2 x^{2}-y^{2}\right ) y
\] |
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\[
{}x \left (2 y^{2}+x^{2}\right ) y^{\prime } = \left (2 x^{2}+3 y^{2}\right ) y
\] |
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\[
{}2 x \left (5 x^{2}+y^{2}\right ) y^{\prime } = x^{2} y-y^{3}
\] |
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\[
{}x \left (x^{2}+a x y+2 y^{2}\right ) y^{\prime } = \left (a x +2 y\right ) y^{2}
\] |
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\[
{}3 y^{2} y^{\prime } x = 2 x -y^{3}
\] |
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\[
{}\left (1-4 x +3 x y^{2}\right ) y^{\prime } = \left (2-y^{2}\right ) y
\] |
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\[
{}x \left (x -3 y^{2}\right ) y^{\prime }+\left (2 x -y^{2}\right ) y = 0
\] |
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\[
{}3 x \left (y^{2}+x \right ) y^{\prime }+x^{3}-3 x y-2 y^{3} = 0
\] |
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\[
{}x \left (x^{3}-3 x^{3} y+4 y^{2}\right ) y^{\prime } = 6 y^{3}
\] |
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\[
{}6 y^{2} y^{\prime } x +x +2 y^{3} = 0
\] |
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\[
{}x \left (x +6 y^{2}\right ) y^{\prime }+x y-3 y^{3} = 0
\] |
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\[
{}x \left (x^{2}-6 y^{2}\right ) y^{\prime } = 4 \left (x^{2}+3 y^{2}\right ) y
\] |
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\[
{}x \left (3 x -7 y^{2}\right ) y^{\prime }+\left (5 x -3 y^{2}\right ) y = 0
\] |
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\[
{}y^{2} y^{\prime } x^{2}+1-x +x^{3} = 0
\] |
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\[
{}\left (1-x^{2} y^{2}\right ) y^{\prime } = x y^{3}
\] |
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\[
{}\left (1-x^{2} y^{2}\right ) y^{\prime } = \left (x y+1\right ) y^{2}
\] |
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\[
{}x \left (x y^{2}+1\right ) y^{\prime }+y = 0
\] |
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\[
{}x \left (x y^{2}+1\right ) y^{\prime } = \left (2-3 x y^{2}\right ) y
\] |
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\[
{}x^{2} \left (a +y\right )^{2} y^{\prime } = \left (x^{2}+1\right ) \left (y^{2}+a^{2}\right )
\] |
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\[
{}\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y^{2}\right ) = 0
\] |
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\[
{}\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y\right )^{2} = 0
\] |
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\[
{}\left (1-x^{3}+6 x^{2} y^{2}\right ) y^{\prime } = \left (6+3 x y-4 y^{3}\right ) x
\] |
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\[
{}x \left (3+5 x -12 x y^{2}+4 x^{2} y\right ) y^{\prime }+\left (3+10 x -8 x y^{2}+6 x^{2} y\right ) y = 0
\] |
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\[
{}x^{3} \left (1+y^{2}\right ) y^{\prime }+3 x^{2} y = 0
\] |
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\[
{}x \left (1-x y\right )^{2} y^{\prime }+\left (1+x^{2} y^{2}\right ) y = 0
\] |
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\[
{}\left (1-y^{2} x^{4}\right ) y^{\prime } = x^{3} y^{3}
\] |
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\[
{}\left (3 x -y^{3}\right ) y^{\prime } = x^{2}-3 y
\] |
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\[
{}\left (x^{3}-y^{3}\right ) y^{\prime }+x^{2} y = 0
\] |
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\[
{}\left (y^{3}+x^{3}\right ) y^{\prime }+x^{2} \left (a x +3 y\right ) = 0
\] |
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\[
{}\left (x -x^{2} y-y^{3}\right ) y^{\prime } = x^{3}-y+x y^{2}
\] |
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\[
{}\left (x \,a^{2}+y \left (x^{2}-y^{2}\right )\right ) y^{\prime }+x \left (x^{2}-y^{2}\right ) = a^{2} y
\] |
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\[
{}\left (a +x^{2}+y^{2}\right ) y y^{\prime } = x \left (a -x^{2}-y^{2}\right )
\] |
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\[
{}\left (3 x^{2}+y^{2}\right ) y y^{\prime }+x \left (x^{2}+3 y^{2}\right ) = 0
\] |
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\[
{}\left (a -3 x^{2}-y^{2}\right ) y y^{\prime }+x \left (a -x^{2}+y^{2}\right ) = 0
\] |
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\[
{}2 y^{3} y^{\prime } = x^{3}-x y^{2}
\] |
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\[
{}y \left (2 y^{2}+1\right ) y^{\prime } = x \left (2 x^{2}+1\right )
\] |
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\[
{}\left (3 x^{2}+2 y^{2}\right ) y y^{\prime }+x^{3} = 0
\] |
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\[
{}\left (5 x^{2}+2 y^{2}\right ) y y^{\prime }+x \left (x^{2}+5 y^{2}\right ) = 0
\] |
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\[
{}\left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3} = 0
\] |
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\[
{}\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3} = 0
\] |
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\[
{}\left (x^{3}+a y^{3}\right ) y^{\prime } = x^{2} y
\] |
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\[
{}x y^{3} y^{\prime } = \left (-x^{2}+1\right ) \left (1+y^{2}\right )
\] |
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\[
{}x \left (x -y^{3}\right ) y^{\prime } = \left (3 x +y^{3}\right ) y
\] |
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\[
{}x \left (y^{3}+2 x^{3}\right ) y^{\prime } = \left (2 x^{3}-x^{2} y+y^{3}\right ) y
\] |
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\[
{}x \left (-y^{3}+2 x^{3}\right ) y^{\prime } = \left (-2 y^{3}+x^{3}\right ) y
\] |
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\[
{}x \left (x^{3}+3 x^{2} y+y^{3}\right ) y^{\prime } = \left (3 x^{2}+y^{2}\right ) y^{2}
\] |
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\[
{}x \left (-2 y^{3}+x^{3}\right ) y^{\prime } = \left (-y^{3}+2 x^{3}\right ) y
\] |
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\[
{}x \left (x^{4}-2 y^{3}\right ) y^{\prime }+\left (2 x^{4}+y^{3}\right ) y = 0
\] |
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\[
{}x \left (x +y+2 y^{3}\right ) y^{\prime } = y \left (x -y\right )
\] |
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\[
{}\left (5 x -y-7 x y^{3}\right ) y^{\prime }+5 y-y^{4} = 0
\] |
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\[
{}x \left (1-2 x y^{3}\right ) y^{\prime }+\left (1-2 x^{3} y\right ) y = 0
\] |
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\[
{}x \left (2-x y^{2}-2 x y^{3}\right ) y^{\prime }+1+2 y = 0
\] |
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\[
{}\left (2-10 x^{2} y^{3}+3 y^{2}\right ) y^{\prime } = x \left (1+5 y^{4}\right )
\] |
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\[
{}x \left (a +b x y^{3}\right ) y^{\prime }+\left (a +c \,x^{3} y\right ) y = 0
\] |
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\[
{}x \left (1-2 x^{2} y^{3}\right ) y^{\prime }+\left (1-2 y^{2} x^{3}\right ) y = 0
\] |
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\[
{}x \left (1-x y\right ) \left (1-x^{2} y^{2}\right ) y^{\prime }+\left (x y+1\right ) \left (1+x^{2} y^{2}\right ) y = 0
\] |
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\[
{}\left (x^{2}-y^{4}\right ) y^{\prime } = x y
\] |
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\[
{}\left (x^{3}-y^{4}\right ) y^{\prime } = 3 x^{2} y
\] |
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\[
{}\left (a^{2} x^{2}+\left (x^{2}+y^{2}\right )^{2}\right ) y^{\prime } = a^{2} y x
\] |
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\[
{}2 \left (x -y^{4}\right ) y^{\prime } = y
\] |
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\[
{}\left (4 x -x y^{3}-2 y^{4}\right ) y^{\prime } = \left (2+y^{3}\right ) y
\] |
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\[
{}\left (a \,x^{3}+\left (a x +b y\right )^{3}\right ) y y^{\prime }+x \left (\left (a x +b y\right )^{3}+b y^{3}\right ) = 0
\] |
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\[
{}\left (x +2 y+2 x^{2} y^{3}+y^{4} x \right ) y^{\prime }+\left (y^{4}+1\right ) y = 0
\] |
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\[
{}2 x \left (x^{3}+y^{4}\right ) y^{\prime } = \left (x^{3}+2 y^{4}\right ) y
\] |
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\[
{}x \left (1-x^{2} y^{4}\right ) y^{\prime }+y = 0
\] |
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\[
{}\left (x^{2}-y^{5}\right ) y^{\prime } = 2 x y
\] |
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\[
{}x \left (x^{3}+y^{5}\right ) y^{\prime } = \left (x^{3}-y^{5}\right ) y
\] |
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\[
{}x^{3} \left (1+5 x^{3} y^{7}\right ) y^{\prime }+\left (3 x^{5} y^{5}-1\right ) y^{3} = 0
\] |
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\[
{}\left (1+a \left (x +y\right )\right )^{n} y^{\prime }+a \left (x +y\right )^{n} = 0
\] |
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\[
{}x \left (a +x y^{n}\right ) y^{\prime }+b y = 0
\] |
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\[
{}f \left (x \right ) y^{m} y^{\prime }+g \left (x \right ) y^{m +1}+h \left (x \right ) y^{n} = 0
\] |
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\[
{}y^{\prime } \sqrt {b^{2}+y^{2}} = \sqrt {a^{2}+x^{2}}
\] |
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\[
{}y^{\prime } \sqrt {b^{2}-y^{2}} = \sqrt {a^{2}-x^{2}}
\] |
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\[
{}y^{\prime } \sqrt {y} = \sqrt {x}
\] |
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\[
{}\left (1+\sqrt {x +y}\right ) y^{\prime }+1 = 0
\] |
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\[
{}y^{\prime } \sqrt {x y}+x -y = \sqrt {x y}
\] |
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