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Mathematica |
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\[
{}x \left (1-x \right ) y^{\prime }+2-3 x y+y = 0
\] |
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\[
{}x \left (1+x \right ) y^{\prime } = \left (1+x \right ) \left (x^{2}-1\right )+\left (x^{2}+x -1\right ) y
\] |
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\[
{}\left (x -2\right ) \left (x -3\right ) y^{\prime }+x^{2}-8 y+3 x y = 0
\] |
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\[
{}x \left (x +a \right ) y^{\prime } = \left (b +c y\right ) y
\] |
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\[
{}\left (x +a \right )^{2} y^{\prime } = 2 \left (x +a \right ) \left (b +y\right )
\] |
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\[
{}\left (x -a \right )^{2} y^{\prime }+k \left (x +y-a \right )^{2}+y^{2} = 0
\] |
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\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k y = 0
\] |
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\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime } = \left (x -a \right ) \left (x -b \right )+\left (2 x -a -b \right ) y
\] |
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\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime } = c y^{2}
\] |
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\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (y-a \right ) \left (y-b \right ) = 0
\] |
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\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2} = 0
\] |
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\[
{}2 x^{2} y^{\prime } = y
\] |
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\[
{}2 x^{2} y^{\prime }+x \cot \left (x \right )-1+2 x^{2} y \cot \left (x \right ) = 0
\] |
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\[
{}2 x^{2} y^{\prime }+1+2 x y-x^{2} y^{2} = 0
\] |
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\[
{}2 x^{2} y^{\prime } = 2 x y+\left (1-x \cot \left (x \right )\right ) \left (x^{2}-y^{2}\right )
\] |
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\[
{}2 \left (-x^{2}+1\right ) y^{\prime } = \sqrt {-x^{2}+1}+\left (1+x \right ) y
\] |
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\[
{}x \left (1-2 x \right ) y^{\prime }+1+\left (1-4 x \right ) y = 0
\] |
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\[
{}x \left (1-2 x \right ) y^{\prime } = 4 x -\left (4 x +1\right ) y+y^{2}
\] |
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\[
{}2 x \left (1-x \right ) y^{\prime }+x +\left (1-2 x \right ) y = 0
\] |
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\[
{}2 x \left (1-x \right ) y^{\prime }+x +\left (1-x \right ) y^{2} = 0
\] |
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\[
{}2 \left (x^{2}+x +1\right ) y^{\prime } = 1+8 x^{2}-\left (2 x +1\right ) y
\] |
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\[
{}4 \left (x^{2}+1\right ) y^{\prime }-4 x y-x^{2} = 0
\] |
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\[
{}a \,x^{2} y^{\prime } = x^{2}+a x y+y^{2} b^{2}
\] |
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\[
{}\left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2}
\] |
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\[
{}\left (b \,x^{2}+a \right ) y^{\prime } = c x y \ln \left (y\right )
\] |
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\[
{}x \left (a x +1\right ) y^{\prime }+a -y = 0
\] |
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\[
{}\left (b x +a \right )^{2} y^{\prime }+c y^{2}+\left (b x +a \right ) y^{3} = 0
\] |
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\[
{}x^{3} y^{\prime } = a +b \,x^{2} y
\] |
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\[
{}x^{3} y^{\prime } = 3-x^{2}+x^{2} y
\] |
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\[
{}x^{3} y^{\prime } = x^{4}+y^{2}
\] |
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\[
{}x^{3} y^{\prime } = y \left (x^{2}+y\right )
\] |
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\[
{}x^{3} y^{\prime } = x^{2} \left (y-1\right )+y^{2}
\] |
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\[
{}x^{3} y^{\prime } = \left (1+x \right ) y^{2}
\] |
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\[
{}x^{3} y^{\prime }+20+x^{2} y \left (1-x^{2} y\right ) = 0
\] |
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\[
{}x^{3} y^{\prime }+3+\left (3-2 x \right ) x^{2} y-y^{2} x^{6} = 0
\] |
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\[
{}x^{3} y^{\prime } = \left (2 x^{2}+y^{2}\right ) y
\] |
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\[
{}x^{3} y^{\prime } = \cos \left (y\right ) \left (\cos \left (y\right )-2 x^{2} \sin \left (y\right )\right )
\] |
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\[
{}x \left (x^{2}+1\right ) y^{\prime } = a \,x^{2}+y
\] |
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\[
{}x \left (-x^{2}+1\right ) y^{\prime } = a \,x^{2}+y
\] |
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\[
{}x \left (x^{2}+1\right ) y^{\prime } = a \,x^{3}+y
\] |
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\[
{}x \left (x^{2}+1\right ) y^{\prime } = a -x^{2} y
\] |
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\[
{}x \left (x^{2}+1\right ) y^{\prime } = \left (-x^{2}+1\right ) y
\] |
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\[
{}x \left (-x^{2}+1\right ) y^{\prime } = \left (x^{2}-x +1\right ) y
\] |
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\[
{}x \left (-x^{2}+1\right ) y^{\prime } = a \,x^{3}+\left (-2 x^{2}+1\right ) y
\] |
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\[
{}x \left (-x^{2}+1\right ) y^{\prime } = x^{3} \left (-x^{2}+1\right )+\left (-2 x^{2}+1\right ) y
\] |
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\[
{}x \left (x^{2}+1\right ) y^{\prime } = 2-4 x^{2} y
\] |
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\[
{}x \left (x^{2}+1\right ) y^{\prime } = x -\left (5 x^{2}+3\right ) y
\] |
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\[
{}x \left (-x^{2}+1\right ) y^{\prime }+x^{2}+\left (-x^{2}+1\right ) y^{2} = 0
\] |
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\[
{}x^{2} \left (1-x \right ) y^{\prime } = \left (2-x \right ) x y-y^{2}
\] |
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\[
{}2 x^{3} y^{\prime } = \left (x^{2}-y^{2}\right ) y
\] |
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\[
{}2 x^{3} y^{\prime } = \left (3 x^{2}+y^{2} a \right ) y
\] |
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\[
{}6 x^{3} y^{\prime } = 4 x^{2} y+\left (1-3 x \right ) y^{4}
\] |
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\[
{}x \left (c \,x^{2}+b x +a \right ) y^{\prime }+x^{2}-\left (c \,x^{2}+b x +a \right ) y = y^{2}
\] |
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\[
{}x^{4} y^{\prime } = \left (x^{3}+y\right ) y
\] |
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\[
{}x^{4} y^{\prime }+a^{2}+y^{2} x^{4} = 0
\] |
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\[
{}x^{4} y^{\prime }+x^{3} y+\csc \left (x y\right ) = 0
\] |
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\[
{}\left (-x^{4}+1\right ) y^{\prime } = 2 x \left (1-y^{2}\right )
\] |
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\[
{}x \left (-x^{3}+1\right ) y^{\prime } = 2 x -\left (-4 x^{3}+1\right ) y
\] |
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\[
{}x \left (-x^{3}+1\right ) y^{\prime } = x^{2}+\left (1-2 x y\right ) y
\] |
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\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime } = \left (x -3 x^{3} y\right ) y
\] |
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\[
{}x \left (-2 x^{3}+1\right ) y^{\prime } = 2 \left (-x^{3}+1\right ) y
\] |
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\[
{}\left (c \,x^{2}+b x +a \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0
\] |
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\[
{}x^{5} y^{\prime } = 1-3 x^{4} y
\] |
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\[
{}x \left (-x^{4}+1\right ) y^{\prime } = 2 x \left (x^{2}-y^{2}\right )+\left (-x^{4}+1\right ) y
\] |
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\[
{}x^{7} y^{\prime }+5 y^{2} x^{3}+2 \left (x^{2}+1\right ) y^{3} = 0
\] |
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\[
{}x^{n} y^{\prime } = a +b \,x^{n -1} y
\] |
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\[
{}x^{n} y^{\prime } = x^{2 n -1}-y^{2}
\] |
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\[
{}x^{n} y^{\prime }+x^{2 n -2}+y^{2}+\left (1-n \right ) x^{n -1} = 0
\] |
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\[
{}x^{n} y^{\prime } = a^{2} x^{2 n -2}+y^{2} b^{2}
\] |
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\[
{}x^{n} y^{\prime } = x^{n -1} \left (a \,x^{2 n}+n y-b y^{2}\right )
\] |
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\[
{}x^{k} y^{\prime } = a \,x^{m}+b y^{n}
\] |
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\[
{}y^{\prime } \sqrt {x^{2}+1} = 2 x -y
\] |
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\[
{}y^{\prime } \sqrt {-x^{2}+1} = 1+y^{2}
\] |
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\[
{}\left (x -\sqrt {x^{2}+1}\right ) y^{\prime } = y+\sqrt {1+y^{2}}
\] |
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\[
{}y^{\prime } \sqrt {a^{2}+x^{2}}+x +y = \sqrt {a^{2}+x^{2}}
\] |
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\[
{}y^{\prime } \sqrt {b^{2}+x^{2}} = \sqrt {y^{2}+a^{2}}
\] |
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\[
{}y^{\prime } \sqrt {b^{2}-x^{2}} = \sqrt {a^{2}-y^{2}}
\] |
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\[
{}x y^{\prime } \sqrt {a^{2}+x^{2}} = y \sqrt {b^{2}+y^{2}}
\] |
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\[
{}x y^{\prime } \sqrt {-a^{2}+x^{2}} = y \sqrt {y^{2}-b^{2}}
\] |
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\[
{}y^{\prime } \sqrt {X}+\sqrt {Y} = 0
\] |
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\[
{}y^{\prime } \sqrt {X} = \sqrt {Y}
\] |
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\[
{}x^{{3}/{2}} y^{\prime } = a +b \,x^{{3}/{2}} y^{2}
\] |
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\[
{}y^{\prime } \sqrt {x^{3}+1} = \sqrt {y^{3}+1}
\] |
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\[
{}y^{\prime } \sqrt {x \left (1-x \right ) \left (-a x +1\right )} = \sqrt {y \left (1-y\right ) \left (1-a y\right )}
\] |
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\[
{}y^{\prime } \sqrt {-x^{4}+1} = \sqrt {1-y^{4}}
\] |
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\[
{}y^{\prime } \sqrt {x^{4}+x^{2}+1} = \sqrt {1+y^{2}+y^{4}}
\] |
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\[
{}y^{\prime } \sqrt {X} = 0
\] |
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\[
{}y^{\prime } \sqrt {X}+\sqrt {Y} = 0
\] |
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\[
{}y^{\prime } \sqrt {X} = \sqrt {Y}
\] |
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\[
{}y^{\prime } \left (x^{3}+1\right )^{{2}/{3}}+\left (y^{3}+1\right )^{{2}/{3}} = 0
\] |
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\[
{}y^{\prime } \left (4 x^{3}+\operatorname {a1} x +\operatorname {a0} \right )^{{2}/{3}}+\left (\operatorname {a0} +\operatorname {a1} y+4 y^{3}\right )^{{2}/{3}} = 0
\] |
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\[
{}X^{{2}/{3}} y^{\prime } = Y^{{2}/{3}}
\] |
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\[
{}y^{\prime } \left (a +\cos \left (\frac {x}{2}\right )^{2}\right ) = y \tan \left (\frac {x}{2}\right ) \left (1+a +\cos \left (\frac {x}{2}\right )^{2}-y\right )
\] |
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\[
{}\left (1-4 \cos \left (x \right )^{2}\right ) y^{\prime } = \tan \left (x \right ) \left (1+4 \cos \left (x \right )^{2}\right ) y
\] |
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\[
{}\left (1-\sin \left (x \right )\right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
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\[
{}\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y \left (\cos \left (x \right )+\sin \left (x \right )\right ) = 0
\] |
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\[
{}\left (\operatorname {a0} +\operatorname {a1} \sin \left (x \right )^{2}\right ) y^{\prime }+\operatorname {a2} x \left (\operatorname {a3} +\operatorname {a1} \sin \left (x \right )^{2}\right )+\operatorname {a1} y \sin \left (2 x \right ) = 0
\] |
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\[
{}\left (x -{\mathrm e}^{x}\right ) y^{\prime }+x \,{\mathrm e}^{x}+\left (1-{\mathrm e}^{x}\right ) y = 0
\] |
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\[
{}y^{\prime } x \ln \left (x \right ) = a x \left (\ln \left (x \right )+1\right )-y
\] |
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\[
{}y y^{\prime }+x = 0
\] |
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