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ODE |
Mathematica |
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\[
{}x y^{\prime } = \left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y
\] |
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\[
{}x y^{\prime }+\left (1-\ln \left (x \right )-\ln \left (y\right )\right ) y = 0
\] |
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\[
{}x y^{\prime } = y-2 x \tanh \left (\frac {y}{x}\right )
\] |
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\[
{}x y^{\prime }+n y = f \left (x \right ) g \left (x^{n} y\right )
\] |
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\[
{}x y^{\prime } = y f \left (x^{m} y^{n}\right )
\] |
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\[
{}\left (1+x \right ) y^{\prime } = x^{3} \left (3 x +4\right )+y
\] |
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\[
{}\left (1+x \right ) y^{\prime } = \left (1+x \right )^{4}+2 y
\] |
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\[
{}\left (1+x \right ) y^{\prime } = {\mathrm e}^{x} \left (1+x \right )^{n +1}+n y
\] |
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\[
{}\left (1+x \right ) y^{\prime } = a y+b x y^{2}
\] |
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\[
{}\left (1+x \right ) y^{\prime }+y+\left (1+x \right )^{4} y^{3} = 0
\] |
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\[
{}\left (1+x \right ) y^{\prime } = \left (1-x y^{3}\right ) y
\] |
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\[
{}\left (1+x \right ) y^{\prime } = 1+y+\left (1+x \right ) \sqrt {1+y}
\] |
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\[
{}\left (x +a \right ) y^{\prime } = b x
\] |
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\[
{}\left (x +a \right ) y^{\prime } = b x +y
\] |
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\[
{}\left (x +a \right ) y^{\prime }+b \,x^{2}+y = 0
\] |
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\[
{}\left (x +a \right ) y^{\prime } = 2 \left (x +a \right )^{5}+3 y
\] |
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\[
{}\left (x +a \right ) y^{\prime } = b +c y
\] |
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\[
{}\left (x +a \right ) y^{\prime } = b x +c y
\] |
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\[
{}\left (x +a \right ) y^{\prime } = y \left (1-a y\right )
\] |
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\[
{}\left (a -x \right ) y^{\prime } = y+\left (c x +b \right ) y^{3}
\] |
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\[
{}2 x y^{\prime } = 2 x^{3}-y
\] |
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\[
{}2 x y^{\prime }+1 = 4 i x y+y^{2}
\] |
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\[
{}2 x y^{\prime } = y \left (1+y^{2}\right )
\] |
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\[
{}2 x y^{\prime }+y \left (1+y^{2}\right ) = 0
\] |
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\[
{}2 x y^{\prime } = \left (1+x -6 y^{2}\right ) y
\] |
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\[
{}2 x y^{\prime }+4 y+a +\sqrt {a^{2}-4 b -4 c y} = 0
\] |
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\[
{}\left (1-2 x \right ) y^{\prime } = 16+32 x -6 y
\] |
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\[
{}\left (2 x +1\right ) y^{\prime } = 4 \,{\mathrm e}^{-y}-2
\] |
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\[
{}2 \left (1-x \right ) y^{\prime } = 4 x \sqrt {1-x}+y
\] |
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\[
{}2 \left (1+x \right ) y^{\prime }+2 y+\left (1+x \right )^{4} y^{3} = 0
\] |
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\[
{}3 x y^{\prime } = 3 x^{{2}/{3}}+\left (1-3 y\right ) y
\] |
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\[
{}3 x y^{\prime } = \left (2+x y^{3}\right ) y
\] |
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\[
{}3 x y^{\prime } = \left (1+3 x y^{3} \ln \left (x \right )\right ) y
\] |
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\[
{}x^{2} y^{\prime } = -y+a
\] |
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\[
{}x^{2} y^{\prime } = a +b x +c \,x^{2}+x y
\] |
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\[
{}x^{2} y^{\prime } = a +b x +c \,x^{2}-x y
\] |
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\[
{}x^{2} y^{\prime }+\left (1-2 x \right ) y = x^{2}
\] |
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\[
{}x^{2} y^{\prime } = a +b x y
\] |
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\[
{}x^{2} y^{\prime } = \left (b x +a \right ) y
\] |
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\[
{}x^{2} y^{\prime }+x \left (x +2\right ) y = x \left (1-{\mathrm e}^{-2 x}\right )-2
\] |
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\[
{}x^{2} y^{\prime }+2 x \left (1-x \right ) y = {\mathrm e}^{x} \left (2 \,{\mathrm e}^{x}-1\right )
\] |
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\[
{}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0
\] |
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\[
{}x^{2} y^{\prime } = \left (1+2 x -y\right )^{2}
\] |
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\[
{}x^{2} y^{\prime } = a +b y^{2}
\] |
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\[
{}x^{2} y^{\prime } = \left (a y+x \right ) y
\] |
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\[
{}x^{2} y^{\prime } = \left (a x +b y\right ) y
\] |
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\[
{}x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2} = 0
\] |
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\[
{}x^{2} y^{\prime } = a +b \,x^{n}+x^{2} y^{2}
\] |
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\[
{}x^{2} y^{\prime }+2+x y \left (4+x y\right ) = 0
\] |
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\[
{}x^{2} y^{\prime }+2+a x \left (1-x y\right )-x^{2} y^{2} = 0
\] |
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\[
{}x^{2} y^{\prime } = a +b \,x^{2} y^{2}
\] |
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\[
{}x^{2} y^{\prime } = a +b \,x^{n}+c \,x^{2} y^{2}
\] |
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\[
{}x^{2} y^{\prime } = a +b x y+c \,x^{2} y^{2}
\] |
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\[
{}x^{2} y^{\prime } = a +b x y+c \,x^{4} y^{2}
\] |
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\[
{}x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y = 0
\] |
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\[
{}x^{2} y^{\prime } = 2 y \left (x -y^{2}\right )
\] |
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\[
{}x^{2} y^{\prime } = a \,x^{2} y^{2}-a y^{3}
\] |
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\[
{}x^{2} y^{\prime }+y^{2} a +b \,x^{2} y^{3} = 0
\] |
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\[
{}x^{2} y^{\prime } = \left (a x +b y^{3}\right ) y
\] |
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\[
{}x^{2} y^{\prime }+x y+\sqrt {y} = 0
\] |
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\[
{}x^{2} y^{\prime } = \sec \left (y\right )+3 x \tan \left (y\right )
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1-x^{2}+y
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime }+1 = x y
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime } = 5-x y
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime }+a +x y = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime }+a -x y = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime }+a -x y = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime }-x +x y = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime }-x^{2}+x y = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime }+x^{2}+x y = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (x^{2}+1\right )-x y
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (3 x^{2}-y\right )
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime }+2 x y = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime } = 2 x \left (x -y\right )
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime } = 2 x \left (x^{2}+1\right )^{2}+2 x y
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime }+\cos \left (x \right ) = 2 x y
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime } = \tan \left (x \right )-2 x y
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime } = a +4 x y
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime } = \left (2 b x +a \right ) y
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2}
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1-y^{2}
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1-y \left (2 x -y\right )
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime } = n \left (1-2 x y+y^{2}\right )
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right ) = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime } = x y \left (1+a y\right )
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2}-2 x y \left (1+y^{2}\right )
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right ) = x \left (x^{2}+1\right ) \cos \left (y\right )^{2}
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+x^{2}-y \,\operatorname {arccot}\left (x \right )
\] |
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\[
{}\left (-x^{2}+4\right ) y^{\prime }+4 y = \left (x +2\right ) y^{2}
\] |
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\[
{}\left (a^{2}+x^{2}\right ) y^{\prime } = b +x y
\] |
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\[
{}\left (a^{2}+x^{2}\right ) y^{\prime } = \left (b +y\right ) \left (x +\sqrt {a^{2}+x^{2}}\right )
\] |
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\[
{}\left (a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right ) = 0
\] |
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\[
{}\left (a^{2}+x^{2}\right ) y^{\prime } = a^{2}+3 x y-2 y^{2}
\] |
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\[
{}\left (a^{2}+x^{2}\right ) y^{\prime }+x y+b x y^{2} = 0
\] |
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\[
{}x \left (1-x \right ) y^{\prime } = a +\left (1+x \right ) y
\] |
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\[
{}x \left (1-x \right ) y^{\prime } = 2+2 x y
\] |
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\[
{}x \left (1-x \right ) y^{\prime } = 2 x y-2
\] |
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\[
{}x \left (1+x \right ) y^{\prime } = \left (1-2 x \right ) y
\] |
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\[
{}x \left (1-x \right ) y^{\prime }+\left (2 x +1\right ) y = a
\] |
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\[
{}x \left (1-x \right ) y^{\prime } = a +2 \left (2-x \right ) y
\] |
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