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ODE |
Mathematica |
Maple |
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\[
{}y y^{\prime }-\left (\left (2 n -1\right ) x -a n \right ) x^{-1-n} y = n \left (x -a \right ) x^{-2 n}
\] |
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\[
{}y y^{\prime }-\left (\left (n +1\right ) x -a n \right ) x^{n -1} \left (x -a \right )^{-n -2} y = n \,x^{2 n} \left (x -a \right )^{-2 n -3}
\] |
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\[
{}y y^{\prime }-a \left (\left (2 k -3\right ) x +1\right ) x^{-k} y = a^{2} \left (k -2\right ) \left (\left (k -1\right ) x +1\right ) x^{2-2 k}
\] |
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\[
{}y y^{\prime }-a \left (\left (n +2 k -3\right ) x +3-2 k \right ) x^{-k} y = a^{2} \left (\left (n +k -1\right ) x^{2}-\left (n +2 k -3\right ) x +k -2\right ) x^{1-2 k}
\] |
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\[
{}y y^{\prime }-\frac {a \left (\left (n +2\right ) x -2\right ) x^{-\frac {2 n +1}{n}} y}{n} = \frac {a^{2} \left (\left (n +1\right ) x^{2}-2 x -n +1\right ) x^{-\frac {3 n +2}{n}}}{n}
\] |
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\[
{}y y^{\prime }-\frac {a \left (\frac {\left (n +4\right ) x}{n +2}-2\right ) x^{-\frac {2 n +1}{n}} y}{n} = \frac {a^{2} \left (2 x^{2}+\left (n^{2}+n -4\right ) x -\left (n -1\right ) \left (n +2\right )\right ) x^{-\frac {3 n +2}{n}}}{n \left (n +2\right )}
\] |
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\[
{}y y^{\prime }+\frac {a \left (\frac {\left (3 n +5\right ) x}{2}+\frac {n -1}{n +1}\right ) x^{-\frac {n +4}{n +3}} y}{n +3} = -\frac {a^{2} \left (\left (n +1\right ) x^{2}-\frac {\left (n^{2}+2 n +5\right ) x}{n +1}+\frac {4}{n +1}\right ) x^{-\frac {n +5}{n +3}}}{2 n +6}
\] |
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\[
{}y y^{\prime }-a \left (\frac {n +2}{n}+b \,x^{n}\right ) y = -\frac {a^{2} x \left (\frac {n +1}{n}+b \,x^{n}\right )}{n}
\] |
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\[
{}y y^{\prime } = \left (a \,{\mathrm e}^{x}+b \right ) y+c \,{\mathrm e}^{2 x}-a b \,{\mathrm e}^{x}-b^{2}
\] |
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\[
{}y y^{\prime } = \left (a \left (2 \mu +\lambda \right ) {\mathrm e}^{\lambda x}+b \right ) {\mathrm e}^{x \mu } y+\left (-a^{2} \mu \,{\mathrm e}^{2 \lambda x}-a b \,{\mathrm e}^{\lambda x}+c \right ) {\mathrm e}^{2 x \mu }
\] |
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\[
{}y y^{\prime } = \left ({\mathrm e}^{\lambda x} a +b \right ) y+c \left (a^{2} {\mathrm e}^{2 \lambda x}+a b \left (\lambda x +1\right ) {\mathrm e}^{\lambda x}+b^{2} \lambda x \right )
\] |
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\[
{}y y^{\prime } = {\mathrm e}^{\lambda x} \left (2 a \lambda x +a +b \right ) y-{\mathrm e}^{2 \lambda x} \left (a^{2} \lambda \,x^{2}+a b x +c \right )
\] |
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\[
{}y y^{\prime } = {\mathrm e}^{a x} \left (2 a \,x^{2}+b +2 x \right ) y+{\mathrm e}^{2 a x} \left (-a \,x^{4}-b \,x^{2}+c \right )
\] |
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\[
{}y y^{\prime }+a \left (2 b x +1\right ) {\mathrm e}^{b x} y = -a^{2} b \,x^{2} {\mathrm e}^{2 b x}
\] |
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\[
{}y y^{\prime }-a \left (1+2 n +2 n \left (n +1\right ) x \right ) {\mathrm e}^{\left (n +1\right ) x} y = -a^{2} n \left (n +1\right ) \left (n x +1\right ) x \,{\mathrm e}^{2 \left (n +1\right ) x}
\] |
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\[
{}y y^{\prime }+a \left (1+2 b \sqrt {x}\right ) {\mathrm e}^{2 b \sqrt {x}} y = -a^{2} b \,x^{{3}/{2}} {\mathrm e}^{4 b \sqrt {x}}
\] |
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\[
{}y y^{\prime } = \left (a \cosh \left (x \right )+b \right ) y-a b \sinh \left (x \right )+c
\] |
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\[
{}y y^{\prime } = \left (a \sinh \left (x \right )+b \right ) y-a b \cosh \left (x \right )+c
\] |
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\[
{}y y^{\prime } = \left (2 \ln \left (x \right )+a +1\right ) y+x \left (-\ln \left (x \right )^{2}-a \ln \left (x \right )+b \right )
\] |
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\[
{}y y^{\prime } = \left (2 \ln \left (x \right )^{2}+2 \ln \left (x \right )+a \right ) y+x \left (-\ln \left (x \right )^{4}-a \ln \left (x \right )^{2}+b \right )
\] |
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\[
{}y y^{\prime } = a x \cos \left (\lambda \,x^{2}\right ) y+x
\] |
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\[
{}y y^{\prime } = a x \sin \left (\lambda \,x^{2}\right ) y+x
\] |
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\[
{}\left (y A +B x +a \right ) y^{\prime }+B y+k x +b = 0
\] |
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\[
{}\left (y+a x +b \right ) y^{\prime } = \alpha y+\beta x +\gamma
\] |
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\[
{}\left (y+a k \,x^{2}+b x +c \right ) y^{\prime } = -y^{2} a +2 a k x y+m y+k \left (k +b -m \right ) x +s
\] |
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\[
{}\left (y+A \,x^{n}+a \right ) y^{\prime }+n A \,x^{n -1} y+k \,x^{m}+b = 0
\] |
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\[
{}\left (y+a \,x^{n +1}+b \,x^{n}\right ) y^{\prime } = \left (a n \,x^{n}+c \,x^{n -1}\right ) y
\] |
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\[
{}x y y^{\prime } = y^{2} a +b y+c \,x^{n}+s
\] |
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\[
{}x y y^{\prime } = -y^{2} n +a \left (2 n +1\right ) x y+b y-a^{2} n \,x^{2}-a b x +c
\] |
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\[
{}\frac {2 x y+1}{y}+\frac {\left (y-x \right ) y^{\prime }}{y^{2}} = 0
\] |
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\[
{}\frac {y^{2}-2 x^{2}}{x y^{2}-x^{3}}+\frac {\left (2 y^{2}-x^{2}\right ) y^{\prime }}{y^{3}-x^{2} y} = 0
\] |
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\[
{}\frac {1}{\sqrt {x^{2}+y^{2}}}+\left (\frac {1}{y}-\frac {x}{y \sqrt {x^{2}+y^{2}}}\right ) y^{\prime } = 0
\] |
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\[
{}y+x +x y^{\prime } = 0
\] |
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\[
{}6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime } = 0
\] |
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\[
{}\sec \left (x \right ) \cos \left (y\right )^{2}-\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0
\] |
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\[
{}\left (1+x \right ) y^{2}-x^{3} y^{\prime } = 0
\] |
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\[
{}2 \left (1-y^{2}\right ) x y+\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime } = 0
\] |
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\[
{}x \,{\mathrm e}^{\frac {y}{x}}+y-x y^{\prime } = 0
\] |
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\[
{}2 x^{2} y+3 y^{3}-\left (x^{3}+2 x y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}y^{2}-x y+x^{2} y^{\prime } = 0
\] |
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\[
{}2 x^{2} y+y^{3}-x^{3} y^{\prime } = 0
\] |
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\[
{}y^{3}+x^{3} y^{\prime } = 0
\] |
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\[
{}x +y \cos \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
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\[
{}4 x +3 y+1+\left (x +y+1\right ) y^{\prime } = 0
\] |
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\[
{}4 x -y+2+\left (x +y+3\right ) y^{\prime } = 0
\] |
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\[
{}2 x +y-\left (4 x +2 y-1\right ) y^{\prime } = 0
\] |
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\[
{}y+2 x y^{2}-x^{2} y^{3}+2 x^{2} y y^{\prime } = 0
\] |
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\[
{}2 y+3 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime } = 0
\] |
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\[
{}y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime }+y \cot \left (x \right ) = \sec \left (x \right )
\] |
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\[
{}x y^{\prime }+\left (1+x \right ) y = {\mathrm e}^{x}
\] |
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\[
{}y^{\prime }-\frac {2 y}{1+x} = \left (1+x \right )^{3}
\] |
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\[
{}\left (x^{3}+x \right ) y^{\prime }+4 x^{2} y = 2
\] |
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\[
{}x^{2} y^{\prime }+\left (1-2 x \right ) y = x^{2}
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime }-2 \left (1+x \right ) y = y^{{5}/{2}}
\] |
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\[
{}y y^{\prime }+x y^{2} = x
\] |
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\[
{}\sin \left (y\right ) y^{\prime }+\sin \left (x \right ) \cos \left (y\right ) = \sin \left (x \right )
\] |
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\[
{}4 x y^{\prime }+3 y+{\mathrm e}^{x} x^{4} y^{5} = 0
\] |
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\[
{}y^{\prime }-\frac {1+y}{1+x} = \sqrt {1+y}
\] |
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\[
{}x^{4} y \left (3 y+2 x y^{\prime }\right )+x^{2} \left (4 y+3 x y^{\prime }\right ) = 0
\] |
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\[
{}y^{2} \left (3 y-6 x y^{\prime }\right )-x \left (y-2 x y^{\prime }\right ) = 0
\] |
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\[
{}2 x^{3} y-y^{2}-\left (2 x^{4}+x y\right ) y^{\prime } = 0
\] |
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\[
{}y^{2}-x y+x^{2} y^{\prime } = 0
\] |
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\[
{}\frac {x y^{\prime }-y}{\sqrt {x^{2}-y^{2}}} = x y^{\prime }
\] |
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\[
{}x +y-\left (x -y\right ) y^{\prime } = 0
\] |
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\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
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\[
{}x -y^{2}+2 x y y^{\prime } = 0
\] |
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\[
{}x y^{\prime }-y = x^{2}+y^{2}
\] |
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\[
{}3 x^{2}+6 x y+3 y^{2}+\left (2 x^{2}+3 x y\right ) y^{\prime } = 0
\] |
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\[
{}2 x +\left (x^{2}+y^{2}+2 y\right ) y^{\prime } = 0
\] |
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\[
{}y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime } = 0
\] |
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\[
{}x^{3} y-y^{4}+\left (x y^{3}-x^{4}\right ) y^{\prime } = 0
\] |
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\[
{}y^{2}-x^{2}+2 m x y+\left (m y^{2}-m \,x^{2}-2 x y\right ) y^{\prime } = 0
\] |
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\[
{}x y^{\prime }-y+2 x^{2} y-x^{3} = 0
\] |
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\[
{}\left (x +y\right ) y^{\prime }-1 = 0
\] |
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\[
{}x +y y^{\prime }+y-x y^{\prime } = 0
\] |
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\[
{}x y^{\prime }-a y+b y^{2} = c \,x^{2 a}
\] |
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\[
{}x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime } = 0
\] |
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\[
{}\sqrt {1-y^{2}}+\sqrt {-x^{2}+1}\, y^{\prime } = 0
\] |
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\[
{}y^{\prime }-x^{2} y = x^{5}
\] |
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\[
{}\left (y-x \right )^{2} y^{\prime } = 1
\] |
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\[
{}x y^{\prime }+y+x^{4} y^{4} {\mathrm e}^{x} = 0
\] |
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\[
{}\left (1-x \right ) y+\left (1-y\right ) x y^{\prime } = 0
\] |
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\[
{}\left (y-x \right ) y^{\prime }+y = 0
\] |
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\[
{}x y^{\prime }-y = \sqrt {x^{2}+y^{2}}
\] |
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\[
{}x y^{\prime }-y = \sqrt {x^{2}-y^{2}}
\] |
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\[
{}\sin \left (\frac {y}{x}\right ) x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
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\[
{}x -2 y+5+\left (2 x -y+4\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime }-x y = a y^{2} x
\] |
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\[
{}x y^{2} \left (3 y+x y^{\prime }\right )+x y^{\prime }-2 y = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime }+y = \arctan \left (x \right )
\] |
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\[
{}5 x y-3 y^{3}+\left (3 x^{2}-7 x y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
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\[
{}x y^{2}+y-x y^{\prime } = 0
\] |
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\[
{}\left (1-x \right ) y-\left (1+y\right ) x y^{\prime } = 0
\] |
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\[
{}3 x^{2} y+\left (x^{3}+y^{2} x^{3}\right ) y^{\prime } = 0
\] |
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\[
{}\left (x^{2}+y^{2}\right ) \left (x +y y^{\prime }\right ) = \left (x^{2}+y^{2}+x \right ) \left (x y^{\prime }-y\right )
\] |
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\[
{}2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime } = 0
\] |
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