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# |
ODE |
Mathematica |
Maple |
Sympy |
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\[
{} y y^{\prime }-\frac {3 a y}{x^{{7}/{4}}} = \frac {a^{2} \left (x -1\right ) \left (x -9\right )}{4 x^{{5}/{2}}}
\]
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\[
{} y y^{\prime }-a \left (\left (k -2\right ) x +2 k -3\right ) x^{-k} y = a^{2} \left (k -2\right ) \left (x -1\right )^{2} x^{1-2 k}
\]
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\[
{} y y^{\prime }-\frac {a \left (\left (4 k -7\right ) x -4 k +5\right ) x^{-k} y}{2} = \frac {a^{2} \left (2 k -3\right ) \left (x -1\right )^{2} x^{1-2 k}}{2}
\]
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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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\[
{} y y^{\prime }+\frac {a \left (\frac {\left (3 n +5\right ) x}{2}+\frac {n -1}{n +1}\right ) x^{-\frac {n +4}{3+n}} y}{3+n} = -\frac {a^{2} \left (\left (n +1\right ) x^{2}-\frac {\left (n^{2}+2 n +5\right ) x}{n +1}+\frac {4}{n +1}\right ) x^{-\frac {n +5}{3+n}}}{6+2 n}
\]
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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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\[
{} y y^{\prime } = {\mathrm e}^{a x} \left (2 a \,x^{2}+b +2 x \right ) y+{\mathrm e}^{2 a x} \left (-a \,x^{4}-b \,x^{2}+c \right )
\]
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\[
{} y y^{\prime } = \left (a \cosh \left (x \right )+b \right ) y-a b \sinh \left (x \right )+c
\]
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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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\[
{} y y^{\prime } = \left (2 \ln \left (x \right )^{2}+2 \ln \left (x \right )+a \right ) y+x \left (-\ln \left (x \right )^{4}-a \ln \left (x \right )^{2}+b \right )
\]
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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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\[
{} \left (y+a k \,x^{2}+b x +c \right ) y^{\prime } = -a y^{2}+2 a k x y+m y+k \left (k +b -m \right ) x +s
\]
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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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\[
{} x y y^{\prime } = a y^{2}+b y+c \,x^{n}+s
\]
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\[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (-c \,x^{2 n}+a \,x^{n +1}+b \,x^{n}+n \,x^{n -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+a \,x^{n} y^{\prime }-b \left (a \,x^{m +n}+b \,x^{2 m}+m \,x^{m -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}+b -c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a b \,x^{n}+b \,x^{n -1}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{n}+1\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a b \,x^{n}+2 b \,x^{n -1}-a^{2} x \right ) y^{\prime }+a \left (a b \,x^{n}+b \,x^{n -1}-a^{2} x \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+c \left (a \,x^{n}+b \,x^{m}-c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a b \,x^{m +n}+b \left (1+m \right ) x^{m -1}-a \,x^{n -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (a b \,x^{m +n}+b c \,x^{m}+a n \,x^{n -1}\right ) y = 0
\]
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\[
{} x y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}-b^{2} x +2 b \right ) y = 0
\]
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\[
{} x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}-c x +b \right ) y = 0
\]
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\[
{} x y^{\prime \prime }+\left (a b \,x^{n}+b -3 n +1\right ) y^{\prime }+a^{2} n \left (b -n \right ) x^{2 n -1} y = 0
\]
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\[
{} x y^{\prime \prime }+\left (a \,x^{n}+b x \right ) y^{\prime }+\left (a b \,x^{n}+a n \,x^{n -1}-b \right ) y = 0
\]
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\[
{} x y^{\prime \prime }+\left (a b \,x^{n}+b \,x^{n -1}+a x -1\right ) y^{\prime }+a^{2} b \,x^{n} y = 0
\]
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\[
{} x y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (c -1\right ) \left (a \,x^{n -1}+b \,x^{m -1}\right ) y = 0
\]
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\[
{} x y^{\prime \prime }+\left (a b \,x^{m +n}+a n \,x^{n}+b \,x^{m}+1-2 n \right ) y^{\prime }+a^{2} b n \,x^{2 n +m -1} y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+\left (a \,x^{2 n} \left (b \,x^{n}+c \right )^{m}+\frac {1}{4}-\frac {n^{2}}{4}\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (a b \,x^{n}+a c \,x^{n -1}+b^{2} x^{2}+2 b x c +c^{2}-c \right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (a b \,x^{n +2 m}-b^{2} x^{4 m +2}+a m \,x^{n -1}-m^{2}-m \right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+\left (a \,x^{n +2}+b \,x^{2}+c \right ) y^{\prime }+\left (a n \,x^{n +1}+a c \,x^{n}+b c \right ) y = 0
\]
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\[
{} x^{3} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x -\left (a \,x^{n}-a b \,x^{n -1}+b \right ) y = 0
\]
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\[
{} \left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (n \,x^{2}+m x +k \right ) y^{\prime }+\left (k -1\right ) \left (\left (-a k +n \right ) x +m -b k \right ) y = 0
\]
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\[
{} \left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (\left (m -a \right ) x^{2}+\left (2 c m -1\right ) x -c \right ) y^{\prime }+\left (-2 m x +1\right ) y = 0
\]
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\[
{} \left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (n \,x^{2}+m x +k \right ) y^{\prime }+\left (-2 \left (a +n \right ) x +1\right ) y = 0
\]
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\[
{} x \left (a \,x^{2}+b x +1\right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y^{\prime }+\left (n x +m \right ) y = 0
\]
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\[
{} \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\left (\alpha \gamma +\beta \right ) x +\beta \lambda \right ) y^{\prime }-\left (\alpha x +\beta \right ) y = 0
\]
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\[
{} x^{4} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (a \,x^{n -1}+a b \,x^{n -2}+b^{2}\right ) y = 0
\]
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\[
{} \left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-\left (b \,x^{n +1}+a \right ) y = 0
\]
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\[
{} \left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-m \left (b \,x^{n +1}+\left (m -1\right ) x^{2}+a \right ) y = 0
\]
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\[
{} x^{n} y^{\prime \prime }+c \left (a x +b \right )^{n -4} y = 0
\]
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\[
{} x^{n} y^{\prime \prime }+a x y^{\prime }-\left (b^{2} x^{n}+2 b \,x^{n -1}+a b x +a \right ) y = 0
\]
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\[
{} x^{n} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{n}+b \right ) y = 0
\]
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\[
{} x^{n} y^{\prime \prime }+\left (a \,x^{n}-x^{n -1}+a b x +b \right ) y^{\prime }+y a^{2} b x = 0
\]
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\[
{} x^{n} y^{\prime \prime }+\left (a \,x^{m +n}+1\right ) y^{\prime }+a \,x^{m} \left (1+m \,x^{n -1}\right ) y = 0
\]
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\[
{} \left (a \,x^{n}+b \right ) y^{\prime \prime }+\left (c \,x^{n}+d \right ) y^{\prime }+\lambda \left (\left (-a \lambda +c \right ) x^{n}+d -\lambda b \right ) y = 0
\]
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\[
{} \left (x^{n}+a \right )^{2} y^{\prime \prime }+b \,x^{m} \left (x^{n}+a \right ) y^{\prime }-x^{n -2} \left (b \,x^{1+m}+a n -a \right ) y = 0
\]
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\[
{} \left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+c \,x^{m} \left (a \,x^{n}+b \right ) y^{\prime }+\left (c \,x^{m}-a n \,x^{n -1}-1\right ) y = 0
\]
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\[
{} \left (a \,x^{n +1}+b \,x^{n}+c \right )^{2} y^{\prime \prime }+\left (\alpha \,x^{n}+\beta \,x^{n -1}+\gamma \right ) y^{\prime }+\left (n \left (-a n -a +\alpha \right ) x^{n -1}+\left (n -1\right ) \left (-b n +\beta \right ) x^{n -2}\right ) y = 0
\]
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\[
{} 2 \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+a n \,x^{n -1} b m \,x^{m -1} y^{\prime }+d y = 0
\]
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\[
{} y^{\prime \prime }+2 k \,{\mathrm e}^{x \mu } y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+k^{2} {\mathrm e}^{2 x \mu }+k \mu \,{\mathrm e}^{x \mu }+c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a +b \,{\mathrm e}^{2 \lambda x}\right ) y^{\prime }+\lambda \left (a -\lambda -b \,{\mathrm e}^{2 \lambda x}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (2 \,{\mathrm e}^{\lambda x} a -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+c \,{\mathrm e}^{x \mu }\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (2 \,{\mathrm e}^{\lambda x} a -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{2 x \mu }+c \,{\mathrm e}^{x \mu }+k \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (2 \,{\mathrm e}^{\lambda x} a +b -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+a b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 x \mu }+d \,{\mathrm e}^{x \mu }+k \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }\right ) y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{x \mu }+\lambda \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }+c \right ) y^{\prime }+\left (a b \,{\mathrm e}^{x \left (\lambda +\mu \right )}+{\mathrm e}^{\lambda x} a c +b \mu \,{\mathrm e}^{x \mu }\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +2 b \,{\mathrm e}^{x \mu }-\lambda \right ) y^{\prime }+\left (a b \,{\mathrm e}^{x \left (\lambda +\mu \right )}+c \,{\mathrm e}^{2 \lambda x}+b^{2} {\mathrm e}^{2 x \mu }+b \left (\mu -\lambda \right ) {\mathrm e}^{x \mu }\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,{\mathrm e}^{x \left (\lambda +\mu \right )}+a \lambda \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{x \mu }-2 \lambda \right ) y^{\prime }+a^{2} b \lambda \,{\mathrm e}^{\left (\mu +2 \lambda \right ) x} y = 0
\]
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\[
{} x^{3} y^{4}+x^{2} y^{3}+x y^{2}+y+\left (x^{4} y^{3}-x^{3} y^{2}-x^{3} y+x \right ) y^{\prime } = 0
\]
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\[
{} \left (x -y^{\prime }-y\right )^{2} = x^{2} \left (2 x y-y^{\prime } x^{2}\right )
\]
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\[
{} \left (x y^{\prime }-y\right ) \left (y y^{\prime }+x \right ) = a^{2} y^{\prime }
\]
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\[
{} x^{2} \left (-x^{3}+1\right ) y^{\prime \prime }-x^{3} y^{\prime }-2 y = 0
\]
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\[
{} {x^{\prime }}^{2}+t x = \sqrt {t +1}
\]
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\[
{} y^{\prime \prime }+y = 0
\]
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\[
{} y^{\prime \prime }+y = 0
\]
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\[
{} 3 x^{2} y+2-\left (x^{3}+y\right ) y^{\prime } = 0
\]
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\[
{} \left (x^{4}-2 x^{3}+x^{2}\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+x^{2} y = 0
\]
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\[
{} \left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+y^{\prime } x^{2}+\left (x -2\right ) y = 0
\]
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\[
{} \left (2 t +1\right ) x^{\prime \prime }+t^{3} x^{\prime }+x = 0
\]
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\[
{} f \left (t \right ) x^{\prime \prime }+x g \left (t \right ) = 0
\]
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\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-4 y \left (t \right )-x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+4 y \left (t \right )-y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = y \left (t \right )+\frac {x \left (t \right ) \left (1-x \left (t \right )^{2}-y \left (t \right )^{2}\right )}{\sqrt {x \left (t \right )^{2}+y \left (t \right )^{2}}}, y^{\prime }\left (t \right ) = -x \left (t \right )+\frac {y \left (t \right ) \left (1-x \left (t \right )^{2}-y \left (t \right )^{2}\right )}{\sqrt {x \left (t \right )^{2}+y \left (t \right )^{2}}}\right ]
\]
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\[
{} x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x = 0
\]
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\[
{} x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x = 0
\]
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\[
{} x^{\prime \prime }+\left (x^{4}+x^{2}\right ) x^{\prime }+x^{3}+x = 0
\]
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\[
{} x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3} = 0
\]
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\[
{} x^{\prime \prime }+\left (1+x^{2}\right ) x^{\prime }+x^{3} = 0
\]
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\[
{} x^{\prime } = -x \left (k^{2}+x^{2}\right )
\]
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\[
{} \left (t \cos \left (t \right )-\sin \left (t \right )\right ) x^{\prime \prime }-x^{\prime } t \sin \left (t \right )-x \sin \left (t \right ) = 0
\]
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✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = x y^{3}+x^{2}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = \sin \left (x y\right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = t \ln \left (y^{2 t}\right )+t^{2}
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = \ln \left (x y\right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+y y^{\prime \prime \prime \prime } = 1
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime \prime }+x y^{\prime \prime }-y^{2} = \sin \left (x \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} {y^{\prime }}^{2}+x y {y^{\prime }}^{2} = \ln \left (x \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \sin \left (y^{\prime \prime }\right )+y y^{\prime \prime \prime \prime } = 1
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \sinh \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime } = x y
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} {y^{\prime \prime \prime }}^{2}+\sqrt {y} = \sin \left (x \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x -3\right ) y^{\prime \prime }+y \ln \left (x \right ) = x^{2}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x y^{\prime \prime }+2 y^{\prime } x^{2}+y \sin \left (x \right ) = \sinh \left (x \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \sin \left (x \right ) y^{\prime \prime }+x y^{\prime }+7 y = 1
\]
|
✗ |
✗ |
✗ |
|