| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y y^{\prime }-\frac {a \left (\left (1+k \right ) x -1\right ) y}{x^{2}} = \frac {a^{2} \left (1+k \right ) \left (x -1\right )}{x^{2}}
\]
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| \[
{} y y^{\prime }-\left (\left (-1+2 n \right ) x -a n \right ) x^{-n -1} y = n \left (x -a \right ) x^{-2 n}
\]
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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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| \[
{} y y^{\prime } = {\mathrm e}^{\lambda x} \left (2 a \lambda x +a +b \right ) y-{\mathrm e}^{2 \lambda x} \left (a^{2} \lambda \,x^{2}+a b x +c \right )
\]
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| \[
{} y y^{\prime }-a \left (1+2 n +2 n \left (n +1\right ) x \right ) {\mathrm e}^{\left (n +1\right ) x} y = -a^{2} n \left (n +1\right ) \left (n x +1\right ) x \,{\mathrm e}^{2 \left (n +1\right ) x}
\]
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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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| \[
{} y y^{\prime } = \left (2 \ln \left (x \right )+a +1\right ) y+x \left (-\ln \left (x \right )^{2}-a \ln \left (x \right )+b \right )
\]
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| \[
{} \left (y+a x +b \right ) y^{\prime } = \alpha y+\beta x +\gamma
\]
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| \[
{} y y^{\prime } x = -n y^{2}+a \left (2 n +1\right ) x y+b y-a^{2} n \,x^{2}-a b x +c
\]
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| \[
{} 2 y y^{\prime } x = \left (-n +1\right ) y^{2}+\left (a \left (2 n +1\right ) x +2 n -1\right ) y-a^{2} n \,x^{2}-b x -n
\]
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| \[
{} \left (a x y-a k y+b x -b k \right ) y^{\prime } = c y^{2}+d x y+\left (-d k +b \right ) y
\]
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| \[
{} \left (A x y+B \,x^{2}+k x \right ) y^{\prime } = A y^{2}+c x y+d \,x^{2}+\left (-A \beta +k \right ) y-c \beta x -k \beta
\]
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| \[
{} \left (A x y+A k y+B \,x^{2}+B k x \right ) y^{\prime } = c y^{2}+d x y+k \left (d -B \right ) y
\]
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| \[
{} \left (A x y+B \,x^{2}+a_{1} x +b_{1} y+c_{1} \right ) y^{\prime } = A y^{2}+B x y+a_{2} x +b_{2} y+c_{2}
\]
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| \[
{} \left (\left (a x +c \right ) y+\left (-n +1\right ) x^{2}+\left (-1+2 n \right ) x -n \right ) y^{\prime } = 2 a y^{2}+2 x y
\]
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| \[
{} y^{\prime \prime }-a \,x^{n -2} \left (a \,x^{n}+n +1\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}+a \,x^{n}+n \,x^{n -1}\right ) y = 0
\]
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✓ |
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| \[
{} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}-a \,x^{n}+n \,x^{n -1}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (x^{2} a +b x \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a \,x^{n}+2 b \right ) y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}+b^{2}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+x^{n} \left (x^{2} a +\left (a c +b \right ) x +b c \right ) y^{\prime }-x^{n} \left (a x +b \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a \left (n +1\right ) x^{n -1}+b \left (1+m \right ) x^{m -1}\right ) y = 0
\]
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✓ |
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| \[
{} x y^{\prime \prime }+a y^{\prime }+b \,x^{n} \left (-b \,x^{n +1}+a +n \right ) y = 0
\]
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| \[
{} x y^{\prime \prime }-\left (2 a x +1\right ) y^{\prime }+b \,x^{3} y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (x^{2} a +b x +c \right ) y^{\prime }+\left (A \,x^{2}+B x +\operatorname {C0} \right ) y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (a \,x^{n}+b \,x^{n -1}+2\right ) y^{\prime }+b \,x^{n -2} y = 0
\]
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| \[
{} \left (x +\gamma \right ) y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (a n \,x^{n -1}+b m \,x^{m -1}\right ) y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-\left (a^{2} x^{2 n}+a \left (2 b +n -1\right ) x^{n}+b \left (b -1\right )\right ) y = 0
\]
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✓ |
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| \[
{} x^{2} y^{\prime \prime }+\left (a \,x^{3 n}+b \,x^{2 n}+\frac {1}{4}-\frac {n^{2}}{4}\right ) y = 0
\]
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✓ |
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| \[
{} x^{2} y^{\prime \prime }+x \left (x^{2} a +b x +c \right ) y^{\prime }+\left (A \,x^{3}+B \,x^{2}+C x +d \right ) y = 0
\]
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| \[
{} \left (a \,x^{3}+x^{2}+b \right ) y^{\prime \prime }+a^{2} x \left (x^{2}-b \right ) y^{\prime }-a^{3} b x y = 0
\]
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| \[
{} \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }-\left (-\lambda ^{2}+x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y = 0
\]
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| \[
{} 2 \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (3 x^{2} a +2 b x +c \right ) y^{\prime }+\lambda y = 0
\]
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| \[
{} 2 \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+3 \left (3 x^{2} a +2 b x +c \right ) y^{\prime }+\left (6 a x +2 b +\lambda \right ) y = 0
\]
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| \[
{} x^{4} y^{\prime \prime }+\left (x^{2} a +b x +c \right ) y = 0
\]
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✓ |
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| \[
{} x^{n} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y = 0
\]
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✓ |
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| \[
{} x^{n} y^{\prime \prime }+\left (a \,x^{n -1}+b x \right ) y^{\prime }+\left (a -1\right ) y = 0
\]
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✓ |
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| \[
{} x^{n} y^{\prime \prime }+\left (2 x^{n -1}+x^{2} a +b x \right ) y^{\prime }+b y = 0
\]
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| \[
{} \left (a \,x^{n}+b x +c \right ) y^{\prime \prime } = a n \left (n -1\right ) x^{n -2} y
\]
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| \[
{} x^{2} \left (a^{2} x^{2 n}-1\right ) y^{\prime \prime }+x \left (a p \,x^{n}+q \right ) y^{\prime }+\left (a r \,x^{n}+s \right ) y = 0
\]
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| \[
{} \left (x^{n}+a \right )^{2} y^{\prime \prime }-b \,x^{n -2} \left (\left (b -1\right ) x^{n}+a \left (n -1\right )\right ) y = 0
\]
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✓ |
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| \[
{} \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda -x \right ) y^{\prime }+y = 0
\]
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✓ |
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| \[
{} \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda ^{2}-x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y = 0
\]
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✓ |
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| \[
{} y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}-\frac {\lambda ^{2}}{4}\right ) y = 0
\]
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✓ |
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| \[
{} y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y = 0
\]
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✓ |
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| \[
{} y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y^{\prime }-b \,{\mathrm e}^{x \mu } \left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }+\mu \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{2 x \mu }+b \right ) y^{\prime }+\mu \left ({\mathrm e}^{\lambda x} \left (b -a \,{\mathrm e}^{2 x \mu }\right )-\mu \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+a \,{\mathrm e}^{b \,x^{n}} y^{\prime }+c \left (a \,{\mathrm e}^{b \,x^{n}}-c \right ) y = 0
\]
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✓ |
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| \[
{} \left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime \prime }-a \,\lambda ^{2} {\mathrm e}^{\lambda x} y = 0
\]
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✓ |
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| \[
{} x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\]
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✓ |
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| \[
{} {y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2} = 0
\]
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✓ |
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| \[
{} {\mathrm e}^{2 y} {y^{\prime }}^{3}+\left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x} = 0
\]
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✓ |
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| \[
{} x^{2} y^{\prime \prime }-2 n x \left (1+x \right ) y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y = 0
\]
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✓ |
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| \[
{} x^{4} y^{\prime \prime }+2 x^{3} \left (1+x \right ) y^{\prime }+n^{2} y = 0
\]
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✓ |
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| \[
{} \frac {1+8 x y^{{2}/{3}}}{x^{{2}/{3}} y^{{1}/{3}}}+\frac {\left (2 x^{{4}/{3}} y^{{2}/{3}}-x^{{1}/{3}}\right ) y^{\prime }}{y^{{4}/{3}}} = 0
\]
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✓ |
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| \[
{} \sin \left (t \right ) x^{\prime \prime }+\cos \left (t \right ) x^{\prime }+2 x = 0
\]
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✓ |
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| \[
{} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cot \left (x \right ) = 0
\]
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✓ |
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\]
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✓ |
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| \[
{} y^{\prime \prime }+\frac {k x}{y^{4}} = 0
\]
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✓ |
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| \[
{} x y^{\prime \prime }+y^{\prime } \sin \left (x \right )+y \cos \left (x \right ) = 0
\]
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| \[
{} \left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime \prime }-x {y^{\prime }}^{2} \sin \left (y\right )+2 \left (\cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime } = \sin \left (x \right ) y
\]
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| \[
{} \left (\cos \left (y\right )-y \sin \left (y\right )\right ) y^{\prime \prime }-{y^{\prime }}^{2} \left (2 \sin \left (y\right )+y \cos \left (y\right )\right ) = \sin \left (x \right )
\]
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| \[
{} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime } = 0
\]
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| \[
{} \sqrt {1-x}\, y^{\prime \prime }-4 y = \sin \left (x \right )
\]
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| \[
{} w^{\prime } = \left (3-w\right ) \left (w+1\right )
\]
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| \[
{} w^{\prime } = \left (3-w\right ) \left (w+1\right )
\]
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| \[
{} y^{\prime } = y \left (-1+y\right ) \left (y-3\right )
\]
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| \[
{} y^{\prime } = y \left (-1+y\right ) \left (y-3\right )
\]
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| \[
{} y^{\prime } = y \left (-1+y\right ) \left (y-3\right )
\]
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| \[
{} y^{\prime } = y^{2}-4 y-12
\]
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| \[
{} y^{\prime } = y^{2}-4 y-12
\]
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| \[
{} y^{\prime } = y^{2}-4 y-12
\]
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| \[
{} y^{\prime } = \cos \left (y\right )
\]
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| \[
{} y^{\prime } = 3-y^{2}
\]
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| \[
{} y^{\prime \prime } = 2 y y^{\prime }
\]
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| \[
{} y^{\prime \prime } = 2 y y^{\prime }
\]
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| \[
{} y^{\prime \prime } = 2 y y^{\prime }
\]
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✓ |
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| \[
{} y^{\prime \prime } = 2 y y^{\prime }
\]
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✓ |
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| \[
{} y y^{\prime }+y^{4} = \sin \left (x \right )
\]
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✓ |
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| \[
{} {y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2} = 0
\]
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✓ |
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| \[
{} {y^{\prime \prime }}^{2}-2 y^{\prime \prime } y^{\prime }+y^{2} = 0
\]
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✓ |
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| \[
{} t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y = t^{3}+2 t
\]
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✓ |
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| \[
{} y^{\prime \prime }+\left (y^{2}-1\right ) y^{\prime }+y = 0
\]
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✓ |
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| \[
{} y^{\prime \prime }+\left (\frac {{y^{\prime }}^{2}}{3}-1\right ) y^{\prime }+y = 0
\]
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✓ |
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| \[
{} t \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right )+y y^{\prime } = 1
\]
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| \[
{} a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime } = 0
\]
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| \[
{} x^{2} \cos \left (y\right ) y^{\prime }+1 = 0
\]
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| \[
{} x^{2} y^{\prime }+\cos \left (2 y\right ) = 1
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2} = 0
\]
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| \[
{} \frac {x}{\sqrt {x^{2}+y^{2}}}+\frac {1}{x}+\frac {1}{y}+\left (\frac {y}{\sqrt {x^{2}+y^{2}}}+\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime } = 0
\]
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| \[
{} 3 x^{2} \tan \left (y\right )-\frac {2 y^{3}}{x^{3}}+\left (x^{3} \sec \left (y\right )^{2}+4 y^{3}+\frac {3 y^{2}}{x^{2}}\right ) y^{\prime } = 0
\]
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| \[
{} \frac {y+\sin \left (x \right ) \cos \left (x y\right )^{2}}{\cos \left (x y\right )^{2}}+\left (\frac {x}{\cos \left (x y\right )^{2}}+\sin \left (y\right )\right ) y^{\prime } = 0
\]
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✓ |
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| \[
{} {y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2} = 0
\]
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✓ |
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| \[
{} 8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2} = 27 y-27 x
\]
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✓ |
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| \[
{} y^{\prime \prime } = y^{\prime } \ln \left (y^{\prime }\right )
\]
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| \[
{} y^{\prime \prime } = 2 y y^{\prime }
\]
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| \[
{} 3 y^{\prime } y^{\prime \prime } = 2 y
\]
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| \[
{} y^{\prime \prime \prime } = 3 y y^{\prime }
\]
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| \[
{} 4 y-4 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right )
\]
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