| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }-a x y^{\prime }+a^{2} \left (x -1\right ) y = 0
\]
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✓ |
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| \[
{} y^{\prime \prime }+4 x y^{\prime }+4 x^{2} y = 0
\]
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✓ |
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| \[
{} y^{\prime \prime }-2 b x y^{\prime }+y b^{2} x^{2} = 0
\]
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✓ |
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| \[
{} y^{\prime \prime }-2 b x y^{\prime }+y b^{2} x^{2} = x
\]
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✓ |
✓ |
✗ |
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| \[
{} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{3}+6 x^{2}+4\right ) y = 0
\]
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✗ |
✗ |
✗ |
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| \[
{} x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = {\mathrm e}^{x} \sec \left (x \right )
\]
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✓ |
✓ |
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| \[
{} -\left (a^{2}+1\right ) y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} y^{\prime \prime }+2 n \cot \left (n x \right ) y^{\prime }+\left (m^{2}-n^{2}\right ) y = 0
\]
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✓ |
✓ |
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| \[
{} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0
\]
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✓ |
✓ |
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| \[
{} x^{2} y^{\prime \prime }-2 n x y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y = 0
\]
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✓ |
✓ |
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| \[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y = {\mathrm e}^{x^{2}}
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2} = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+m^{2} y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }-\sin \left (x \right )^{2} y = 0
\]
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✓ |
✓ |
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| \[
{} \sin \left (x \right )^{2} y^{\prime \prime }+\sin \left (x \right ) \cos \left (x \right ) y^{\prime }+y = 0
\]
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✓ |
✓ |
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| \[
{} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} y^{\prime \prime }+\left (\tan \left (x \right )-1\right )^{2} y^{\prime }-n \left (n -1\right ) y \sec \left (x \right )^{4} = 0
\]
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✓ |
✓ |
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| \[
{} y^{\prime \prime }+\left (3 \sin \left (x \right )-\cot \left (x \right )\right ) y^{\prime }+2 \sin \left (x \right )^{2} y = 0
\]
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✓ |
✓ |
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| \[
{} 3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+2\right ) y^{\prime }-4 y = 0
\]
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✓ |
✓ |
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| \[
{} x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-2 y = x^{2}
\]
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✓ |
✓ |
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| \[
{} x^{2} y^{\prime \prime }+y^{\prime }-\left (x^{2}+1\right ) y = {\mathrm e}^{-x}
\]
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✓ |
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| \[
{} \left (x +2\right ) y^{\prime \prime }-\left (2 x +5\right ) y^{\prime }+2 y = {\mathrm e}^{x} \left (1+x \right )
\]
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✓ |
✓ |
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| \[
{} -y+x y^{\prime }+\left (1-x \right ) y^{\prime \prime } = \left (1-x \right )^{2}
\]
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✓ |
✓ |
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| \[
{} -\left (x^{2}+1\right ) y-4 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = x
\]
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✓ |
✓ |
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| \[
{} 2 \left (1+x \right ) y-2 x \left (1+x \right ) y^{\prime }+x^{2} y^{\prime \prime } = -4 x^{3}
\]
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✓ |
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| \[
{} x y^{\prime }-y = \left (x -1\right ) \left (y^{\prime \prime }-x +1\right )
\]
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✓ |
✓ |
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| \[
{} \left (x y^{\prime }-y\right )^{2}+x^{2} y y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} 2 \left (1+x \right ) y-2 x \left (1+x \right ) y^{\prime }+x^{2} y^{\prime \prime } = x^{3}
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (x^{2}+a \right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = x^{3}+3 x
\]
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✓ |
✓ |
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| \[
{} \left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2} y}{a} = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\frac {a^{2} y}{-x^{2}+1} = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (2 x -1\right ) y^{\prime \prime }-2 y^{\prime }+\left (3-2 x \right ) y = 2 \,{\mathrm e}^{x}
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+5\right ) y = x \,{\mathrm e}^{-\frac {x^{2}}{2}}
\]
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✓ |
✓ |
✗ |
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| \[
{} x \left (-x^{2}+1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) \left (3 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+\left (1-\frac {2}{x^{2}}\right ) y = x^{2}
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (x^{3}-2 x^{2}\right ) y^{\prime \prime }+2 x^{2} y^{\prime }-12 \left (x -2\right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} x y^{\prime \prime }-2 y^{\prime } \left (1+x \right )+\left (x +2\right ) y = \left (x -2\right ) {\mathrm e}^{2 x}
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-a^{2} y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} x y^{\prime \prime } \left (x \cos \left (x \right )-2 \sin \left (x \right )\right )+\left (x^{2}+2\right ) y^{\prime } \sin \left (x \right )-2 y \left (x \sin \left (x \right )+\cos \left (x \right )\right ) = 0
\]
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✗ |
✓ |
✗ |
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| \[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5}
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (x^{2}-1\right ) y^{\prime \prime }-\left (4 x^{2}-3 x -5\right ) y^{\prime }+\left (4 x^{2}-6 x -5\right ) y = {\mathrm e}^{2 x}
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime } = m^{2} y
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x} = 4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x}
\]
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✓ |
✓ |
✗ |
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| \[
{} x y^{\prime \prime }+\left (x^{2}+1\right ) y^{\prime }+2 x y = 2 x
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (x +2\right ) y^{\prime \prime }-\left (2 x +5\right ) y^{\prime }+2 y = {\mathrm e}^{x} \left (1+x \right )
\]
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✓ |
✓ |
✗ |
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| \[
{} -y+x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = x \left (-x^{2}+1\right )^{{3}/{2}}
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+\left (x +2\right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{3}+x y^{2}+a^{2} y+\left (y^{3}+x^{2} y-a^{2} x \right ) y^{\prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (x +2 y^{3}\right ) y^{\prime } = y
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (x +2 y^{3}\right ) y^{\prime } = y
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime }+x \sin \left (2 y\right ) = x^{3} \cos \left (y\right )^{2}
\]
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✓ |
✓ |
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| \[
{} \left (x y \sin \left (x y\right )+\cos \left (x y\right )\right ) y+\left (x y \sin \left (x y\right )-\cos \left (x y\right )\right ) y^{\prime } = 0
\]
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✗ |
✗ |
✗ |
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| \[
{} 3 x^{2} y^{4}+2 x y+\left (2 y^{2} x^{3}-x^{2}\right ) y^{\prime } = 0
\]
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✗ |
✗ |
✗ |
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| \[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 2 \sinh \left (2 x \right )
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{2} \left ({y^{\prime }}^{2}-y^{2}\right )+y^{2} = x^{4}+2 y y^{\prime } x
\]
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✓ |
✓ |
✗ |
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| \[
{} y = \frac {x}{y^{\prime }}-a y^{\prime }
\]
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✓ |
✓ |
✗ |
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| \[
{} {y^{\prime }}^{3}+m {y^{\prime }}^{2} = a \left (y+m x \right )
\]
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✗ |
✓ |
✗ |
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| \[
{} y^{\prime } = \tan \left (x -\frac {y^{\prime }}{1+{y^{\prime }}^{2}}\right )
\]
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✗ |
✓ |
✗ |
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| \[
{} a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} {\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3} = 0
\]
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✗ |
✓ |
✗ |
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| \[
{} y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{2} \left (y-x y^{\prime }\right ) = y {y^{\prime }}^{2}
\]
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✓ |
✓ |
✗ |
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| \[
{} 3 y {y^{\prime }}^{2}-2 y y^{\prime } x +4 y^{2}-x^{2} = 0
\]
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✗ |
✗ |
✗ |
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| \[
{} \left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}} = 0
\]
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✗ |
✓ |
✗ |
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| \[
{} \left (x^{2}+y^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (y y^{\prime }+x \right )+\left (y y^{\prime }+x \right )^{2} = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \sin \left (x y^{\prime }\right ) \cos \left (y\right ) = \cos \left (x y^{\prime }\right ) \sin \left (y\right )+y^{\prime }
\]
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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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| \[
{} {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3} = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{2} {y^{\prime }}^{3}+\left (y+2 x \right ) y y^{\prime }+y^{2} = 0
\]
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✗ |
✓ |
✗ |
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| \[
{} \left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 x y+x^{2}+2\right ) y^{\prime }+2 y^{2}+1 = 0
\]
|
✓ |
✗ |
✗ |
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| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}}
\]
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✓ |
✓ |
✗ |
|
| \[
{} \left (2 x -1\right )^{3} y^{\prime \prime \prime }+\left (2 x -1\right ) y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x +a \right )^{2} y^{\prime \prime }-4 \left (x +a \right ) y^{\prime }+6 y = x
\]
|
✓ |
✓ |
✗ |
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| \[
{} 16 \left (1+x \right )^{4} y^{\prime \prime \prime \prime }+96 \left (1+x \right )^{3} y^{\prime \prime \prime }+104 \left (1+x \right )^{2} y^{\prime \prime }+8 y^{\prime } \left (1+x \right )+y = x^{2}+4 x +3
\]
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✓ |
✓ |
✗ |
|
| \[
{} \left (1+x \right )^{2} y^{\prime \prime }+y^{\prime } \left (1+x \right )+y = 4 \cos \left (\ln \left (1+x \right )\right )
\]
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✓ |
✓ |
✗ |
|
| \[
{} 2 x^{2} y y^{\prime \prime }+4 y^{2} = x^{2} {y^{\prime }}^{2}+2 y y^{\prime } x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}+x +1\right ) y^{\prime \prime \prime }+\left (6 x +3\right ) y^{\prime \prime }+6 y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = \frac {2}{x^{3}}
\]
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✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime \prime }+y^{\prime \prime } \cos \left (x \right )-2 y^{\prime } \sin \left (x \right )-y \cos \left (x \right ) = \sin \left (2 x \right )
\]
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✓ |
✓ |
✗ |
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| \[
{} \sqrt {x}\, y^{\prime \prime }+2 x y^{\prime }+3 y = x
\]
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✓ |
✓ |
✗ |
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| \[
{} 2 x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (3+7 x \right ) y^{\prime }-3 y = x^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x^{2} \cos \left (y\right ) y^{\prime \prime }-2 x^{2} \sin \left (y\right ) {y^{\prime }}^{2}+x \cos \left (y\right ) y^{\prime }-\sin \left (y\right ) = \ln \left (x \right )
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2}-3 y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y+3 x y^{\prime }+2 y {y^{\prime }}^{2}+\left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
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| \[
{} y+x y^{\prime }+2 \left (x +y\right ) {y^{\prime }}^{2}+\left (y^{2}+2 x^{2} y^{\prime }\right ) y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = \ln \left (y\right ) y^{2}
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime }-y y^{\prime \prime } = n \sqrt {{y^{\prime }}^{2}+a^{2} y^{\prime \prime }}
\]
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✗ |
✗ |
✗ |
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| \[
{} x^{4} y^{\prime \prime } = \left (y-x y^{\prime }\right )^{3}
\]
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✓ |
✓ |
✗ |
|
| \[
{} 2 y^{\prime }+x y^{\prime \prime } = -y^{2}+x^{2} y^{\prime }
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \sin \left (x \right )^{2} y^{\prime \prime } = 2 y
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -y+x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = x \left (-x^{2}+1\right )^{{3}/{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x +2\right ) y^{\prime \prime }-\left (2 x +5\right ) y^{\prime }+2 y = {\mathrm e}^{x} \left (1+x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }-\left (1-\cot \left (x \right )\right ) y = {\mathrm e}^{x} \sin \left (x \right )
\]
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✓ |
✓ |
✗ |
|
| \[
{} \left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\]
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✓ |
✓ |
✗ |
|