| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x^{3}+y^{2} \sqrt {x^{2}+y^{2}}-x y \sqrt {x^{2}+y^{2}}\, y^{\prime } = 0
\]
|
✓ |
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| \[
{} 8 \cos \left (y\right )^{2}+\csc \left (x \right )^{2} y^{\prime } = 0
\]
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| \[
{} \left (3 x +8\right ) \left (4+y^{2}\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime } = 0
\]
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| \[
{} x^{2}+2 y^{2}+\left (4 x y-y^{2}\right ) y^{\prime } = 0
\]
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✓ |
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| \[
{} x y^{\prime }+y = \left (x y\right )^{{3}/{2}}
\]
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✓ |
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| \[
{} y^{\prime }+y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 0 & 1\le x \end {array}\right .
\]
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✓ |
✓ |
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| \[
{} y^{\prime }+y = \left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right .
\]
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✓ |
✓ |
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| \[
{} y^{\prime }+y = \left \{\begin {array}{cc} {\mathrm e}^{-x} & 0\le x <2 \\ {\mathrm e}^{-2} & 2\le x \end {array}\right .
\]
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✓ |
✓ |
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| \[
{} \left (x +2\right ) y^{\prime }+y = \left \{\begin {array}{cc} 2 x & 0\le x <2 \\ 4 & 2\le x \end {array}\right .
\]
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| \[
{} y^{\prime } = -y^{2}+x y+1
\]
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✓ |
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| \[
{} \left (3 x^{2} y^{2}-x \right ) y^{\prime }+2 x y^{3}-y = 0
\]
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✓ |
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| \[
{} 8+2 y^{2}+\left (-x^{2}+1\right ) y y^{\prime } = 0
\]
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✓ |
✓ |
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| \[
{} 3 x^{2}+2 x y^{2}+\left (2 x^{2} y+6 y^{2}\right ) y^{\prime } = 0
\]
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✓ |
✓ |
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| \[
{} y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le x <2 \\ 0 & 0<x \end {array}\right .
\]
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✓ |
✓ |
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| \[
{} \left (x +2\right ) y^{\prime }+y = \left \{\begin {array}{cc} 2 x & 0\le x \le 2 \\ 4 & 2<x \end {array}\right .
\]
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✓ |
✓ |
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| \[
{} 5 x y+4 y^{2}+1+\left (x^{2}+2 x y\right ) y^{\prime } = 0
\]
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✓ |
✓ |
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| \[
{} \left (x +y+1\right ) y^{\prime }+1+4 x +3 y = 0
\]
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✓ |
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| \[
{} y^{\prime \prime }+x y^{\prime }+x^{2} y = 0
\]
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✓ |
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| \[
{} \left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
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✓ |
✓ |
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| \[
{} \left (x^{2}-x +1\right ) y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+\left (1+x \right ) y = 0
\]
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✓ |
✓ |
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| \[
{} \left (2 x +1\right ) y^{\prime \prime }-4 y^{\prime } \left (1+x \right )+4 y = 0
\]
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✓ |
✓ |
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| \[
{} \left (x^{3}-x^{2}\right ) y^{\prime \prime }-\left (x^{3}+2 x^{2}-2 x \right ) y^{\prime }+\left (2 x^{2}+2 x -2\right ) y = 0
\]
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✓ |
✓ |
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \frac {1}{{\mathrm e}^{x}+1}
\]
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✓ |
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \frac {1}{{\mathrm e}^{2 x}+1}
\]
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| \[
{} \left (1+x \right )^{2} y^{\prime \prime }-2 y^{\prime } \left (1+x \right )+2 y = 1
\]
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✓ |
✓ |
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| \[
{} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 y^{\prime } \left (1+x \right )+2 y = \left (x +2\right )^{2}
\]
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✓ |
✓ |
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| \[
{} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = x^{3}
\]
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✓ |
✓ |
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|
| \[
{} x \left (x -2\right ) y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 \left (x -1\right ) y = 3 x^{2} \left (x -2\right )^{2} {\mathrm e}^{x}
\]
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✓ |
✓ |
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| \[
{} \left (2 x +1\right ) \left (1+x \right ) y^{\prime \prime }+2 x y^{\prime }-2 y = \left (2 x +1\right )^{2}
\]
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✓ |
✓ |
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| \[
{} \sin \left (x \right )^{2} y^{\prime \prime }-2 \sin \left (x \right ) \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y = \sin \left (x \right )^{3}
\]
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✓ |
✓ |
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| \[
{} \left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y = 0
\]
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✓ |
✓ |
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| \[
{} \left (x^{3}+x^{2}\right ) y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+4 y = 0
\]
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✓ |
✓ |
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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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✓ |
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| \[
{} \left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y = 0
\]
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✓ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-2 x \left (t \right )-4 y \left (t \right ) = {\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-y \left (t \right ) = {\mathrm e}^{4 t}]
\]
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✓ |
✓ |
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| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right ) = -2 t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )-y \left (t \right ) = t^{2}]
\]
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✓ |
✓ |
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| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-3 y \left (t \right ) = {\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right ) = {\mathrm e}^{3 t}]
\]
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✓ |
✓ |
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|
| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-2 y \left (t \right ) = 2 \,{\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )-4 y \left (t \right ) = {\mathrm e}^{2 t}]
\]
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✓ |
✓ |
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| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right ) = \sin \left (t \right ), x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = 0]
\]
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✓ |
✓ |
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|
| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right .
\]
|
✓ |
✓ |
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|
| \[
{} y^{\prime \prime }+5 y^{\prime }+6 y = \left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right .
\]
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✓ |
✓ |
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| \[
{} y^{\prime \prime }+4 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right .
\]
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✓ |
✓ |
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| \[
{} y^{\prime \prime }+6 y^{\prime }+8 y = \left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\]
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✓ |
✓ |
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| \[
{} \left (t^{3}-2 t^{2}\right ) x^{\prime \prime }-\left (t^{3}+2 t^{2}-6 t \right ) x^{\prime }+\left (3 t^{2}-6\right ) x = 0
\]
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✓ |
✓ |
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|
| \[
{} t^{3} x^{\prime \prime \prime }-\left (3+t \right ) t^{2} x^{\prime \prime }+2 t \left (3+t \right ) x^{\prime }-2 \left (3+t \right ) x = 0
\]
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✓ |
✓ |
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| \[
{} \left (2 t +1\right ) x^{\prime \prime }+t^{3} x^{\prime }+x = 0
\]
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✗ |
✗ |
✗ |
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| \[
{} t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} t^{3} x^{\prime \prime }-\left (t^{3}+2 t^{2}-t \right ) x^{\prime }+\left (t^{2}+t -1\right ) x = 0
\]
|
✓ |
✓ |
✗ |
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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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| \[
{} \frac {\left (t +1\right ) x^{\prime \prime }}{t}-\frac {x^{\prime }}{t^{2}}+\frac {x}{t^{3}} = 0
\]
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✓ |
✓ |
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| \[
{} \left (t^{4}+t^{2}\right ) x^{\prime \prime }+2 t^{3} x^{\prime }+3 x = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{\prime \prime }-\tan \left (t \right ) x^{\prime }+x = 0
\]
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✓ |
✓ |
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| \[
{} f \left (t \right ) x^{\prime \prime }+x g \left (t \right ) = 0
\]
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✗ |
✗ |
✗ |
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| \[
{} 2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }+\frac {\lambda y}{x^{2}+1} = 0
\]
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✓ |
✓ |
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| \[
{} -\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y = 0
\]
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✓ |
✓ |
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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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✗ |
✗ |
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| \[
{} x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x = 0
\]
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✗ |
✗ |
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| \[
{} x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x = 0
\]
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✗ |
✗ |
✗ |
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| \[
{} x^{\prime \prime }+\left (x^{4}+x^{2}\right ) x^{\prime }+x^{3}+x = 0
\]
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✗ |
✗ |
✗ |
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| \[
{} x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3} = 0
\]
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✗ |
✗ |
✗ |
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| \[
{} x^{\prime \prime }+\left (1+x^{2}\right ) x^{\prime }+x^{3} = 0
\]
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✗ |
✗ |
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{2}, y^{\prime }\left (t \right ) = 2 y \left (t \right )-y \left (t \right )^{2}]
\]
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✓ |
✓ |
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| \[
{} x^{\prime } = -x \left (k^{2}+x^{2}\right )
\]
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✓ |
✗ |
✗ |
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| \[
{} x^{\prime }+\left (a +\frac {1}{t}\right ) x = b
\]
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✓ |
✓ |
✗ |
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| \[
{} 2 x y-\sec \left (x \right )^{2}+\left (x^{2}+2 y\right ) y^{\prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (x \cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }-\sin \left (x \right ) y+\sin \left (y\right ) = 0
\]
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✓ |
✓ |
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| \[
{} {\mathrm e}^{x} \sin \left (y\right )+y+\left ({\mathrm e}^{x} \cos \left (y\right )+x +{\mathrm e}^{y}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} {\mathrm e}^{-y} \sec \left (x \right )+2 \cos \left (x \right )-{\mathrm e}^{-y} y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} x^{\prime } = \frac {x^{2}+t \sqrt {t^{2}+x^{2}}}{t x}
\]
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✓ |
✓ |
✗ |
|
| \[
{} t^{2} y^{\prime \prime }-\left (t^{2}+2 t \right ) y^{\prime }+\left (t +2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (\cos \left (t \right ) t -\sin \left (t \right )\right ) x^{\prime \prime }-x^{\prime } t \sin \left (t \right )-x \sin \left (t \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (-t^{2}+t \right ) x^{\prime \prime }+\left (-t^{2}+2\right ) x^{\prime }+\left (2-t \right ) x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \tan \left (t \right ) x^{\prime \prime }-3 x^{\prime }+\left (\tan \left (t \right )+3 \cot \left (t \right )\right ) x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\tan \left (x \right )^{2}-1\right ) y^{\prime \prime }-4 \tan \left (x \right )^{3} y^{\prime }+2 y \sec \left (x \right )^{4} = \left (\tan \left (x \right )^{2}-1\right ) \left (1-2 \sin \left (x \right )^{2}\right )
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-n^{2}+x^{2}\right ) y = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} x^{\prime } = {\mathrm e}^{\frac {x}{t}}+\frac {x}{t}
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime } = \frac {y}{y^{3}+x}
\]
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✓ |
✓ |
✗ |
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| \[
{} y = {y^{\prime }}^{4}-{y^{\prime }}^{3}-2
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime } = x +y^{2}
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = x y^{3}+x^{2}
\]
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✗ |
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| \[
{} y^{\prime } = x^{2}-y^{2}
\]
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✓ |
✓ |
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| \[
{} y = 5 x y^{\prime }-{y^{\prime }}^{2}
\]
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✓ |
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| \[
{} y^{\prime } = x -y^{2}
\]
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✓ |
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✗ |
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| \[
{} y = x y^{\prime }+{y^{\prime }}^{2}
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{2}-y+\left (x^{2} y^{2}+x \right ) y^{\prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (-x +y^{2}\right ) y^{\prime }-y+x^{2} = 0
\]
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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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| \[
{} y^{\prime \prime }+\frac {2 {y^{\prime }}^{2}}{1-y} = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{3} x^{\prime \prime }+1 = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} {y^{\prime \prime \prime }}^{2}+{y^{\prime \prime }}^{2} = 1
\]
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✓ |
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✗ |
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| \[
{} y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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✓ |
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| \[
{} y^{\prime \prime } = 3 \sqrt {y}
\]
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✓ |
✓ |
✗ |
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| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = \frac {y y^{\prime }}{\sqrt {x^{2}+1}}
\]
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✓ |
✓ |
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| \[
{} y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}+{y^{\prime \prime }}^{2}
\]
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✓ |
✓ |
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| \[
{} y+2 y^{\prime }+y^{\prime \prime } = \sinh \left (x \right )
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (x^{2}-1\right ) y^{\prime \prime }-6 y = 1
\]
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✓ |
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| \[
{} m x^{\prime \prime } = f \left (x\right )
\]
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|