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# |
ODE |
CAS classification |
Solved? |
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\[
{}x^{2} y^{\prime } = x y+x^{2} {\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x^{2} y^{\prime } = x y+x^{2} {\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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|
\[
{}x y^{\prime } = {\mathrm e}^{\frac {y}{x}} x +y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+x \,{\mathrm e}^{-\frac {y}{x}}}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\sec \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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|
\[
{}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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|
\[
{}y^{\prime } = \frac {y}{x}+\cosh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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|
\[
{}{\mathrm e}^{\frac {y}{x}} x +y = x y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}y^{\prime } = \frac {y}{x}+\tanh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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|
\[
{}x y^{\prime } = x \tan \left (\frac {y}{x}\right )+y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x y^{\prime } = x \tan \left (\frac {y}{x}\right )+y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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|
\[
{}x y^{\prime } = y+2 \,{\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
|
|
\[
{}-y+x y^{\prime } = x \cot \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
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\[
{}x \cos \left (\frac {y}{x}\right )^{2}-y+x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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|
\[
{}y-2 x^{3} \tan \left (\frac {y}{x}\right )-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
|
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\[
{}x y^{\prime } = y-{\mathrm e}^{\frac {y}{x}} x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}-y+x y^{\prime } = x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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|
\[
{}x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x +\sin \left (\frac {y}{x}\right )^{2} \left (y-x y^{\prime }\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x y^{\prime } = y-x \cos \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x y^{\prime }-y+x \sec \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x y^{\prime } = y+x \sec \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x y^{\prime } = y+x \sin \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x y^{\prime } = y-x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
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\[
{}x y^{\prime } = {\mathrm e}^{\frac {y}{x}} x +y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
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\[
{}x y^{\prime } = y-2 x \tanh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {y}{x}} x +y = x y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
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\[
{}y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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|
\[
{}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}y^{\prime } = \frac {y}{x}-\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}-y+x y^{\prime } = x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
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\[
{}x y^{\prime } = y-{\mathrm e}^{\frac {y}{x}} x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}y^{\prime } = \frac {y+x \,{\mathrm e}^{-\frac {2 y}{x}}}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x y^{\prime } = y+2 x \,{\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}y^{\prime } = 2 x^{2} \sin \left (\frac {y}{x}\right )^{2}+\frac {y}{x}
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
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\[
{}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x y^{\prime }+x \tan \left (\frac {y}{x}\right )-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}\left (-y+x y^{\prime }\right ) \cos \left (\frac {y}{x}\right )^{2}+x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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|
\[
{}{\mathrm e}^{\frac {y}{x}} x +y-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x +y \cos \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x \tan \left (\frac {y}{x}\right )+y-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x^{\prime } = {\mathrm e}^{\frac {x}{t}}+\frac {x}{t}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x \cos \left (\frac {y}{x}\right ) y^{\prime } = y \cos \left (\frac {y}{x}\right )-x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x y^{\prime } = y+x \cos \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x y^{\prime } = y+2 x \,{\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )-x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
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