These are ode’s called First order homogeneous type D as defined by Maple here Number of problems in this table is 938
Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}x^{2} y^{\prime } = {\mathrm e}^{\frac {y}{x}} x^{2}+x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.047 |
|
|
\[ {}x y^{\prime } = x \,{\mathrm e}^{\frac {y}{x}}+y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.954 |
|
|
\[ {}y^{\prime } = \frac {y+x \,{\mathrm e}^{-\frac {y}{x}}}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.342 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\sec \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.759 |
|
|
\[ {}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.111 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\cosh \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.426 |
|
|
\[ {}x \,{\mathrm e}^{\frac {y}{x}}+y = x y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.766 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.964 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\tanh \left (\frac {y}{x}\right ) \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.241 |
|
|
\[ {}x y^{\prime } = x \tan \left (\frac {y}{x}\right )+y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.953 |
|
|
\[ {}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.435 |
|
|
\[ {}x y^{\prime } = y+2 \,{\mathrm e}^{-\frac {y}{x}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
0.848 |
|
|
\[ {}-y+x y^{\prime } = x \cot \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.013 |
|
|
\[ {}x \cos \left (\frac {y}{x}\right )^{2}-y+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.566 |
|
|
\[ {}y-2 x^{3} \tan \left (\frac {y}{x}\right )-x y^{\prime } = 0 \] |
1 |
2 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
3.208 |
|
|
\[ {}x y^{\prime } = y-x \,{\mathrm e}^{\frac {y}{x}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.384 |
|
|
\[ {}x y^{\prime } = y-x \cos \left (\frac {y}{x}\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.992 |
|
|
\[ {}x y^{\prime }-y+x \sec \left (\frac {y}{x}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.012 |
|
|
\[ {}x y^{\prime } = y+x \sec \left (\frac {y}{x}\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.026 |
|
|
\[ {}x y^{\prime } = y+x \sin \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.843 |
|
|
\[ {}x y^{\prime } = y-x \tan \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.0 |
|
|
\[ {}x y^{\prime } = x \,{\mathrm e}^{\frac {y}{x}}+y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.691 |
|
|
\[ {}x y^{\prime } = y-2 x \tanh \left (\frac {y}{x}\right ) \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.108 |
|
|
\[ {}x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.442 |
|
|
\[ {}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.28 |
|
|
\[ {}x \,{\mathrm e}^{\frac {y}{x}}+y = x y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.81 |
|
|
\[ {}y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right ) = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.86 |
|
|
\[ {}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.015 |
|
|
\[ {}y^{\prime } = \frac {y}{x}-\tan \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.213 |
|
|
\[ {}y^{\prime } = 2 x^{2} \sin \left (\frac {y}{x}\right )^{2}+\frac {y}{x} \] |
1 |
2 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
4.247 |
|
|
\[ {}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.385 |
|
|
\[ {}x y^{\prime }+x \tan \left (\frac {y}{x}\right )-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.679 |
|
|
\[ {}\left (-y+x y^{\prime }\right ) \cos \left (\frac {y}{x}\right )^{2}+x = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.676 |
|
|
\[ {}y^{\prime } = \frac {y+F \left (\frac {y}{x}\right ) x^{2}}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
0.601 |
|
|
\[ {}x \,{\mathrm e}^{\frac {y}{x}}+y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.009 |
|
|
\[ {}x +y \cos \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.654 |
|
|
\[ {}x \tan \left (\frac {y}{x}\right )+y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.308 |
|
|
\[ {}x^{\prime } = {\mathrm e}^{\frac {x}{t}}+\frac {x}{t} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.42 |
|
|
\[ {}x \cos \left (\frac {y}{x}\right ) y^{\prime } = y \cos \left (\frac {y}{x}\right )-x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.165 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.951 |
|
|
\[ {}x y^{\prime } = y+x \cos \left (\frac {y}{x}\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.314 |
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