Ode’s of the form \(y'=g(x) e^{a(x) + b y}+ f(x)\) for an example \(y'=x e^{\sin (x)+y}+x^2\). This form did not fit into any of the other forms, so had its own solver. Number of problems in this table is 39
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) |
|
\[ {}y^{\prime } = 6 \,{\mathrm e}^{2 x -y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.887 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x +y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.915 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{3+t +y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.211 |
|
|
\[ {}y^{\prime } = -x \,{\mathrm e}^{y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.436 |
|
|
\[ {}{\mathrm e}^{2 y}+\left (1+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.772 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x -2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.099 |
|
|
\[ {}{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.299 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{y} \sin \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.816 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x -y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.619 |
|
|
\[ {}y^{\prime } = x \,{\mathrm e}^{-2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.018 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{y}+x \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
0.646 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x +y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.585 |
|
|
\[ {}y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.698 |
|
|
\[ {}y^{\prime } = 8 x^{3} {\mathrm e}^{-2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.196 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{3 x -2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.455 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{x -y}}{1+{\mathrm e}^{x}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.982 |
|
|
\[ {}x^{2} y^{\prime }+{\mathrm e}^{-y} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.014 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x +y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.191 |
|
|
\[ {}y^{\prime } = 10+{\mathrm e}^{x +y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
3.434 |
|
|
\[ {}y^{\prime } = 10 \,{\mathrm e}^{x +y}+x^{2} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
1.578 |
|
|
\[ {}y^{\prime } = x \,{\mathrm e}^{x +y}+\sin \left (x \right ) \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
3.373 |
|
|
\[ {}y^{\prime } = 5 \,{\mathrm e}^{x^{2}+20 y}+\sin \left (x \right ) \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
3.355 |
|
|
\[ {}y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.88 |
|
|
\[ {}x^{\prime } = t^{2} {\mathrm e}^{-x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.192 |
|
|
\[ {}x^{\prime } = {\mathrm e}^{t +x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.159 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x -y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.956 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x -y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.626 |
|
|
\[ {}y^{\prime } = x \,{\mathrm e}^{y-x^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.371 |
|
|
\[ {}x \,{\mathrm e}^{y}+y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.982 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{2 x -3 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.785 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{4 x +3 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.825 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{4 x +3 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.732 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{2 y+10 t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.952 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{3 y+2 t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.931 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{t -y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.177 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x -y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.232 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{2 x -y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.476 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{8 y}}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.113 |
|
|
\[ {}y^{\prime }-1 = {\mathrm e}^{2 y+x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.79 |
|
|
|
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