|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}x y^{\prime }-a y+y^{2} = x^{-\frac {2 a}{3}} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
2.211 |
|
|
\[ {}u^{\prime }+u^{2} = \frac {c}{x^{\frac {4}{3}}} \] |
riccati |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
0.856 |
|
|
\[ {}u^{\prime }+b u^{2} = \frac {c}{x^{4}} \] |
riccati |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
0.313 |
|
|
\[ {}u^{\prime }-u^{2} = \frac {2}{x^{\frac {8}{3}}} \] |
riccati |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
1.391 |
|
|
\[ {}\frac {\sqrt {f \,x^{4}+c \,x^{3}+c \,x^{2}+b x +a}\, y^{\prime }}{\sqrt {a +b y+c y^{2}+c y^{3}+f y^{4}}} = -1 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
96.521 |
|
|
\[ {}{y^{\prime }}^{2}-5 y^{\prime }+6 = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.249 |
|
|
\[ {}{y^{\prime }}^{2}-\frac {a^{2}}{x^{2}} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.291 |
|
|
\[ {}{y^{\prime }}^{2} = \frac {1-x}{x} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.854 |
|
|
\[ {}{y^{\prime }}^{2}+\frac {2 x y^{\prime }}{y}-1 = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.858 |
|
|
\[ {}y = a y^{\prime }+b {y^{\prime }}^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
2.165 |
|
|
\[ {}x = a y^{\prime }+b {y^{\prime }}^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.504 |
|
|
\[ {}y = \sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \] |
quadrature |
[_quadrature] |
✓ |
✓ |
2.484 |
|
|
\[ {}x = \sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \] |
quadrature |
[_quadrature] |
✓ |
✓ |
2.289 |
|
|
\[ {}y^{\prime }-\frac {\sqrt {1+{y^{\prime }}^{2}}}{x} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.679 |
|
|
\[ {}x^{2} \left (1+{y^{\prime }}^{2}\right )^{3}-a^{2} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
5.812 |
|
|
\[ {}1+{y^{\prime }}^{2} = \frac {\left (x +a \right )^{2}}{2 x a +x^{2}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.461 |
|
|
\[ {}y = x y^{\prime }+y^{\prime }-{y^{\prime }}^{2} \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.26 |
|
|
\[ {}y = x y^{\prime }+\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}} \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
4.908 |
|
|
\[ {}y = x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}} \] |
bernoulli, dAlembert, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
5.283 |
|
|
\[ {}y = x y^{\prime }+a x \sqrt {1+{y^{\prime }}^{2}} \] |
dAlembert |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.856 |
|
|
\[ {}x -y y^{\prime } = a {y^{\prime }}^{2} \] |
dAlembert |
[_dAlembert] |
✓ |
✓ |
90.835 |
|
|
\[ {}y y^{\prime }+x = a \sqrt {1+{y^{\prime }}^{2}} \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
38.324 |
|
|
\[ {}y y^{\prime } = x +y^{2}-y^{2} {y^{\prime }}^{2} \] |
unknown |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
3.847 |
|
|
\[ {}y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}} = x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \] |
dAlembert |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
91.131 |
|
|
\[ {}y-2 x y^{\prime } = x {y^{\prime }}^{2} \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.322 |
|
|
\[ {}\frac {y-x y^{\prime }}{y^{2}+y^{\prime }} = \frac {y-x y^{\prime }}{1+x^{2} y^{\prime }} \] |
separable |
[_separable] |
✓ |
✓ |
0.897 |
|
|
\[ {}2 x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
9.542 |
|
|
\[ {}\left (x +\sqrt {y^{2}-x y}\right ) y^{\prime }-y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.41 |
|
|
\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.359 |
|
|
\[ {}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0 \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.28 |
|
|
\[ {}2 x^{2} y+y^{3}+\left (x y^{2}-2 x^{3}\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.447 |
|
|
\[ {}y^{2}+\left (x \sqrt {-x^{2}+y^{2}}-x y\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
5.064 |
|
|
\[ {}\frac {y \cos \left (\frac {y}{x}\right )}{x}-\left (\frac {x \sin \left (\frac {y}{x}\right )}{y}+\cos \left (\frac {y}{x}\right )\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.806 |
|
|
\[ {}y+x \ln \left (\frac {y}{x}\right ) y^{\prime }-2 x y^{\prime } = 0 \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.474 |
|
|
\[ {}2 y \,{\mathrm e}^{\frac {x}{y}}+\left (y-2 x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.985 |
|
|
\[ {}x \,{\mathrm e}^{\frac {y}{x}}-y \sin \left (\frac {y}{x}\right )+x \sin \left (\frac {y}{x}\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.615 |
|
|
\[ {}x^{2}+y^{2} = 2 x y y^{\prime } \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.574 |
|
|
\[ {}x \,{\mathrm e}^{\frac {y}{x}}+y = x y^{\prime } \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.81 |
|
|
\[ {}y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right ) = 0 \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.86 |
|
|
\[ {}x y-y^{2}-x^{2} y^{\prime } = 0 \] |
riccati, bernoulli, exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.472 |
|
|
\[ {}x +2 y-4-\left (2 x -4 y\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.886 |
|
|
\[ {}3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.258 |
|
|
\[ {}x +y+1+\left (2 x +2 y+2\right ) y^{\prime } = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.13 |
|
|
\[ {}x +y-1+\left (2 x +2 y-3\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.178 |
|
|
\[ {}x +y-1-\left (x -y-1\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.878 |
|
|
\[ {}x +y+\left (2 x +2 y-1\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.141 |
|
|
\[ {}7 y-3+\left (2 x +1\right ) y^{\prime } = 0 \] |
exact, linear, separable, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.137 |
|
|
\[ {}x +2 y+\left (3 x +6 y+3\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.178 |
|
|
\[ {}x +2 y+\left (y-1\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.835 |
|
|
\[ {}3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.572 |
|
|
\[ {}x +y+\left (3 x +3 y-4\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.444 |
|
|
\[ {}3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.75 |
|
|
\[ {}y+7+\left (2 x +y+3\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.445 |
|
|
\[ {}x +y+2-\left (x -y-4\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.932 |
|
|
\[ {}3 x^{2} y+8 x y^{2}+\left (x^{3}+8 x^{2} y+12 y^{2}\right ) y^{\prime } = 0 \] |
exact |
[_exact, _rational] |
✓ |
✓ |
0.43 |
|
|
\[ {}\frac {2 x y+1}{y}+\frac {\left (y-x \right ) y^{\prime }}{y^{2}} = 0 \] |
exact |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.494 |
|
|
\[ {}2 x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
exact |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
0.262 |
|
|
\[ {}{\mathrm e}^{x} \sin \left (y\right )+{\mathrm e}^{-y}-\left (x \,{\mathrm e}^{-y}-{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
0.45 |
|
|
\[ {}\cos \left (y\right )-\left (x \sin \left (y\right )-y^{2}\right ) y^{\prime } = 0 \] |
exact |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
0.364 |
|
|
\[ {}x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
1.805 |
|
|
\[ {}x^{2}-x +y^{2}-\left ({\mathrm e}^{y}-2 x y\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
1.616 |
|
|
\[ {}2 x +y \cos \left (x \right )+\left (2 y+\sin \left (x \right )-\sin \left (y\right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
0.403 |
|
|
\[ {}x \sqrt {x^{2}+y^{2}}-\frac {x^{2} y y^{\prime }}{y-\sqrt {x^{2}+y^{2}}} = 0 \] |
exact |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
0.998 |
|
|
\[ {}4 x^{3}-\sin \left (x \right )+y^{3}-\left (y^{2}+1-3 x y^{2}\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
0.685 |
|
|
\[ {}{\mathrm e}^{x} \left (y^{3}+x y^{3}+1\right )+3 y^{2} \left (x \,{\mathrm e}^{x}-6\right ) y^{\prime } = 0 \] |
exact |
[_exact, _Bernoulli] |
✓ |
✓ |
1.176 |
|
|
\[ {}\sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0 \] |
exact |
[_separable] |
✓ |
✓ |
31.728 |
|
|
\[ {}y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
3.813 |
|
|
\[ {}y^{2}+y-x y^{\prime } = 0 \] |
exact |
[_separable] |
✓ |
✓ |
1.007 |
|
|
\[ {}y \sec \left (x \right )+\sin \left (x \right ) y^{\prime } = 0 \] |
exact |
[_separable] |
✓ |
✓ |
0.883 |
|
|
\[ {}{\mathrm e}^{x}-\sin \left (y\right )+\cos \left (y\right ) y^{\prime } = 0 \] |
exact |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
0.29 |
|
|
\[ {}x y+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
exact |
[_separable] |
✓ |
✓ |
0.407 |
|
|
\[ {}y^{3}+x y^{2}+y+\left (x^{3}+x^{2} y+x \right ) y^{\prime } = 0 \] |
exact |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
0.377 |
|
|
\[ {}3 y-x y^{\prime } = 0 \] |
exact |
[_separable] |
✓ |
✓ |
0.804 |
|
|
\[ {}y-3 x y^{\prime } = 0 \] |
exact |
[_separable] |
✓ |
✓ |
0.34 |
|
|
\[ {}y \left (2 x^{2} y^{3}+3\right )+x \left (x^{2} y^{3}-1\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.148 |
|
|
\[ {}2 x y+x^{2}+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
exact |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
0.328 |
|
|
\[ {}x^{2}+y \cos \left (x \right )+\left (y^{3}+\sin \left (x \right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
0.353 |
|
|
\[ {}x^{2}+y^{2}+x +x y y^{\prime } = 0 \] |
exact |
[_rational, _Bernoulli] |
✓ |
✓ |
0.24 |
|
|
\[ {}x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
0.333 |
|
|
\[ {}{\mathrm e}^{x} \sin \left (y\right )+{\mathrm e}^{-y}-\left (x \,{\mathrm e}^{-y}-{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
0.341 |
|
|
\[ {}x^{2}-y^{2}-y-\left (x^{2}-y^{2}-x \right ) y^{\prime } = 0 \] |
exactByInspection, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
2.471 |
|
|
\[ {}x^{4} y^{2}-y+\left (y^{4} x^{2}-x \right ) y^{\prime } = 0 \] |
exact |
[_rational] |
✓ |
✓ |
0.397 |
|
|
\[ {}y \left (2 x +y^{3}\right )-x \left (2 x -y^{3}\right ) y^{\prime } = 0 \] |
exact |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
0.32 |
|
|
\[ {}\arctan \left (x y\right )+\frac {x y-2 x y^{2}}{1+x^{2} y^{2}}+\frac {\left (x^{2}-2 x^{2} y\right ) y^{\prime }}{1+x^{2} y^{2}} = 0 \] |
exact |
[_exact] |
✓ |
✓ |
0.739 |
|
|
\[ {}{\mathrm e}^{x} \left (1+x \right )+\left (y \,{\mathrm e}^{y}-x \,{\mathrm e}^{x}\right ) y^{\prime } = 0 \] |
exact |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
0.317 |
|
|
\[ {}\frac {x y+1}{y}+\frac {\left (2 y-x \right ) y^{\prime }}{y^{2}} = 0 \] |
exact |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.508 |
|
|
\[ {}y^{2}-3 x y-2 x^{2}+\left (x y-x^{2}\right ) y^{\prime } = 0 \] |
exact |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.293 |
|
|
\[ {}y \left (y+2 x +1\right )-x \left (x +2 y-1\right ) y^{\prime } = 0 \] |
exact |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.45 |
|
|
\[ {}y \left (2 x -y-1\right )+x \left (2 y-x -1\right ) y^{\prime } = 0 \] |
exact |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.445 |
|
|
\[ {}y^{2}+12 x^{2} y+\left (2 x y+4 x^{3}\right ) y^{\prime } = 0 \] |
exact |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.308 |
|
|
\[ {}3 \left (x +y\right )^{2}+x \left (2 x +3 y\right ) y^{\prime } = 0 \] |
exact |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.264 |
|
|
\[ {}y-\left (x +x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
exactByInspection |
[_rational] |
✓ |
✓ |
1.223 |
|
|
\[ {}2 x y+\left (x^{2}+y^{2}+a \right ) y^{\prime } = 0 \] |
exact |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
0.378 |
|
|
\[ {}2 x y+x^{2}+b +\left (x^{2}+y^{2}+a \right ) y^{\prime } = 0 \] |
exact |
[_exact, _rational] |
✓ |
✓ |
0.435 |
|
|
\[ {}x y^{\prime }+y = x^{3} \] |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.864 |
|
|
\[ {}y^{\prime }+a y = b \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.48 |
|
|
\[ {}x y^{\prime }+y = y^{2} \ln \left (x \right ) \] |
riccati, bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
1.133 |
|
|
\[ {}x^{\prime }+2 x y = {\mathrm e}^{-y^{2}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.774 |
|
|
\[ {}r^{\prime } = \left (r+{\mathrm e}^{-\theta }\right ) \tan \left (\theta \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.231 |
|
|
\[ {}y^{\prime }-\frac {2 x y}{x^{2}+1} = 1 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.866 |
|
|
|
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|
|
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