# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
\[ {}2 y = \left (y^{4}+x \right ) y^{\prime } \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.933 |
|
\[ {}\cos \left (\theta \right ) r^{\prime } = 2+2 r \sin \left (\theta \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.42 |
|
\[ {}\sin \left (\theta \right ) r^{\prime }+1+r \tan \left (\theta \right ) = \cos \left (\theta \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
9.127 |
|
\[ {}y x^{\prime } = 2 y \,{\mathrm e}^{3 y}+x \left (3 y +2\right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.64 |
|
\[ {}y^{2}+1+\left (2 x y-y^{2}\right ) y^{\prime } = 0 \] |
exact |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
7.053 |
|
\[ {}y^{\prime }+y \cot \left (x \right )-\sec \left (x \right ) = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.962 |
|
\[ {}y+y^{3}+4 \left (x y^{2}-1\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
3.215 |
|
\[ {}2 y-x y-3+x y^{\prime } = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.361 |
|
\[ {}y+2 \left (x -2 y^{2}\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
5.5 |
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right )^{2}+4 y = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.448 |
|
\[ {}3 y^{2} y^{\prime }-x y^{3} = {\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right ) \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
3.883 |
|
\[ {}y^{3} y^{\prime }+y^{4} x = x \,{\mathrm e}^{-x^{2}} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
2.7 |
|
\[ {}\cosh \left (y\right ) y^{\prime }+\sinh \left (y\right )-{\mathrm e}^{-x} = 0 \] |
exactWithIntegrationFactor |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
3.327 |
|
\[ {}\sin \left (\theta \right ) \theta ^{\prime }+\cos \left (\theta \right )-t \,{\mathrm e}^{-t} = 0 \] |
exactWithIntegrationFactor |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
3.487 |
|
\[ {}x y y^{\prime } = x^{2}-y^{2} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.55 |
|
\[ {}y^{\prime }-x y = \sqrt {y}\, x \,{\mathrm e}^{x^{2}} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
3.466 |
|
\[ {}t x^{\prime }+x \left (1-x^{2} t^{4}\right ) = 0 \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.024 |
|
\[ {}x^{2} y^{\prime }+y^{2} = x y \] |
riccati, bernoulli, exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.638 |
|
\[ {}\csc \left (y\right ) \cot \left (y\right ) y^{\prime } = \csc \left (y\right )+{\mathrm e}^{x} \] |
exactWithIntegrationFactor |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
3.766 |
|
\[ {}y^{\prime }-x y = \frac {x}{y} \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.956 |
|
\[ {}y+x y^{\prime } = y^{2} x^{2} \cos \left (x \right ) \] |
riccati, bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
3.555 |
|
\[ {}r^{\prime }+\left (r-\frac {1}{r}\right ) \theta = 0 \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
4.374 |
|
\[ {}x y^{\prime }+2 y = 3 x^{3} y^{\frac {4}{3}} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
3.454 |
|
\[ {}3 y^{\prime }+\frac {2 y}{1+x} = \frac {x}{y^{2}} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
3.15 |
|
\[ {}\cos \left (y\right ) y^{\prime }+\left (\sin \left (y\right )-1\right ) \cos \left (x \right ) = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
40.737 |
|
\[ {}\left (x \tan \left (y\right )^{2}-x \right ) y^{\prime } = 2 x^{2}+\tan \left (y\right ) \] |
unknown |
[‘y=_G(x,y’)‘] |
❇ |
N/A |
6.686 |
|
\[ {}y^{\prime }+y \cos \left (x \right ) = y^{3} \sin \left (x \right ) \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
5.372 |
|
\[ {}y^{\prime }+y = y^{2} {\mathrm e}^{-t} \] |
riccati, bernoulli, first_order_ode_lie_symmetry_lookup |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
1.988 |
|
\[ {}y^{\prime } = x \left (1-{\mathrm e}^{2 y-x^{2}}\right ) \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
3.736 |
|
\[ {}2 y = \left (y^{4} x^{2}+x \right ) y^{\prime } \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.773 |
|
\[ {}1+x y \left (1+x y^{2}\right ) y^{\prime } = 0 \] |
unknown |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✗ |
N/A |
1.826 |
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }+x y = x \left (-x^{2}+1\right ) \sqrt {y} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
19.409 |
|
\[ {}\left (1-x \right ) y^{\prime }-y-1 = 0 \] |
exact, linear, separable, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.467 |
|
\[ {}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.587 |
|
\[ {}2 x +y-\left (x -2 y\right ) y^{\prime } = 0 \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.431 |
|
\[ {}x \ln \left (x \right ) y^{\prime }+y-x = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.645 |
|
\[ {}x -2 y+1+\left (y-2\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.158 |
|
\[ {}2 x y-2 x y^{3}+x^{3}+\left (x^{2}+y^{2}-3 x^{2} y^{2}\right ) y^{\prime } = 0 \] |
exact |
[_exact, _rational] |
✓ |
✓ |
2.935 |
|
\[ {}2 \,{\mathrm e}^{x}-t^{2}+t \,{\mathrm e}^{x} x^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
3.315 |
|
\[ {}6+2 y = x y y^{\prime } \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
4.969 |
|
\[ {}x -3 y = \left (3 y-x +2\right ) y^{\prime } \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.128 |
|
\[ {}\sin \left (x \right ) y-2 \cos \left (y\right )+\tan \left (x \right )-\left (\cos \left (x \right )-2 \sin \left (y\right ) x +\sin \left (y\right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
39.367 |
|
\[ {}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.58 |
|
\[ {}y-x y^{\prime } = 2 y^{\prime }+2 y^{2} \] |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
4.532 |
|
\[ {}\tan \left (y\right ) = \left (3 x +4\right ) y^{\prime } \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.477 |
|
\[ {}y^{\prime }+y \ln \left (y\right ) \tan \left (x \right ) = 2 y \] |
unknown |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
3.003 |
|
\[ {}2 x y+y^{4}+\left (x y^{3}-2 x^{2}\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.268 |
|
\[ {}y+\left (3 x -2 y\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
6.609 |
|
\[ {}r^{\prime } = r \cot \left (\theta \right ) \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.394 |
|
\[ {}\left (3 x +4 y\right ) y^{\prime }+y+2 x = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.538 |
|
\[ {}2 x^{3}-y^{3}-3 x +3 x y^{2} y^{\prime } = 0 \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
2.457 |
|
\[ {}x y^{\prime }-y-\sqrt {x^{2}+y^{2}} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
6.164 |
|
\[ {}y^{\prime } = \cos \left (y\right ) \cos \left (x \right )^{2} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
5.968 |
|
\[ {}x +y+\left (2 x +3 y-1\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.397 |
|
\[ {}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0 \] |
exact, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
3.323 |
|
\[ {}y^{\prime }+x +y \cot \left (x \right ) = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.445 |
|
\[ {}-6+3 x = x y y^{\prime } \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.77 |
|
\[ {}x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
3.02 |
|
\[ {}2 x y^{\prime }-y+\frac {x^{2}}{y^{2}} = 0 \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.127 |
|
\[ {}x y^{\prime }+y \left (1+y^{2}\right ) = 0 \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
5.533 |
|
\[ {}y \sqrt {x^{2}+y^{2}}+x y = x^{2} y^{\prime } \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
6.528 |
|
\[ {}3 \,{\mathrm e}^{x} \tan \left (y\right ) = \left (-{\mathrm e}^{x}+1\right ) \sec \left (y\right )^{2} y^{\prime } \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
7.693 |
|
\[ {}\sec \left (y\right )^{2} y^{\prime } = \tan \left (y\right )+2 x \,{\mathrm e}^{x} \] |
exactWithIntegrationFactor |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
4.887 |
|
\[ {}2 x \tan \left (y\right )+3 y^{2}+x^{2}+\left (x^{2} \sec \left (y\right )^{2}+6 x y-y^{2}\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
72.064 |
|
\[ {}y \cos \left (\frac {x}{y}\right )-\left (y+x \cos \left (\frac {x}{y}\right )\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.761 |
|
\[ {}y \left (3 x^{2}+y\right )-x \left (x^{2}-y\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
6.574 |
|
\[ {}x +\left (2 x +3 y+2\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
5.302 |
|
\[ {}x y^{\prime }-5 y-x \sqrt {y} = 0 \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.575 |
|
\[ {}x \sqrt {1-y}-\sqrt {-x^{2}+1}\, y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
6.065 |
|
\[ {}x y-y^{2}-x^{2} y^{\prime } = 0 \] |
riccati, bernoulli, exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.412 |
|
\[ {}x \,{\mathrm e}^{-y^{2}}+y y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.505 |
|
\[ {}\frac {2 y^{3}-2 x^{2} y^{3}-x +x y^{2} \ln \left (y\right )}{x y^{2}}+\frac {\left (2 y^{3} \ln \left (x \right )-x^{2} y^{3}+2 x +x y^{2}\right ) y^{\prime }}{y^{3}} = 0 \] |
exact |
[_exact] |
✓ |
✓ |
10.904 |
|
\[ {}x y^{\prime }-2 y-2 x^{4} y^{3} = 0 \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.782 |
|
\[ {}\left (-2 x^{2}-3 x y\right ) y^{\prime }+y^{2} = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.416 |
|
\[ {}x y^{\prime } = x^{4}+4 y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.769 |
|
\[ {}y+x y^{\prime } = x^{3} y^{6} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.024 |
|
\[ {}x^{\prime } = x+x^{2} {\mathrm e}^{\theta } \] |
riccati, bernoulli, first_order_ode_lie_symmetry_lookup |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
2.016 |
|
\[ {}x^{2}+y^{2} = 2 x y y^{\prime } \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
3.538 |
|
\[ {}3 x y+\left (3 x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
6.322 |
|
\[ {}y^{\prime }+2 y = 3 \,{\mathrm e}^{2 x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.713 |
|
\[ {}4 x y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.096 |
|
\[ {}x -2 y+3 = \left (x -2 y+1\right ) y^{\prime } \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.958 |
|
\[ {}y^{2}+\left (x^{3}-2 x y\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
15.165 |
|
\[ {}2 x y-2 y+1+x \left (-1+x \right ) y^{\prime } = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.252 |
|
\[ {}y^{3}+2 x^{2} y+\left (-3 x^{3}-2 x y^{2}\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
10.947 |
|
\[ {}2 \left (x^{2}+1\right ) y^{\prime } = \left (2 y^{2}-1\right ) x y \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
12.092 |
|
\[ {}y^{\prime }-y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.385 |
|
\[ {}y^{\prime \prime }-4 y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.031 |
|
\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.438 |
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.421 |
|
\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.471 |
|
\[ {}2 y^{\prime \prime }+3 y^{\prime }-2 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.454 |
|
\[ {}y^{\prime \prime }-2 y^{\prime }-y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.514 |
|
\[ {}y^{\prime \prime }-2 y^{\prime }-2 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.463 |
|
\[ {}y^{\prime \prime }-3 y^{\prime }+y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.506 |
|
\[ {}2 y^{\prime \prime }+2 y^{\prime }-y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.531 |
|
\[ {}2 y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.428 |
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.428 |
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.405 |
|
\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime }+8 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.507 |
|
|
||||||
|
||||||