|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}1-\left (1+2 x \tan \left (y\right )\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.132 |
|
|
\[ {}\left (y^{3}+\frac {x}{y}\right ) y^{\prime } = 1 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.215 |
|
|
\[ {}1+\left (x -y^{2}\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
0.944 |
|
|
\[ {}y^{2}+\left (x y+y^{2}-1\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
1.112 |
|
|
\[ {}y = \left ({\mathrm e}^{y}+2 x y-2 x \right ) y^{\prime } \] |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.802 |
|
|
\[ {}\left (2 x +3\right ) y^{\prime } = y+\sqrt {2 x +3} \] |
linear |
[_linear] |
✓ |
✓ |
0.312 |
|
|
\[ {}y+\left (y^{2} {\mathrm e}^{y}-x \right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.271 |
|
|
\[ {}y^{\prime } = 1+3 y \tan \left (x \right ) \] |
linear |
[_linear] |
✓ |
✓ |
0.371 |
|
|
\[ {}\left (\cos \left (x \right )+1\right ) y^{\prime } = \sin \left (x \right ) \left (\sin \left (x \right )+\sin \left (x \right ) \cos \left (x \right )-y\right ) \] |
linear |
[_linear] |
✓ |
✓ |
0.499 |
|
|
\[ {}y^{\prime } = \left (\sin \left (x \right )^{2}-y\right ) \cos \left (x \right ) \] |
linear |
[_linear] |
✓ |
✓ |
0.522 |
|
|
\[ {}\left (1+x \right ) y^{\prime }-y = x \left (1+x \right )^{2} \] |
linear |
[_linear] |
✓ |
✓ |
0.263 |
|
|
\[ {}1+y+\left (x -y \left (y+1\right )^{2}\right ) y^{\prime } = 0 \] |
exact, differentialType, first_order_ode_lie_symmetry_calculated |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
4.974 |
|
|
\[ {}y^{\prime }+y^{2} = x^{2}+1 \] |
riccati |
[_Riccati] |
✓ |
✓ |
0.535 |
|
|
\[ {}3 x y^{\prime }-3 x y^{4} \ln \left (x \right )-y = 0 \] |
bernoulli |
[_Bernoulli] |
✓ |
✓ |
1.372 |
|
|
\[ {}y^{\prime } = \frac {4 x^{3} y^{2}}{y x^{4}+2} \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.477 |
|
|
\[ {}y \left (6 y^{2}-x -1\right )+2 x y^{\prime } = 0 \] |
bernoulli |
[_rational, _Bernoulli] |
✓ |
✓ |
0.606 |
|
|
\[ {}\left (1+x \right ) \left (y^{\prime }+y^{2}\right )-y = 0 \] |
bernoulli |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
0.238 |
|
|
\[ {}x y y^{\prime }+y^{2}-\sin \left (x \right ) = 0 \] |
bernoulli |
[_Bernoulli] |
✓ |
✓ |
0.791 |
|
|
\[ {}2 x^{3}-y^{4}+x y^{3} y^{\prime } = 0 \] |
bernoulli |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.724 |
|
|
\[ {}y^{\prime }-y \tan \left (x \right )+y^{2} \cos \left (x \right ) = 0 \] |
bernoulli |
[_Bernoulli] |
✓ |
✓ |
0.339 |
|
|
\[ {}6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.864 |
|
|
\[ {}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1 = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.201 |
|
|
\[ {}y = x y^{\prime }+{y^{\prime }}^{3} \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.59 |
|
|
\[ {}x \left ({y^{\prime }}^{2}-1\right ) = 2 y^{\prime } \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.622 |
|
|
\[ {}x y^{\prime } \left (y^{\prime }+2\right ) = y \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.412 |
|
|
\[ {}x = y^{\prime } \sqrt {1+{y^{\prime }}^{2}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
20.843 |
|
|
\[ {}2 {y^{\prime }}^{2} \left (y-x y^{\prime }\right ) = 1 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.995 |
|
|
\[ {}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
84.592 |
|
|
\[ {}{y^{\prime }}^{3}+y^{2} = x y y^{\prime } \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
111.411 |
|
|
\[ {}2 x y^{\prime }-y = y^{\prime } \ln \left (y y^{\prime }\right ) \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
2.922 |
|
|
\[ {}y = x y^{\prime }-x^{2} {y^{\prime }}^{3} \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
92.662 |
|
|
\[ {}y \left (y-2 x y^{\prime }\right )^{3} = {y^{\prime }}^{2} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
103.855 |
|
|
\[ {}x y^{\prime }+y = 4 \sqrt {y^{\prime }} \] |
dAlembert |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
11.989 |
|
|
\[ {}2 x y^{\prime }-y = \ln \left (y^{\prime }\right ) \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
2.606 |
|
|
\[ {}x y^{2} \left (x y^{\prime }+y\right ) = 1 \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.256 |
|
|
\[ {}5 y+{y^{\prime }}^{2} = x \left (x +y^{\prime }\right ) \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
4.176 |
|
|
\[ {}y^{\prime } = \frac {y+2}{1+x} \] |
exact, linear, separable, homogeneousTypeD2, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.021 |
|
|
\[ {}x y^{\prime } = y-x \,{\mathrm e}^{\frac {y}{x}} \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.384 |
|
|
\[ {}1+\sin \left (2 x \right ) y^{2}-2 y \cos \left (x \right )^{2} y^{\prime } = 0 \] |
exact, bernoulli, first_order_ode_lie_symmetry_lookup |
[_exact, _Bernoulli] |
✓ |
✓ |
11.411 |
|
|
\[ {}2 \sqrt {x y}-y-x y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
13.593 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{\frac {x y^{\prime }}{y}} \] |
dAlembert, homogeneousTypeD2 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.599 |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.427 |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }+9 y^{\prime }+9 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.437 |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.368 |
|
|
\[ {}y^{\prime \prime \prime }+8 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.727 |
|
|
\[ {}y^{\prime \prime \prime }-8 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.682 |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.776 |
|
|
\[ {}y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.324 |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime }+16 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
1.32 |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.923 |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+5 y^{\prime \prime }+5 y^{\prime }-6 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.306 |
|
|
\[ {}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.372 |
|
|
\[ {}y^{\left (6\right )}-64 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
4.147 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+10 y = 3 x \,{\mathrm e}^{-3 x}-2 \,{\mathrm e}^{3 x} \cos \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.997 |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.506 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = \left (x +{\mathrm e}^{x}\right ) \sin \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.297 |
|
|
\[ {}y^{\prime \prime }+4 y = \sinh \left (x \right ) \sin \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.947 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \cosh \left (x \right ) \sin \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.684 |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime } = \sin \left (x \right )+\cos \left (x \right ) x \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
2.874 |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y = {\mathrm e}^{2 x} \sin \left (2 x \right )+2 x^{2} \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
13.993 |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+3 y^{\prime } = x^{2}+{\mathrm e}^{2 x} x \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
1.353 |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime } = 7 x -3 \cos \left (x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_y]] |
✓ |
✓ |
0.595 |
|
|
\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = \sin \left (x \right ) \cos \left (2 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
7.136 |
|
|
\[ {}y^{\prime } = a f \left (x \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.254 |
|
|
\[ {}y^{\prime } = x +\sin \left (x \right )+y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.786 |
|
|
\[ {}y^{\prime } = x^{2}+3 \cosh \left (x \right )+2 y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.769 |
|
|
\[ {}y^{\prime } = a +b x +c y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.579 |
|
|
\[ {}y^{\prime } = a \cos \left (b x +c \right )+k y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.238 |
|
|
\[ {}y^{\prime } = a \sin \left (b x +c \right )+k y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.006 |
|
|
\[ {}y^{\prime } = a +b \,{\mathrm e}^{k x}+c y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.674 |
|
|
\[ {}y^{\prime } = x \left (x^{2}-y\right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.328 |
|
|
\[ {}y^{\prime } = x \left ({\mathrm e}^{-x^{2}}+a y\right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.71 |
|
|
\[ {}y^{\prime } = x^{2} \left (a \,x^{3}+b y\right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.734 |
|
|
\[ {}y^{\prime } = a \,x^{n} y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.195 |
|
|
\[ {}y^{\prime } = \sin \left (x \right ) \cos \left (x \right )+y \cos \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.138 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{\sin \left (x \right )}+y \cos \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.684 |
|
|
\[ {}y^{\prime } = y \cot \left (x \right ) \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.142 |
|
|
\[ {}y^{\prime } = 1-y \cot \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.454 |
|
|
\[ {}y^{\prime } = x \csc \left (x \right )-y \cot \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.486 |
|
|
\[ {}y^{\prime } = \left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
4.082 |
|
|
\[ {}y^{\prime } = \sec \left (x \right )-y \cot \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.72 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x} \sin \left (x \right )+y \cot \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.099 |
|
|
\[ {}y^{\prime }+\csc \left (x \right )+2 y \cot \left (x \right ) = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.667 |
|
|
\[ {}y^{\prime } = 4 \csc \left (x \right ) x \sec \left (x \right )^{2}-2 y \cot \left (2 x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
4.425 |
|
|
\[ {}y^{\prime } = 2 \cot \left (x \right )^{2} \cos \left (2 x \right )-2 y \csc \left (2 x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.731 |
|
|
\[ {}y^{\prime } = 4 \csc \left (x \right ) x \left (\sin \left (x \right )^{3}+y\right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
8.142 |
|
|
\[ {}y^{\prime } = 4 \csc \left (x \right ) x \left (1-\tan \left (x \right )^{2}+y\right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
76.021 |
|
|
\[ {}y^{\prime } = y \sec \left (x \right ) \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.773 |
|
|
\[ {}y^{\prime }+\tan \left (x \right ) = \left (1-y\right ) \sec \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.483 |
|
|
\[ {}y^{\prime } = y \tan \left (x \right ) \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.871 |
|
|
\[ {}y^{\prime } = \cos \left (x \right )+y \tan \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.931 |
|
|
\[ {}y^{\prime } = \cos \left (x \right )-y \tan \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.838 |
|
|
\[ {}y^{\prime } = \sec \left (x \right )-y \tan \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.866 |
|
|
\[ {}y^{\prime } = \sin \left (2 x \right )+y \tan \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.98 |
|
|
\[ {}y^{\prime } = \sin \left (2 x \right )-y \tan \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.915 |
|
|
\[ {}y^{\prime } = \sin \left (x \right )+2 y \tan \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.968 |
|
|
\[ {}y^{\prime } = 2+2 \sec \left (2 x \right )+2 y \tan \left (2 x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.793 |
|
|
\[ {}y^{\prime } = \csc \left (x \right )+3 y \tan \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.534 |
|
|
\[ {}y^{\prime } = \left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.095 |
|
|
\[ {}y^{\prime } = 6 \,{\mathrm e}^{2 x}-y \tanh \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.088 |
|
|
|
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