|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}x y^{\prime } = x^{3}-y \] |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.597 |
|
|
\[ {}x y^{\prime } = 1+x^{3}+y \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.631 |
|
|
\[ {}x y^{\prime } = x^{m}+y \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.914 |
|
|
\[ {}x y^{\prime } = x \sin \left (x \right )-y \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.633 |
|
|
\[ {}x y^{\prime } = x^{2} \sin \left (x \right )+y \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.682 |
|
|
\[ {}x y^{\prime } = x^{n} \ln \left (x \right )-y \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.89 |
|
|
\[ {}x y^{\prime } = \sin \left (x \right )-2 y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.685 |
|
|
\[ {}x y^{\prime } = a y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.015 |
|
|
\[ {}x y^{\prime } = 1+x +a y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.866 |
|
|
\[ {}x y^{\prime } = x a +b y \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.046 |
|
|
\[ {}x y^{\prime } = x^{2} a +b y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.842 |
|
|
\[ {}x y^{\prime } = a +b \,x^{n}+c y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.005 |
|
|
\[ {}x y^{\prime }+2+\left (-x +3\right ) y = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.68 |
|
|
\[ {}x y^{\prime }+x +\left (x a +2\right ) y = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.884 |
|
|
\[ {}x y^{\prime }+\left (b x +a \right ) y = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.05 |
|
|
\[ {}x y^{\prime } = x^{3}+\left (-2 x^{2}+1\right ) y \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.874 |
|
|
\[ {}x y^{\prime } = x a -\left (-b \,x^{2}+1\right ) y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.952 |
|
|
\[ {}x y^{\prime }+x +\left (-x^{2} a +2\right ) y = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.012 |
|
|
\[ {}x y^{\prime }+x^{2}+y^{2} = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
0.814 |
|
|
\[ {}x y^{\prime } = x^{2}+y \left (y+1\right ) \] |
riccati, exactByInspection, homogeneousTypeD2 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.05 |
|
|
\[ {}x y^{\prime }-y+y^{2} = x^{\frac {2}{3}} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
6.918 |
|
|
\[ {}x y^{\prime } = a +b y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.995 |
|
|
\[ {}x y^{\prime } = x^{2} a +y+b y^{2} \] |
riccati, homogeneousTypeD2 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.128 |
|
|
\[ {}x y^{\prime } = a \,x^{2 n}+\left (n +b y\right ) y \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.394 |
|
|
\[ {}x y^{\prime } = a \,x^{n}+b y+c y^{2} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.53 |
|
|
\[ {}x y^{\prime } = k +a \,x^{n}+b y+c y^{2} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.668 |
|
|
\[ {}x y^{\prime }+a +x y^{2} = 0 \] |
riccati |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
0.944 |
|
|
\[ {}x y^{\prime }+\left (1-x y\right ) y = 0 \] |
riccati, bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.727 |
|
|
\[ {}x y^{\prime } = \left (1-x y\right ) y \] |
riccati, bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.707 |
|
|
\[ {}x y^{\prime } = \left (x y+1\right ) y \] |
riccati, bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.716 |
|
|
\[ {}x y^{\prime } = a \,x^{3} \left (1-x y\right ) y \] |
riccati, bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
1.191 |
|
|
\[ {}x y^{\prime } = x^{3}+\left (2 x^{2}+1\right ) y+x y^{2} \] |
riccati, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.095 |
|
|
\[ {}x y^{\prime } = y \left (2 x y+1\right ) \] |
riccati, bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.711 |
|
|
\[ {}x y^{\prime }+b x +\left (2+a x y\right ) y = 0 \] |
riccati |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
1.043 |
|
|
\[ {}x y^{\prime }+\operatorname {a0} +\operatorname {a1} x +\left (\operatorname {a2} +\operatorname {a3} x y\right ) y = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
3.273 |
|
|
\[ {}x y^{\prime }+a \,x^{2} y^{2}+2 y = b \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.247 |
|
|
\[ {}x y^{\prime }+x^{m}+\frac {\left (n -m \right ) y}{2}+x^{n} y^{2} = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.462 |
|
|
\[ {}x y^{\prime }+\left (a +b \,x^{n} y\right ) y = 0 \] |
riccati, bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.899 |
|
|
\[ {}x y^{\prime } = a \,x^{m}-b y-c \,x^{n} y^{2} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
2.053 |
|
|
\[ {}x y^{\prime } = 2 x -y+a \,x^{n} \left (x -y\right )^{2} \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
✓ |
1.286 |
|
|
\[ {}x y^{\prime }+\left (1-a y \ln \left (x \right )\right ) y = 0 \] |
riccati, bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
0.99 |
|
|
\[ {}x y^{\prime } = y+\left (x^{2}-y^{2}\right ) f \left (x \right ) \] |
riccati, exactByInspection, homogeneousTypeD2 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
1.607 |
|
|
\[ {}x y^{\prime } = y \left (1+y^{2}\right ) \] |
exact, bernoulli, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.431 |
|
|
\[ {}x y^{\prime }+y \left (1-x y^{2}\right ) = 0 \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.803 |
|
|
\[ {}x y^{\prime }+y = a \left (x^{2}+1\right ) y^{3} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
0.915 |
|
|
\[ {}x y^{\prime } = a y+b \left (x^{2}+1\right ) y^{3} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
1.003 |
|
|
\[ {}x y^{\prime }+2 y = a \,x^{2 k} y^{k} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.387 |
|
|
\[ {}x y^{\prime } = 4 y-4 \sqrt {y} \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.38 |
|
|
\[ {}x y^{\prime }+2 y = \sqrt {1+y^{2}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.276 |
|
|
\[ {}x y^{\prime } = y+\sqrt {x^{2}+y^{2}} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.869 |
|
|
\[ {}x y^{\prime } = y+\sqrt {x^{2}-y^{2}} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.917 |
|
|
\[ {}x y^{\prime } = y+x \sqrt {x^{2}+y^{2}} \] |
unknown |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.05 |
|
|
\[ {}x y^{\prime } = y-x \left (x -y\right ) \sqrt {x^{2}+y^{2}} \] |
unknown |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.285 |
|
|
\[ {}x y^{\prime } = y+a \sqrt {y^{2}+b^{2} x^{2}} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.506 |
|
|
\[ {}x y^{\prime }+\left (\sin \left (y\right )-3 x^{2} \cos \left (y\right )\right ) \cos \left (y\right ) = 0 \] |
exactWithIntegrationFactor |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
1.823 |
|
|
\[ {}x y^{\prime }+x -y+x \cos \left (\frac {y}{x}\right ) = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.011 |
|
|
\[ {}x y^{\prime } = y-x \cos \left (\frac {y}{x}\right )^{2} \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.992 |
|
|
\[ {}x y^{\prime } = \left (-2 x^{2}+1\right ) \cot \left (y\right )^{2} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.883 |
|
|
\[ {}x y^{\prime } = y-\cot \left (y\right )^{2} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.818 |
|
|
\[ {}x y^{\prime }+y+2 x \sec \left (x y\right ) = 0 \] |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
3.558 |
|
|
\[ {}x y^{\prime }-y+x \sec \left (\frac {y}{x}\right ) = 0 \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.012 |
|
|
\[ {}x y^{\prime } = y+x \sec \left (\frac {y}{x}\right )^{2} \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.026 |
|
|
\[ {}x y^{\prime } = \sin \left (x -y\right ) \] |
unknown |
[‘y=_G(x,y’)‘] |
❇ |
N/A |
1.537 |
|
|
\[ {}x y^{\prime } = y+x \sin \left (\frac {y}{x}\right ) \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.843 |
|
|
\[ {}x y^{\prime }+\tan \left (y\right ) = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.08 |
|
|
\[ {}x y^{\prime }+x +\tan \left (x +y\right ) = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.714 |
|
|
\[ {}x y^{\prime } = y-x \tan \left (\frac {y}{x}\right ) \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.0 |
|
|
\[ {}x y^{\prime } = \left (1+y^{2}\right ) \left (x^{2}+\arctan \left (y\right )\right ) \] |
first_order_ode_lie_symmetry_calculated |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
1.962 |
|
|
\[ {}x y^{\prime } = y+x \,{\mathrm e}^{\frac {y}{x}} \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.691 |
|
|
\[ {}x y^{\prime } = x +y+x \,{\mathrm e}^{\frac {y}{x}} \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.001 |
|
|
\[ {}x y^{\prime } = y \ln \left (y\right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.782 |
|
|
\[ {}x y^{\prime } = \left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.326 |
|
|
\[ {}x y^{\prime }+\left (1-\ln \left (x \right )-\ln \left (y\right )\right ) y = 0 \] |
exactByInspection, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
1.304 |
|
|
\[ {}x y^{\prime } = y-2 x \tanh \left (\frac {y}{x}\right ) \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.108 |
|
|
\[ {}x y^{\prime }+n y = f \left (x \right ) g \left (x^{n} y\right ) \] |
unknown |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.086 |
|
|
\[ {}x y^{\prime } = y f \left (x^{m} y^{n}\right ) \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
0.991 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = x^{3} \left (3 x +4\right )+y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.649 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = \left (1+x \right )^{4}+2 y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.658 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = {\mathrm e}^{x} \left (1+x \right )^{n +1}+n y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.98 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = a y+b x y^{2} \] |
riccati, bernoulli, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
0.895 |
|
|
\[ {}\left (1+x \right ) y^{\prime }+y+\left (1+x \right )^{4} y^{3} = 0 \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
0.829 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = \left (1-x y^{3}\right ) y \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
1.029 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = 1+y+\left (1+x \right ) \sqrt {y+1} \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.514 |
|
|
\[ {}\left (x +a \right ) y^{\prime } = b x \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.276 |
|
|
\[ {}\left (x +a \right ) y^{\prime } = b x +y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.889 |
|
|
\[ {}\left (x +a \right ) y^{\prime }+b \,x^{2}+y = 0 \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.796 |
|
|
\[ {}\left (x +a \right ) y^{\prime } = 2 \left (x +a \right )^{5}+3 y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.908 |
|
|
\[ {}\left (x +a \right ) y^{\prime } = b +c y \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.058 |
|
|
\[ {}\left (x +a \right ) y^{\prime } = b x +c y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.96 |
|
|
\[ {}\left (x +a \right ) y^{\prime } = y \left (1-a y\right ) \] |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.45 |
|
|
\[ {}\left (a -x \right ) y^{\prime } = y+\left (c x +b \right ) y^{3} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
0.899 |
|
|
\[ {}2 x y^{\prime } = 2 x^{3}-y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.668 |
|
|
\[ {}2 x y^{\prime }+1 = 4 i x y+y^{2} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.587 |
|
|
\[ {}2 x y^{\prime } = y \left (1+y^{2}\right ) \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.427 |
|
|
\[ {}2 x y^{\prime }+y \left (1+y^{2}\right ) = 0 \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.734 |
|
|
\[ {}2 x y^{\prime } = \left (1+x -6 y^{2}\right ) y \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
0.672 |
|
|
\[ {}2 x y^{\prime }+4 y+a +\sqrt {a^{2}-4 b -4 c y} = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
18.974 |
|
|
\[ {}\left (1-2 x \right ) y^{\prime } = 16+32 x -6 y \] |
linear, homogeneousTypeMapleC, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.954 |
|
|
\[ {}\left (2 x +1\right ) y^{\prime } = 4 \,{\mathrm e}^{-y}-2 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.921 |
|
|
\[ {}2 \left (1-x \right ) y^{\prime } = 4 x \sqrt {1-x}+y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.608 |
|
|
|
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