|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.387 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.86 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t^{2} & 0 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.085 |
|
|
\[ {}y^{\prime \prime }+4 y = \delta \left (t -\pi \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.691 |
|
|
\[ {}y^{\prime \prime }+16 y = 4 \delta \left (t -3 \pi \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.795 |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.767 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (-1+t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.085 |
|
|
\[ {}4 y^{\prime \prime }+24 y^{\prime }+37 y = 17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.625 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 10 \sin \left (t \right )+10 \delta \left (-1+t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.142 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.918 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = \delta \left (t -\frac {\pi }{2}\right )+\operatorname {Heaviside}\left (t -\pi \right ) \cos \left (t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.856 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = \operatorname {Heaviside}\left (-1+t \right )+\delta \left (t -2\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.821 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 25 t -100 \delta \left (t -\pi \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.044 |
|
|
\[ {}y^{\prime } = \frac {x^{2}}{y} \] |
separable |
[_separable] |
✓ |
✓ |
0.309 |
|
|
\[ {}y^{\prime } = \frac {x^{2}}{y \left (x^{3}+1\right )} \] |
separable |
[_separable] |
✓ |
✓ |
0.181 |
|
|
\[ {}y^{\prime } = y \sin \left (x \right ) \] |
separable |
[_separable] |
✓ |
✓ |
0.265 |
|
|
\[ {}x y^{\prime } = \sqrt {1-y^{2}} \] |
separable |
[_separable] |
✓ |
✓ |
0.757 |
|
|
\[ {}y^{\prime } = \frac {x^{2}}{1+y^{2}} \] |
separable |
[_separable] |
✓ |
✓ |
156.172 |
|
|
\[ {}x y y^{\prime } = \sqrt {1+y^{2}} \] |
separable |
[_separable] |
✓ |
✓ |
0.33 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+2 x y^{2} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.523 |
|
|
\[ {}y^{\prime } = 3 y^{\frac {2}{3}} \] |
separable |
[_quadrature] |
✓ |
✓ |
0.492 |
|
|
\[ {}x y^{\prime }+y = y^{2} \] |
separable |
[_separable] |
✓ |
✓ |
0.662 |
|
|
\[ {}2 x^{2} y y^{\prime }+y^{2} = 2 \] |
separable |
[_separable] |
✓ |
✓ |
0.775 |
|
|
\[ {}y^{\prime }-x y^{2} = 2 x y \] |
separable |
[_separable] |
✓ |
✓ |
0.595 |
|
|
\[ {}\left (1+z^{\prime }\right ) {\mathrm e}^{-z} = 1 \] |
separable |
[_quadrature] |
✓ |
✓ |
0.446 |
|
|
\[ {}y^{\prime } = \frac {3 x^{2}+4 x +2}{2 y-2} \] |
separable |
[_separable] |
✓ |
✓ |
0.828 |
|
|
\[ {}{\mathrm e}^{x}-\left (1+{\mathrm e}^{x}\right ) y y^{\prime } = 0 \] |
separable |
[_separable] |
✓ |
✓ |
1.022 |
|
|
\[ {}\frac {y}{-1+x}+\frac {x y^{\prime }}{y+1} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.474 |
|
|
\[ {}x +2 x^{3}+\left (y+2 y^{3}\right ) y^{\prime } = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.3 |
|
|
\[ {}\frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.27 |
|
|
\[ {}\frac {1}{\sqrt {-x^{2}+1}}+\frac {y^{\prime }}{\sqrt {1-y^{2}}} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.385 |
|
|
\[ {}2 x \sqrt {1-y^{2}}+y y^{\prime } = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.428 |
|
|
\[ {}y^{\prime } = \left (y-1\right ) \left (1+x \right ) \] |
separable |
[_separable] |
✓ |
✓ |
0.286 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x -y} \] |
separable |
[_separable] |
✓ |
✓ |
0.161 |
|
|
\[ {}y^{\prime } = \frac {\sqrt {y}}{\sqrt {x}} \] |
separable |
[_separable] |
✓ |
✓ |
0.244 |
|
|
\[ {}y^{\prime } = \frac {\sqrt {y}}{x} \] |
separable |
[_separable] |
✓ |
✓ |
0.21 |
|
|
\[ {}z^{\prime } = 10^{x +z} \] |
separable |
[_separable] |
✓ |
✓ |
0.222 |
|
|
\[ {}x^{\prime }+t = 1 \] |
separable |
[_quadrature] |
✓ |
✓ |
0.129 |
|
|
\[ {}y^{\prime } = \cos \left (x -y\right ) \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.181 |
|
|
\[ {}y^{\prime }-y = 2 x -3 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.591 |
|
|
\[ {}\left (2 y+x \right ) y^{\prime } = 1 \] |
homogeneousTypeC, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.563 |
|
|
\[ {}y^{\prime }+y = 2 x +1 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.585 |
|
|
\[ {}y^{\prime } = \cos \left (x -y-1\right ) \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.274 |
|
|
\[ {}y^{\prime }+\sin \left (x +y\right )^{2} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.364 |
|
|
\[ {}y^{\prime } = 2 \sqrt {y+2 x +1} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
4.118 |
|
|
\[ {}y^{\prime } = \left (1+x +y\right )^{2} \] |
riccati, homogeneousTypeC, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.776 |
|
|
\[ {}y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.765 |
|
|
\[ {}\left (1+y^{2}\right ) \left ({\mathrm e}^{2 x}-{\mathrm e}^{y} y^{\prime }\right )-\left (y+1\right ) y^{\prime } = 0 \] |
separable |
[_separable] |
✓ |
✓ |
1.892 |
|
|
\[ {}x -y+\left (x +y\right ) y^{\prime } = 0 \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.62 |
|
|
\[ {}y-2 x y+x^{2} y^{\prime } = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.016 |
|
|
\[ {}2 x y^{\prime } = y \left (2 x^{2}-y^{2}\right ) \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
1.091 |
|
|
\[ {}y^{2}+x^{2} y^{\prime } = x y y^{\prime } \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.435 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) y^{\prime } = 2 x y \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.681 |
|
|
\[ {}-y+x y^{\prime } = x \tan \left (\frac {y}{x}\right ) \] |
homogeneous |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.096 |
|
|
\[ {}x y^{\prime } = y-x \,{\mathrm e}^{\frac {y}{x}} \] |
homogeneous |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.381 |
|
|
\[ {}-y+x y^{\prime } = \left (x +y\right ) \ln \left (\frac {x +y}{x}\right ) \] |
homogeneous |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.677 |
|
|
\[ {}x y^{\prime } = y \cos \left (\frac {y}{x}\right ) \] |
homogeneous |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.194 |
|
|
\[ {}y+\sqrt {x y}-x y^{\prime } = 0 \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.49 |
|
|
\[ {}x y^{\prime }-\sqrt {x^{2}-y^{2}}-y = 0 \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.134 |
|
|
\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.603 |
|
|
\[ {}x^{2}+2 x y-y^{2}+\left (y^{2}+2 x y-x^{2}\right ) y^{\prime } = 0 \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.068 |
|
|
\[ {}-y+x y^{\prime } = y y^{\prime } \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.46 |
|
|
\[ {}y^{2}+\left (x^{2}-x y\right ) y^{\prime } = 0 \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.436 |
|
|
\[ {}x^{2}+x y+y^{2} = x^{2} y^{\prime } \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.477 |
|
|
\[ {}\frac {1}{x^{2}-x y+y^{2}} = \frac {y^{\prime }}{2 y^{2}-x y} \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
12.835 |
|
|
\[ {}y^{\prime } = \frac {2 x y}{3 x^{2}-y^{2}} \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.686 |
|
|
\[ {}y^{\prime } = \frac {x}{y}+\frac {y}{x} \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.636 |
|
|
\[ {}x y^{\prime } = y+\sqrt {-x^{2}+y^{2}} \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.382 |
|
|
\[ {}y+\left (2 \sqrt {x y}-x \right ) y^{\prime } = 0 \] |
homogeneous |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.884 |
|
|
\[ {}x y^{\prime } = y \ln \left (\frac {y}{x}\right ) \] |
homogeneous |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.492 |
|
|
\[ {}y^{\prime } \left (y^{\prime }+y\right ) = x \left (x +y\right ) \] |
linear, quadrature |
[_quadrature] |
✓ |
✓ |
0.649 |
|
|
\[ {}\left (x y^{\prime }+y\right )^{2} = y^{2} y^{\prime } \] |
homogeneous |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
5.827 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-3 x y y^{\prime }+2 y^{2} = 0 \] |
homogeneous |
[_separable] |
✓ |
✓ |
0.859 |
|
|
\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.688 |
|
|
\[ {}y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.971 |
|
|
\[ {}y^{\prime }+\frac {2 y+x}{x} = 0 \] |
homogeneous |
[_linear] |
✓ |
✓ |
0.663 |
|
|
\[ {}y^{\prime } = \frac {y}{x +y} \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.464 |
|
|
\[ {}x y^{\prime } = x +\frac {y}{2} \] |
homogeneous |
[_linear] |
✗ |
N/A |
0.697 |
|
|
\[ {}y^{\prime } = \frac {x +y-2}{y-x -4} \] |
polynomial |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.264 |
|
|
\[ {}2 x -4 y+6+\left (x +y-2\right ) y^{\prime } = 0 \] |
polynomial |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.81 |
|
|
\[ {}y^{\prime } = \frac {2 y-x +5}{2 x -y-4} \] |
polynomial |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.946 |
|
|
\[ {}y^{\prime } = -\frac {4 x +3 y+15}{2 x +y+7} \] |
polynomial |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.898 |
|
|
\[ {}y^{\prime } = \frac {x +3 y-5}{x -y-1} \] |
polynomial |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.607 |
|
|
\[ {}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (1+x +y\right )^{2}} \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
1.73 |
|
|
\[ {}2 x +y+1-\left (4 x +2 y-3\right ) y^{\prime } = 0 \] |
polynomial |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.326 |
|
|
\[ {}x -y-1+\left (-x +y+2\right ) y^{\prime } = 0 \] |
polynomial |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.306 |
|
|
\[ {}\left (x +4 y\right ) y^{\prime } = 2 x +3 y-5 \] |
polynomial |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.892 |
|
|
\[ {}y+2 = \left (2 x +y-4\right ) y^{\prime } \] |
homogeneousTypeMapleC, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.622 |
|
|
\[ {}\left (1+y^{\prime }\right ) \ln \left (\frac {x +y}{x +3}\right ) = \frac {x +y}{x +3} \] |
exact, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
6.257 |
|
|
\[ {}y^{\prime } = \frac {x -2 y+5}{y-2 x -4} \] |
polynomial |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.926 |
|
|
\[ {}y^{\prime } = \frac {3 x -y+1}{2 x +y+4} \] |
polynomial |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.9 |
|
|
\[ {}2 x y^{\prime }+\left (y^{4} x^{2}+1\right ) y = 0 \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.036 |
|
|
\[ {}2 x y^{\prime } \left (x -y^{2}\right )+y^{3} = 0 \] |
isobaric |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
0.254 |
|
|
\[ {}x^{3} \left (y^{\prime }-x \right ) = y^{2} \] |
isobaric |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
0.309 |
|
|
\[ {}2 x^{2} y^{\prime } = y^{3}+x y \] |
isobaric |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.221 |
|
|
\[ {}y+x \left (2 x y+1\right ) y^{\prime } = 0 \] |
isobaric |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.223 |
|
|
\[ {}2 y^{\prime }+x = 4 \sqrt {y} \] |
isobaric |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
✓ |
0.579 |
|
|
\[ {}y^{\prime } = y^{2}-\frac {2}{x^{2}} \] |
isobaric |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
0.358 |
|
|
\[ {}2 x y^{\prime }+y = y^{2} \sqrt {x -x^{2} y^{2}} \] |
isobaric |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
0.716 |
|
|
\[ {}\frac {2 x y y^{\prime }}{3} = \sqrt {x^{6}-y^{4}}+y^{2} \] |
isobaric |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
1.222 |
|
|
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