|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 2 x +1
\] |
[_quadrature] |
✓ |
0.834 |
|
|
\[
{}y^{\prime } = \left (-2+x \right )^{2}
\] |
[_quadrature] |
✓ |
0.795 |
|
|
\[
{}y^{\prime } = \sqrt {x}
\] |
[_quadrature] |
✓ |
0.582 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}}
\] |
[_quadrature] |
✓ |
0.731 |
|
|
\[
{}y^{\prime } = \frac {1}{\sqrt {x +2}}
\] |
[_quadrature] |
✓ |
0.518 |
|
|
\[
{}y^{\prime } = x \sqrt {x^{2}+9}
\] |
[_quadrature] |
✓ |
2.612 |
|
|
\[
{}y^{\prime } = \frac {10}{x^{2}+1}
\] |
[_quadrature] |
✓ |
0.785 |
|
|
\[
{}y^{\prime } = \cos \left (2 x \right )
\] |
[_quadrature] |
✓ |
0.808 |
|
|
\[
{}y^{\prime } = \frac {1}{\sqrt {-x^{2}+1}}
\] |
[_quadrature] |
✓ |
0.536 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{-x}
\] |
[_quadrature] |
✓ |
0.750 |
|
|
\[
{}x^{\prime \prime } = 50
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.931 |
|
|
\[
{}x^{\prime \prime } = -20
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.818 |
|
|
\[
{}x^{\prime \prime } = 3 t
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.608 |
|
|
\[
{}x^{\prime \prime } = 2 t +1
\] |
[[_2nd_order, _quadrature]] |
✓ |
5.444 |
|
|
\[
{}x^{\prime \prime } = 4 \left (3+t \right )^{2}
\] |
[[_2nd_order, _quadrature]] |
✓ |
5.635 |
|
|
\[
{}x^{\prime \prime } = \frac {1}{\sqrt {t +4}}
\] |
[[_2nd_order, _quadrature]] |
✓ |
5.783 |
|
|
\[
{}x^{\prime \prime } = \frac {1}{\left (t +1\right )^{3}}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.979 |
|
|
\[
{}x^{\prime \prime } = 50 \sin \left (5 t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
7.481 |
|
|
\[
{}y^{\prime } = -y-\sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.517 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.292 |
|
|
\[
{}y^{\prime } = y-\sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.503 |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.286 |
|
|
\[
{}y^{\prime } = y-x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.591 |
|
|
\[
{}y^{\prime } = x -y+1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.566 |
|
|
\[
{}y^{\prime } = x^{2}-y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.303 |
|
|
\[
{}y^{\prime } = x^{2}-y-2
\] |
[[_linear, ‘class A‘]] |
✓ |
1.360 |
|
|
\[
{}y^{\prime } = 2 y^{2} x^{2}
\] |
[_separable] |
✓ |
2.743 |
|
|
\[
{}y^{\prime } = \ln \left (y\right ) x
\] |
[_separable] |
✓ |
2.202 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
3.217 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
2.420 |
|
|
\[
{}y^{\prime } = \sqrt {x -y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.902 |
|
|
\[
{}y^{\prime } = \sqrt {x -y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
6.678 |
|
|
\[
{}y y^{\prime } = -1+x
\] |
[_separable] |
✓ |
5.536 |
|
|
\[
{}y y^{\prime } = -1+x
\] |
[_separable] |
✓ |
7.396 |
|
|
\[
{}y^{\prime } = \ln \left (1+y^{2}\right )
\] |
[_quadrature] |
✓ |
2.107 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✗ |
1.722 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.559 |
|
|
\[
{}y^{\prime } = y-x
\] |
[[_linear, ‘class A‘]] |
✓ |
1.610 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}-1
\] |
[_Riccati] |
✗ |
6.495 |
|
|
\[
{}y^{\prime } = x +\frac {y^{2}}{2}
\] |
[[_Riccati, _special]] |
✓ |
1.932 |
|
|
\[
{}y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
1.715 |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
2.217 |
|
|
\[
{}y^{\prime } = y \sin \left (x \right )
\] |
[_separable] |
✓ |
2.066 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = 4 y
\] |
[_separable] |
✓ |
2.068 |
|
|
\[
{}2 \sqrt {x}\, y^{\prime } = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
8.996 |
|
|
\[
{}y^{\prime } = 3 \sqrt {x y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
9.192 |
|
|
\[
{}y^{\prime } = 64^{{1}/{3}} \left (x y\right )^{{1}/{3}}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
5.958 |
|
|
\[
{}y^{\prime } = 2 x \sec \left (y\right )
\] |
[_separable] |
✓ |
1.537 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 2 y
\] |
[_separable] |
✓ |
1.853 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime } = \left (y+1\right )^{2}
\] |
[_separable] |
✓ |
2.730 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
3.801 |
|
|
\[
{}y y^{\prime } = x \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
2.245 |
|
|
\[
{}y^{3} y^{\prime } = \left (1+y^{4}\right ) \cos \left (x \right )
\] |
[_separable] |
✓ |
5.855 |
|
|
\[
{}y^{\prime } = \frac {1+\sqrt {x}}{1+\sqrt {y}}
\] |
[_separable] |
✓ |
1.657 |
|
|
\[
{}y^{\prime } = \frac {\left (-1+x \right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )}
\] |
[_separable] |
✓ |
1.964 |
|
|
\[
{}\left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime } = x
\] |
[_separable] |
✓ |
2.025 |
|
|
\[
{}y^{\prime } = 1+x +y+x y
\] |
[_separable] |
✓ |
1.614 |
|
|
\[
{}x^{2} y^{\prime } = 1-x^{2}+y^{2}-y^{2} x^{2}
\] |
[_separable] |
✓ |
2.568 |
|
|
\[
{}y^{\prime } = y \,{\mathrm e}^{x}
\] |
[_separable] |
✓ |
2.531 |
|
|
\[
{}y^{\prime } = 3 x^{2} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
2.752 |
|
|
\[
{}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-16}}
\] |
[_separable] |
✓ |
3.056 |
|
|
\[
{}y^{\prime } = 4 x^{3} y-y
\] |
[_separable] |
✓ |
1.705 |
|
|
\[
{}y^{\prime }+1 = 2 y
\] |
[_quadrature] |
✓ |
1.975 |
|
|
\[
{}\tan \left (x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
2.504 |
|
|
\[
{}x y^{\prime }-y = 2 x^{2} y
\] |
[_separable] |
✓ |
2.199 |
|
|
\[
{}y^{\prime } = 2 x y^{2}+3 y^{2} x^{2}
\] |
[_separable] |
✓ |
2.376 |
|
|
\[
{}y^{\prime } = 6 \,{\mathrm e}^{2 x -y}
\] |
[_separable] |
✓ |
4.342 |
|
|
\[
{}2 \sqrt {x}\, y^{\prime } = \cos \left (y\right )^{2}
\] |
[_separable] |
✓ |
2.057 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
2.162 |
|
|
\[
{}{y^{\prime }}^{2} = 4 y
\] |
[_quadrature] |
✓ |
0.480 |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
140.006 |
|
|
\[
{}y^{\prime } = y \sqrt {y^{2}-1}
\] |
[_quadrature] |
✓ |
18.289 |
|
|
\[
{}y^{\prime }+y = 2
\] |
[_quadrature] |
✓ |
2.008 |
|
|
\[
{}y^{\prime }-2 y = 3 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.706 |
|
|
\[
{}y^{\prime }+3 y = 2 x \,{\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.924 |
|
|
\[
{}y^{\prime }-2 x y = {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
1.809 |
|
|
\[
{}x y^{\prime }+2 y = 3 x
\] |
[_linear] |
✓ |
3.361 |
|
|
\[
{}x y^{\prime }+5 y = 7 x^{2}
\] |
[_linear] |
✓ |
2.182 |
|
|
\[
{}2 x y^{\prime }+y = 10 \sqrt {x}
\] |
[_linear] |
✓ |
4.495 |
|
|
\[
{}3 x y^{\prime }+y = 12 x
\] |
[_linear] |
✓ |
2.560 |
|
|
\[
{}x y^{\prime }-y = x
\] |
[_linear] |
✓ |
2.081 |
|
|
\[
{}2 x y^{\prime }-3 y = 9 x^{3}
\] |
[_linear] |
✓ |
1.745 |
|
|
\[
{}x y^{\prime }+y = 3 x y
\] |
[_separable] |
✓ |
2.533 |
|
|
\[
{}x y^{\prime }+3 y = 2 x^{5}
\] |
[_linear] |
✓ |
1.878 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.641 |
|
|
\[
{}x y^{\prime }-3 y = x^{3}
\] |
[_linear] |
✓ |
1.720 |
|
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
2.046 |
|
|
\[
{}y^{\prime } = \left (1-y\right ) \cos \left (x \right )
\] |
[_separable] |
✓ |
2.350 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+y = \cos \left (x \right )
\] |
[_linear] |
✓ |
2.013 |
|
|
\[
{}x y^{\prime } = 2 y+x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.937 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = \cos \left (x \right )
\] |
[_linear] |
✓ |
2.074 |
|
|
\[
{}y^{\prime } = 1+x +y+x y
\] |
[_separable] |
✓ |
2.027 |
|
|
\[
{}x y^{\prime } = 3 y+x^{4} \cos \left (x \right )
\] |
[_linear] |
✓ |
3.041 |
|
|
\[
{}y^{\prime } = 2 x y+3 x^{2} {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
3.119 |
|
|
\[
{}x y^{\prime }+\left (2 x -3\right ) y = 4 x^{4}
\] |
[_linear] |
✓ |
2.724 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime }+3 x y = x
\] |
[_separable] |
✓ |
2.523 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+3 x^{3} y = 6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}}
\] |
[_linear] |
✓ |
2.648 |
|
|
\[
{}\frac {1-4 x y^{2}}{x^{\prime }} = y^{3}
\] |
[_linear] |
✓ |
2.091 |
|
|
\[
{}\frac {x+y \,{\mathrm e}^{y}}{x^{\prime }} = 1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.931 |
|
|
\[
{}\frac {1+2 x y}{x^{\prime }} = y^{2}+1
\] |
[_linear] |
✓ |
1.845 |
|