|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 2 x +1
\] |
[_quadrature] |
✓ |
0.284 |
|
|
\[
{}y^{\prime } = \left (x -2\right )^{2}
\] |
[_quadrature] |
✓ |
0.310 |
|
|
\[
{}y^{\prime } = \sqrt {x}
\] |
[_quadrature] |
✓ |
0.330 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}}
\] |
[_quadrature] |
✓ |
0.214 |
|
|
\[
{}y^{\prime } = \frac {1}{\sqrt {x +2}}
\] |
[_quadrature] |
✓ |
0.307 |
|
|
\[
{}y^{\prime } = x \sqrt {x^{2}+9}
\] |
[_quadrature] |
✓ |
0.495 |
|
|
\[
{}y^{\prime } = \frac {10}{x^{2}+1}
\] |
[_quadrature] |
✓ |
0.294 |
|
|
\[
{}y^{\prime } = \cos \left (2 x \right )
\] |
[_quadrature] |
✓ |
0.373 |
|
|
\[
{}y^{\prime } = \frac {1}{\sqrt {-x^{2}+1}}
\] |
[_quadrature] |
✓ |
0.266 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{-x}
\] |
[_quadrature] |
✓ |
0.349 |
|
|
\[
{}x^{\prime \prime } = 50
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.674 |
|
|
\[
{}x^{\prime \prime } = -20
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.300 |
|
|
\[
{}x^{\prime \prime } = 3 t
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.023 |
|
|
\[
{}x^{\prime \prime } = 2 t +1
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.064 |
|
|
\[
{}x^{\prime \prime } = 4 \left (t +3\right )^{2}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.145 |
|
|
\[
{}x^{\prime \prime } = \frac {1}{\sqrt {t +4}}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.169 |
|
|
\[
{}x^{\prime \prime } = \frac {1}{\left (1+t \right )^{3}}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.112 |
|
|
\[
{}x^{\prime \prime } = 50 \sin \left (5 t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.697 |
|
|
\[
{}y^{\prime } = -y-\sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.101 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.614 |
|
|
\[
{}y^{\prime } = y-\sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.194 |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.611 |
|
|
\[
{}y^{\prime } = y-x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
0.855 |
|
|
\[
{}y^{\prime } = x -y+1
\] |
[[_linear, ‘class A‘]] |
✓ |
0.791 |
|
|
\[
{}y^{\prime } = x^{2}-y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.607 |
|
|
\[
{}y^{\prime } = x^{2}-y-2
\] |
[[_linear, ‘class A‘]] |
✓ |
0.747 |
|
|
\[
{}y^{\prime } = 2 x^{2} y^{2}
\] |
[_separable] |
✓ |
1.691 |
|
|
\[
{}y^{\prime } = x \ln \left (y\right )
\] |
[_separable] |
✓ |
1.909 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
0.569 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
0.660 |
|
|
\[
{}y^{\prime } = \sqrt {x -y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.155 |
|
|
\[
{}y^{\prime } = \sqrt {x -y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.633 |
|
|
\[
{}y y^{\prime } = x -1
\] |
[_separable] |
✓ |
4.776 |
|
|
\[
{}y y^{\prime } = x -1
\] |
[_separable] |
✓ |
3.760 |
|
|
\[
{}y^{\prime } = \ln \left (1+y^{2}\right )
\] |
[_quadrature] |
✓ |
0.788 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✗ |
1.347 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.936 |
|
|
\[
{}y^{\prime } = -x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.083 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}-1
\] |
[_Riccati] |
✓ |
3.155 |
|
|
\[
{}y^{\prime } = x +\frac {y^{2}}{2}
\] |
[[_Riccati, _special]] |
✓ |
1.848 |
|
|
\[
{}y^{\prime }+2 y x = 0
\] |
[_separable] |
✓ |
0.978 |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
1.462 |
|
|
\[
{}y^{\prime } = y \sin \left (x \right )
\] |
[_separable] |
✓ |
1.170 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = 4 y
\] |
[_separable] |
✓ |
1.283 |
|
|
\[
{}2 \sqrt {x}\, y^{\prime } = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
1.604 |
|
|
\[
{}y^{\prime } = 3 \sqrt {y x}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
98.263 |
|
|
\[
{}y^{\prime } = 64^{{1}/{3}} \left (y x \right )^{{1}/{3}}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
91.005 |
|
|
\[
{}y^{\prime } = 2 x \sec \left (y\right )
\] |
[_separable] |
✓ |
8.772 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 2 y
\] |
[_separable] |
✓ |
3.369 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime } = \left (1+y\right )^{2}
\] |
[_separable] |
✓ |
8.914 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
1.842 |
|
|
\[
{}y y^{\prime } = x \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
1.430 |
|
|
\[
{}y^{3} y^{\prime } = \left (1+y^{4}\right ) \cos \left (x \right )
\] |
[_separable] |
✓ |
4.497 |
|
|
\[
{}y^{\prime } = \frac {1+\sqrt {x}}{1+\sqrt {y}}
\] |
[_separable] |
✓ |
1.447 |
|
|
\[
{}y^{\prime } = \frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )}
\] |
[_separable] |
✓ |
1.605 |
|
|
\[
{}\left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime } = x
\] |
[_separable] |
✓ |
1.490 |
|
|
\[
{}y^{\prime } = 1+x +y+y x
\] |
[_separable] |
✓ |
0.787 |
|
|
\[
{}x^{2} y^{\prime } = 1-x^{2}+y^{2}-x^{2} y^{2}
\] |
[_separable] |
✓ |
1.940 |
|
|
\[
{}y^{\prime } = y \,{\mathrm e}^{x}
\] |
[_separable] |
✓ |
1.136 |
|
|
\[
{}y^{\prime } = 3 x^{2} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
1.743 |
|
|
\[
{}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-16}}
\] |
[_separable] |
✓ |
1.800 |
|
|
\[
{}y^{\prime } = 4 x^{3} y-y
\] |
[_separable] |
✓ |
1.201 |
|
|
\[
{}y^{\prime }+1 = 2 y
\] |
[_quadrature] |
✓ |
0.430 |
|
|
\[
{}\tan \left (x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
1.434 |
|
|
\[
{}y^{\prime } x -y = 2 x^{2} y
\] |
[_separable] |
✓ |
1.132 |
|
|
\[
{}y^{\prime } = 2 x y^{2}+3 x^{2} y^{2}
\] |
[_separable] |
✓ |
1.658 |
|
|
\[
{}y^{\prime } = 6 \,{\mathrm e}^{2 x -y}
\] |
[_separable] |
✓ |
2.439 |
|
|
\[
{}2 \sqrt {x}\, y^{\prime } = \cos \left (y\right )^{2}
\] |
[_separable] |
✓ |
2.152 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
0.332 |
|
|
\[
{}{y^{\prime }}^{2} = 4 y
\] |
[_quadrature] |
✓ |
0.374 |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
0.526 |
|
|
\[
{}y^{\prime } = y \sqrt {-1+y^{2}}
\] |
[_quadrature] |
✓ |
5.411 |
|
|
\[
{}y^{\prime }+y = 2
\] |
[_quadrature] |
✓ |
0.473 |
|
|
\[
{}y^{\prime }-2 y = 3 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.982 |
|
|
\[
{}y^{\prime }+3 y = 2 x \,{\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.480 |
|
|
\[
{}y^{\prime }-2 y x = {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
1.385 |
|
|
\[
{}y^{\prime } x +2 y = 3 x
\] |
[_linear] |
✓ |
1.912 |
|
|
\[
{}y^{\prime } x +5 y = 7 x^{2}
\] |
[_linear] |
✓ |
1.376 |
|
|
\[
{}2 y^{\prime } x +y = 10 \sqrt {x}
\] |
[_linear] |
✓ |
3.961 |
|
|
\[
{}3 y^{\prime } x +y = 12 x
\] |
[_linear] |
✓ |
1.436 |
|
|
\[
{}y^{\prime } x -y = x
\] |
[_linear] |
✓ |
1.321 |
|
|
\[
{}2 y^{\prime } x -3 y = 9 x^{3}
\] |
[_linear] |
✓ |
0.956 |
|
|
\[
{}y^{\prime } x +y = 3 y x
\] |
[_separable] |
✓ |
1.261 |
|
|
\[
{}y^{\prime } x +3 y = 2 x^{5}
\] |
[_linear] |
✓ |
1.409 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.836 |
|
|
\[
{}y^{\prime } x -3 y = x^{3}
\] |
[_linear] |
✓ |
1.053 |
|
|
\[
{}y^{\prime }+2 y x = x
\] |
[_separable] |
✓ |
1.069 |
|
|
\[
{}y^{\prime } = \left (1-y\right ) \cos \left (x \right )
\] |
[_separable] |
✓ |
1.426 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+y = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.564 |
|
|
\[
{}y^{\prime } x = 2 y+x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.542 |
|
|
\[
{}y^{\prime }+\cot \left (x \right ) y = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.679 |
|
|
\[
{}y^{\prime } = 1+x +y+y x
\] |
[_separable] |
✓ |
1.246 |
|
|
\[
{}y^{\prime } x = 3 y+x^{4} \cos \left (x \right )
\] |
[_linear] |
✓ |
2.506 |
|
|
\[
{}y^{\prime } = 2 y x +3 x^{2} {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
2.567 |
|
|
\[
{}y^{\prime } x +\left (2 x -3\right ) y = 4 x^{4}
\] |
[_linear] |
✓ |
2.171 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime }+3 y x = x
\] |
[_separable] |
✓ |
1.319 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+3 x^{3} y = 6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}}
\] |
[_linear] |
✓ |
1.793 |
|
|
\[
{}\frac {1-4 x y^{2}}{x^{\prime }} = y^{3}
\] |
[_linear] |
✓ |
1.135 |
|
|
\[
{}\frac {x+y \,{\mathrm e}^{y}}{x^{\prime }} = 1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.198 |
|
|
\[
{}\frac {1+2 x y}{x^{\prime }} = y^{2}+1
\] |
[_linear] |
✓ |
0.975 |
|