|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.944 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.888 |
|
|
\[
{}\left (2 x +1\right )^{2} y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }+16 x \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.691 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-6\right ) y = 0
\] |
[_Bessel] |
✓ |
0.839 |
|
|
\[
{}x y^{\prime \prime }+5 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
1.152 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (36 x^{4}-16\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.787 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.462 |
|
|
\[
{}4 x y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.759 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+36 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.740 |
|
|
\[
{}y^{\prime \prime }+k^{2} x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.520 |
|
|
\[
{}y^{\prime \prime }+k^{2} x^{4} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.522 |
|
|
\[
{}x y^{\prime \prime }-5 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
1.180 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.524 |
|
|
\[
{}x y^{\prime \prime }+\left (-2 x +1\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.802 |
|
|
\[
{}\left (x -1\right )^{2} y^{\prime \prime }-\left (x -1\right ) y^{\prime }-35 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.641 |
|
|
\[
{}16 \left (x +1\right )^{2} y^{\prime \prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.618 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-5\right ) y = 0
\] |
[_Bessel] |
✓ |
0.905 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.908 |
|
|
\[
{}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
0.881 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.728 |
|
|
\[
{}y^{\prime \prime }+\frac {y}{4 x} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.138 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.711 |
|
|
\[
{}y^{\prime }+\frac {26 y}{5} = \frac {97 \sin \left (2 t \right )}{5}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.379 |
|
|
\[
{}y^{\prime }+2 y = 0
\] |
[_quadrature] |
✓ |
0.278 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.275 |
|
|
\[
{}y^{\prime \prime }+9 y = 10 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.337 |
|
|
\[
{}y^{\prime \prime }-\frac {y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.246 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+5 y = 29 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.389 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+12 y = 21 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.300 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.258 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 6 t -8
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.271 |
|
|
\[
{}y^{\prime \prime }+\frac {y}{25} = \frac {t^{2}}{50}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.224 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4} = 9 t^{3}+64
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.285 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.423 |
|
|
\[
{}y^{\prime }-6 y = 0
\] |
[_quadrature] |
✓ |
0.291 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 50 t -100
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.514 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.352 |
|
|
\[
{}9 y^{\prime \prime }-6 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.224 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-3 t}-{\mathrm e}^{-5 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.283 |
|
|
\[
{}y^{\prime \prime }+10 y^{\prime }+24 y = 144 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.236 |
|
|
\[
{}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.695 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.119 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = \left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0<t <2 \pi \\ 3 \sin \left (2 t \right )-\cos \left (2 t \right ) & 2 \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.088 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.717 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <1 \\ 0 & 1<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.775 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.780 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.321 |
|
|
\[
{}y^{\prime \prime }+4 y = \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.508 |
|
|
\[
{}y^{\prime \prime }+16 y = 4 \delta \left (t -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.539 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.526 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.801 |
|
|
\[
{}4 y^{\prime \prime }+24 y^{\prime }+37 y = 17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.904 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 10 \sin \left (t \right )+10 \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.755 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.224 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = \delta \left (t -\frac {\pi }{2}\right )+\cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.938 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right )+\delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.862 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 25 t -100 \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.648 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{y}
\] |
[_separable] |
✓ |
1.789 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{y \left (x^{3}+1\right )}
\] |
[_separable] |
✓ |
1.256 |
|
|
\[
{}y^{\prime } = y \sin \left (x \right )
\] |
[_separable] |
✓ |
1.391 |
|
|
\[
{}x y^{\prime } = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
2.099 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{1+y^{2}}
\] |
[_separable] |
✓ |
1.030 |
|
|
\[
{}x y y^{\prime } = \sqrt {1+y^{2}}
\] |
[_separable] |
✓ |
5.875 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
2.179 |
|
|
\[
{}y^{\prime } = 3 y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
1.593 |
|
|
\[
{}x y^{\prime }+y = y^{2}
\] |
[_separable] |
✓ |
2.047 |
|
|
\[
{}2 x^{2} y y^{\prime }+y^{2} = 2
\] |
[_separable] |
✓ |
2.132 |
|
|
\[
{}y^{\prime }-x y^{2} = 2 x y
\] |
[_separable] |
✓ |
1.836 |
|
|
\[
{}\left (1+z^{\prime }\right ) {\mathrm e}^{-z} = 1
\] |
[_quadrature] |
✓ |
1.082 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}+4 x +2}{2 y-2}
\] |
[_separable] |
✓ |
2.139 |
|
|
\[
{}{\mathrm e}^{x}-\left (1+{\mathrm e}^{x}\right ) y y^{\prime } = 0
\] |
[_separable] |
✓ |
3.041 |
|
|
\[
{}\frac {y}{x -1}+\frac {x y^{\prime }}{y+1} = 0
\] |
[_separable] |
✓ |
2.530 |
|
|
\[
{}x +2 x^{3}+\left (y+2 y^{3}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.896 |
|
|
\[
{}\frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}} = 0
\] |
[_separable] |
✓ |
15.310 |
|
|
\[
{}\frac {1}{\sqrt {-x^{2}+1}}+\frac {y^{\prime }}{\sqrt {1-y^{2}}} = 0
\] |
[_separable] |
✓ |
19.743 |
|
|
\[
{}2 x \sqrt {1-y^{2}}+y^{\prime } y = 0
\] |
[_separable] |
✓ |
2.051 |
|
|
\[
{}y^{\prime } = \left (y-1\right ) \left (x +1\right )
\] |
[_separable] |
✓ |
1.147 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
1.489 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{\sqrt {x}}
\] |
[_separable] |
✓ |
10.286 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
3.643 |
|
|
\[
{}z^{\prime } = 10^{x +z}
\] |
[_separable] |
✓ |
2.005 |
|
|
\[
{}x^{\prime }+t = 1
\] |
[_quadrature] |
✓ |
0.249 |
|
|
\[
{}y^{\prime } = \cos \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.398 |
|
|
\[
{}y^{\prime }-y = 2 x -3
\] |
[[_linear, ‘class A‘]] |
✓ |
0.969 |
|
|
\[
{}\left (x +2 y\right ) y^{\prime } = 1
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
2.102 |
|
|
\[
{}y^{\prime }+y = 2 x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
0.946 |
|
|
\[
{}y^{\prime } = \cos \left (x -y-1\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.579 |
|
|
\[
{}y^{\prime }+\sin \left (x +y\right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
5.667 |
|
|
\[
{}y^{\prime } = 2 \sqrt {2 x +y+1}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.953 |
|
|
\[
{}y^{\prime } = \left (x +y+1\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
4.171 |
|
|
\[
{}y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.566 |
|
|
\[
{}\left (1+y^{2}\right ) \left ({\mathrm e}^{2 x}-{\mathrm e}^{y} y^{\prime }\right )-\left (y+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.029 |
|
|
\[
{}x -y+\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.644 |
|
|
\[
{}y-2 x y+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.428 |
|
|
\[
{}2 x y^{\prime } = y \left (2 x^{2}-y^{2}\right )
\] |
[_rational, _Bernoulli] |
✓ |
1.334 |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
37.118 |
|
|
\[
{}\left (y^{2}+x^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.756 |
|
|
\[
{}-y+x y^{\prime } = x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.849 |
|
|
\[
{}x y^{\prime } = y-x \,{\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
7.934 |
|
|
\[
{}-y+x y^{\prime } = \left (x +y\right ) \ln \left (\frac {x +y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.217 |
|