|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.557 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.477 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = \left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0<t <2 \pi \\ 3 \sin \left (2 t \right )-\cos \left (2 t \right ) & 2 \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.817 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.465 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <1 \\ 0 & 1<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.534 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.709 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.687 |
|
|
\[
{}y^{\prime \prime }+4 y = \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.375 |
|
|
\[
{}y^{\prime \prime }+16 y = 4 \delta \left (t -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.448 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.378 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.465 |
|
|
\[
{}4 y^{\prime \prime }+24 y^{\prime }+37 y = 17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.445 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 10 \sin \left (t \right )+10 \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.455 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.585 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = \delta \left (t -\frac {\pi }{2}\right )+\operatorname {Heaviside}\left (t -\pi \right ) \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.513 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right )+\delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.385 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 25 t -100 \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.444 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{y}
\] |
[_separable] |
✓ |
1.455 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{y \left (x^{3}+1\right )}
\] |
[_separable] |
✓ |
1.122 |
|
|
\[
{}y^{\prime } = y \sin \left (x \right )
\] |
[_separable] |
✓ |
1.290 |
|
|
\[
{}y^{\prime } x = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
2.185 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{1+y^{2}}
\] |
[_separable] |
✓ |
1.128 |
|
|
\[
{}x y y^{\prime } = \sqrt {1+y^{2}}
\] |
[_separable] |
✓ |
5.816 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
1.860 |
|
|
\[
{}y^{\prime } = 3 y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
0.626 |
|
|
\[
{}y^{\prime } x +y = y^{2}
\] |
[_separable] |
✓ |
1.955 |
|
|
\[
{}2 x^{2} y y^{\prime }+y^{2} = 2
\] |
[_separable] |
✓ |
2.046 |
|
|
\[
{}y^{\prime }-x y^{2} = 2 y x
\] |
[_separable] |
✓ |
1.818 |
|
|
\[
{}\left (1+z^{\prime }\right ) {\mathrm e}^{-z} = 1
\] |
[_quadrature] |
✓ |
0.429 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}+4 x +2}{-2+2 y}
\] |
[_separable] |
✓ |
1.382 |
|
|
\[
{}{\mathrm e}^{x}-\left (1+{\mathrm e}^{x}\right ) y y^{\prime } = 0
\] |
[_separable] |
✓ |
1.431 |
|
|
\[
{}\frac {y}{x -1}+\frac {x y^{\prime }}{1+y} = 0
\] |
[_separable] |
✓ |
2.445 |
|
|
\[
{}x +2 x^{3}+\left (y+2 y^{3}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.777 |
|
|
\[
{}\frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}} = 0
\] |
[_separable] |
✓ |
14.425 |
|
|
\[
{}\frac {1}{\sqrt {-x^{2}+1}}+\frac {y^{\prime }}{\sqrt {1-y^{2}}} = 0
\] |
[_separable] |
✓ |
20.856 |
|
|
\[
{}2 x \sqrt {1-y^{2}}+y y^{\prime } = 0
\] |
[_separable] |
✓ |
1.868 |
|
|
\[
{}y^{\prime } = \left (-1+y\right ) \left (x +1\right )
\] |
[_separable] |
✓ |
1.055 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
1.355 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{\sqrt {x}}
\] |
[_separable] |
✓ |
9.376 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
2.946 |
|
|
\[
{}z^{\prime } = 10^{x +z}
\] |
[_separable] |
✓ |
1.833 |
|
|
\[
{}x^{\prime }+t = 1
\] |
[_quadrature] |
✓ |
0.213 |
|
|
\[
{}y^{\prime } = \cos \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.231 |
|
|
\[
{}y^{\prime }-y = 2 x -3
\] |
[[_linear, ‘class A‘]] |
✓ |
0.870 |
|
|
\[
{}\left (x +2 y\right ) y^{\prime } = 1
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
1.927 |
|
|
\[
{}y^{\prime }+y = 2 x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
0.852 |
|
|
\[
{}y^{\prime } = \cos \left (x -y-1\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.444 |
|
|
\[
{}y^{\prime }+\sin \left (x +y\right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
5.788 |
|
|
\[
{}y^{\prime } = 2 \sqrt {2 x +y+1}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.888 |
|
|
\[
{}y^{\prime } = \left (x +y+1\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
4.359 |
|
|
\[
{}y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.667 |
|
|
\[
{}\left (1+y^{2}\right ) \left ({\mathrm e}^{2 x}-{\mathrm e}^{y} y^{\prime }\right )-\left (1+y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.151 |
|
|
\[
{}x -y+\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.545 |
|
|
\[
{}y-2 y x +x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.342 |
|
|
\[
{}2 y^{\prime } x = y \left (2 x^{2}-y^{2}\right )
\] |
[_rational, _Bernoulli] |
✓ |
1.247 |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
36.344 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime } = 2 y x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.692 |
|
|
\[
{}-y+y^{\prime } x = x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.848 |
|
|
\[
{}y^{\prime } x = y-x \,{\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
8.628 |
|
|
\[
{}-y+y^{\prime } x = \left (x +y\right ) \ln \left (\frac {x +y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.155 |
|
|
\[
{}y^{\prime } x = y \cos \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.885 |
|
|
\[
{}y+\sqrt {y x}-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
7.442 |
|
|
\[
{}y^{\prime } x -\sqrt {x^{2}-y^{2}}-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
66.923 |
|
|
\[
{}x +y-\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.474 |
|
|
\[
{}x^{2}+2 y x -y^{2}+\left (y^{2}+2 y x -x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.964 |
|
|
\[
{}-y+y^{\prime } x = y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.159 |
|
|
\[
{}y^{2}+\left (x^{2}-y x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
36.849 |
|
|
\[
{}x^{2}+y x +y^{2} = x^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
1.927 |
|
|
\[
{}\frac {1}{x^{2}-y x +y^{2}} = \frac {y^{\prime }}{2 y^{2}-y x}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
24.757 |
|
|
\[
{}y^{\prime } = \frac {2 x y}{3 x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.484 |
|
|
\[
{}y^{\prime } = \frac {x}{y}+\frac {y}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.227 |
|
|
\[
{}y^{\prime } x = y+\sqrt {y^{2}-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.097 |
|
|
\[
{}y+\left (2 \sqrt {y x}-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
82.382 |
|
|
\[
{}y^{\prime } x = y \ln \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.750 |
|
|
\[
{}y^{\prime } \left (y^{\prime }+y\right ) = x \left (x +y\right )
\] |
[_quadrature] |
✓ |
1.262 |
|
|
\[
{}\left (y^{\prime } x +y\right )^{2} = y^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
151.661 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
2.473 |
|
|
\[
{}-y+y^{\prime } x = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.044 |
|
|
\[
{}y {y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.958 |
|
|
\[
{}y^{\prime }+\frac {x +2 y}{x} = 0
\] |
[_linear] |
✓ |
1.790 |
|
|
\[
{}y^{\prime } = \frac {y}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.056 |
|
|
\[
{}y^{\prime } x = x +\frac {y}{2}
\] |
[_linear] |
✓ |
5.359 |
|
|
\[
{}y^{\prime } = \frac {x +y-2}{y-x -4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.377 |
|
|
\[
{}2 x -4 y+6+\left (x +y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.071 |
|
|
\[
{}y^{\prime } = \frac {2 y-x +5}{2 x -y-4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.017 |
|
|
\[
{}y^{\prime } = -\frac {4 x +3 y+15}{2 x +y+7}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.516 |
|
|
\[
{}y^{\prime } = \frac {x +3 y-5}{x -y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.746 |
|
|
\[
{}y^{\prime } = \frac {2 \left (2+y\right )^{2}}{\left (x +y+1\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
1.670 |
|
|
\[
{}2 x +y+1-\left (4 x +2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.323 |
|
|
\[
{}x -y-1+\left (y-x +2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.380 |
|
|
\[
{}\left (x +4 y\right ) y^{\prime } = 2 x +3 y-5
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.687 |
|
|
\[
{}2+y = \left (2 x +y-4\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.837 |
|
|
\[
{}\left (1+y^{\prime }\right ) \ln \left (\frac {x +y}{x +3}\right ) = \frac {x +y}{x +3}
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
6.984 |
|
|
\[
{}y^{\prime } = \frac {x -2 y+5}{y-2 x -4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.932 |
|
|
\[
{}y^{\prime } = \frac {3 x -y+1}{2 x +y+4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.395 |
|
|
\[
{}2 y^{\prime } x +\left (x^{2} y^{4}+1\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.017 |
|
|
\[
{}2 x y^{\prime } \left (x -y^{2}\right )+y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
0.529 |
|
|
\[
{}x^{3} \left (y^{\prime }-x \right ) = y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
0.264 |
|
|
\[
{}2 x^{2} y^{\prime } = y^{3}+y x
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
0.575 |
|
|
\[
{}y+x \left (2 y x +1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.399 |
|