|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.451 |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = \cos \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.222 |
|
|
\[
{}y^{\prime \prime }+\cot \left (x \right ) y^{\prime }-\csc \left (x \right )^{2} y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.664 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime \prime }+2 y^{\prime }-\frac {y}{x} = 1
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.140 |
|
|
\[
{}x y^{\prime \prime }+\left (6 x y^{2}+1\right ) y^{\prime }+2 y^{3}+1 = 0
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
1.653 |
|
|
\[
{}\frac {x y^{\prime \prime }}{1+y}+\frac {y y^{\prime }-x {y^{\prime }}^{2}+y^{\prime }}{\left (1+y\right )^{2}} = x \sin \left (x \right )
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.438 |
|
|
\[
{}\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime \prime }-x {y^{\prime }}^{2} \sin \left (y\right )+2 \left (\cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime } = y \sin \left (x \right )
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
46.667 |
|
|
\[
{}y y^{\prime \prime } \sin \left (x \right )+\left (\sin \left (x \right ) y^{\prime }+y \cos \left (x \right )\right ) y^{\prime } = \cos \left (x \right )
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.637 |
|
|
\[
{}\left (1-y\right ) y^{\prime \prime }-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.537 |
|
|
\[
{}\left (\cos \left (y\right )-y \sin \left (y\right )\right ) y^{\prime \prime }-{y^{\prime }}^{2} \left (2 \sin \left (y\right )+y \cos \left (y\right )\right ) = \sin \left (x \right )
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.899 |
|
|
\[
{}y^{\prime \prime }+\frac {2 x y^{\prime }}{2 x -1}-\frac {4 x y}{\left (2 x -1\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.765 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime } = \left (25-6 x \right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.430 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x +1}-\frac {\left (x +2\right ) y}{x^{2} \left (x +1\right )} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.210 |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.268 |
|
|
\[
{}\frac {\left (x^{2}-x \right ) y^{\prime \prime }}{x}+\frac {\left (3 x +1\right ) y^{\prime }}{x}+\frac {y}{x} = 3 x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.349 |
|
|
\[
{}\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
9.366 |
|
|
\[
{}y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x}+\frac {y}{x^{3}} = \frac {{\mathrm e}^{-\frac {1}{x}}}{x^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.493 |
|
|
\[
{}y^{\prime \prime }+\left (2 x +5\right ) y^{\prime }+\left (4 x +8\right ) y = {\mathrm e}^{-2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.814 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.266 |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.311 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.227 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.270 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.233 |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+37 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.375 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.241 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.270 |
|
|
\[
{}4 y^{\prime \prime }-12 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.270 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.328 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.215 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.610 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.281 |
|
|
\[
{}y^{\prime \prime }-20 y^{\prime }+51 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.252 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.247 |
|
|
\[
{}3 y^{\prime \prime }+8 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.247 |
|
|
\[
{}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.314 |
|
|
\[
{}4 y^{\prime \prime }+40 y^{\prime }+101 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.269 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+34 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.313 |
|
|
\[
{}y^{\prime \prime \prime }+8 y^{\prime \prime }+16 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.266 |
|
|
\[
{}y^{\prime \prime \prime }+6 y^{\prime \prime }+13 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.314 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+13 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.316 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.339 |
|
|
\[
{}y^{\prime \prime \prime }+6 y^{\prime \prime }+25 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.323 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+10 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.314 |
|
|
\[
{}y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.466 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = 9 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.339 |
|
|
\[
{}4 y^{\prime \prime }+16 y^{\prime }+17 y = 17 t -1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.301 |
|
|
\[
{}4 y^{\prime \prime }+5 y^{\prime }+4 y = 3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.495 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = t^{2} {\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.243 |
|
|
\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.326 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime }+17 y = 17 t -1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.532 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.245 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = t +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.387 |
|
|
\[
{}2 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.393 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+20 y = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.413 |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.282 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }-y = 4 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.410 |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.378 |
|
|
\[
{}3 y^{\prime \prime }+5 y^{\prime }-2 y = 7 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.270 |
|
|
\[
{}y^{\prime }+y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.468 |
|
|
\[
{}y^{\prime }-2 y = 4 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right )\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.770 |
|
|
\[
{}y^{\prime \prime }+9 y = 24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.499 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.630 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.430 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.743 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = 39 \operatorname {Heaviside}\left (t \right )-507 \left (t -2\right ) \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.254 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (t -4\right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.598 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+5 y = 25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.799 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.149 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right .
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.584 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.725 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.618 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.661 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.488 |
|
|
\[
{}y^{\prime \prime }+4 \pi ^{2} y = 3 \delta \left (t -\frac {1}{3}\right )-\delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.654 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 3 \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.501 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+29 y = 5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.111 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 1-\delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.523 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}} \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.345 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+6 y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.342 |
|
|
\[
{}10 Q^{\prime }+100 Q = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.648 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }+4 y^{\prime }+4 y = 8
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.352 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 4 t
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.299 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 8 \,{\mathrm e}^{2 t}-5 \,{\mathrm e}^{t}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.360 |
|
|
\[
{}y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y = -t^{2}+2 t -10
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
1.797 |
|
|
\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 12 \operatorname {Heaviside}\left (t \right )-12 \operatorname {Heaviside}\left (t -1\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
9.463 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 32 \operatorname {Heaviside}\left (t \right )-32 \operatorname {Heaviside}\left (t -\pi \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
5.098 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = t^{7}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.704 |
|
|
\[
{}t^{2} y^{\prime \prime }-6 t y^{\prime }+\sin \left (2 t \right ) y = \ln \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
1.001 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+\frac {y}{t} = t
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.492 |
|
|
\[
{}y^{\prime \prime }+t y^{\prime }-y \ln \left (t \right ) = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.519 |
|
|
\[
{}t^{3} y^{\prime \prime }-2 t y^{\prime }+y = t^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.501 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.298 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.535 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-7 y = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.810 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 5
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.101 |
|
|
\[
{}3 y^{\prime \prime }+5 y^{\prime }-2 y = 3 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.543 |
|
|
\[
{}y^{\prime \prime \prime } = 2 y^{\prime \prime }-4 y^{\prime }+\sin \left (t \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.137 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.412 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }=\frac {x}{2}-\frac {3 y}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.604 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+2 y=0 \\ y^{\prime }+y-x=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.442 |
|