|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.594 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.997 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.122 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.128 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 y^{\prime } x -18 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.123 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 y^{\prime } x -8 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.123 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+9 y^{\prime } x +16 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.144 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 y^{\prime } x +9 y = 0
\] |
[[_high_order, _exact, _linear, _homogeneous]] |
✓ |
0.135 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.172 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_high_order, _exact, _linear, _homogeneous]] |
✓ |
0.139 |
|
|
\[
{}y^{\prime \prime }+4 y = 24 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.251 |
|
|
\[
{}y^{\prime \prime }+4 y = 24 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.270 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-8 y = 8 x^{2}-3
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.205 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-8 y = 8 x^{2}-3
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.442 |
|
|
\[
{}y^{\prime \prime }-9 y = 36
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.163 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = -6 \,{\mathrm e}^{4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.848 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = 7 \,{\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.965 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 169 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.203 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 10 x +12
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.378 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime } = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = {\mathrm e}^{4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.250 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = {\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.343 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = -18 \,{\mathrm e}^{4 x}+14 \,{\mathrm e}^{5 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.502 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = 35 \,{\mathrm e}^{5 x}+12 \,{\mathrm e}^{4 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.510 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.490 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.578 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 22 x +24
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.633 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.467 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.460 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.378 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = 4 x^{2}+2 x +3
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.528 |
|
|
\[
{}y^{\prime \prime }+9 y = 52 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.529 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.362 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-5 y = 30 \,{\mathrm e}^{-4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.286 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{\frac {x}{2}}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.139 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = -5 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.860 |
|
|
\[
{}y^{\prime \prime }+9 y = 10 \cos \left (2 x \right )+15 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.150 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 25 \sin \left (6 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.768 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.765 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-5 y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.609 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = -4 \cos \left (x \right )+7 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.733 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = -200
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.222 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-5 y = x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.717 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 18 x^{2}+3 x +4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.408 |
|
|
\[
{}y^{\prime \prime }+9 y = 9 x^{4}-9
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.731 |
|
|
\[
{}y^{\prime \prime }+9 y = x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.604 |
|
|
\[
{}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.273 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.684 |
|
|
\[
{}y^{\prime \prime }+9 y = 54 x^{2} {\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.832 |
|
|
\[
{}y^{\prime \prime } = 6 x \,{\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.683 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \left (-6 x -8\right ) \cos \left (2 x \right )+\left (8 x -11\right ) \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.064 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \left (12 x -4\right ) {\mathrm e}^{-5 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.391 |
|
|
\[
{}y^{\prime \prime }+9 y = 39 x \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.067 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = -3 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.387 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 20
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.232 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.266 |
|
|
\[
{}y^{\prime \prime }+9 y = 3 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.815 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 10 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.391 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = \left (72 x^{2}-1\right ) {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.341 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = 4 x \,{\mathrm e}^{6 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.319 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.367 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{-5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.392 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 24 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.334 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 8 \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
8.259 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.291 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{-x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.048 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 100
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.516 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.959 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 10 x^{2}+4 x +8
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
10.387 |
|
|
\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.656 |
|
|
\[
{}y^{\prime \prime }+y = 6 \cos \left (x \right )-3 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.058 |
|
|
\[
{}y^{\prime \prime }+y = 6 \cos \left (2 x \right )-3 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.409 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = x^{3} {\mathrm e}^{-x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
16.437 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = x^{3} {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.057 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.511 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.395 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{-8 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.259 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.245 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.372 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.221 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.974 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{4 x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
22.819 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{2 x} \sin \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
14.502 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+20 y = x^{3} \sin \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
24.823 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{2} {\mathrm e}^{5 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.381 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.450 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 12 \,{\mathrm e}^{-2 x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.114 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 10 \sin \left (2 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.150 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 32 \,{\mathrm e}^{4 x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 32 x
\] |
[[_high_order, _missing_y]] |
✓ |
0.116 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = x^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.115 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 30 \cos \left (2 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.150 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 6 \,{\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.124 |
|
|
\[
{}y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} {\mathrm e}^{3 x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.154 |
|
|
\[
{}y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} \sin \left (3 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.779 |
|
|
\[
{}y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.464 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 30 x \cos \left (2 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.215 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 3 x \cos \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.609 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 3 x \,{\mathrm e}^{x} \cos \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.180 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 5 x^{5} {\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.154 |
|