|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.585 |
|
|
\[
{}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.368 |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.774 |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.602 |
|
|
\[
{}x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }-x \left (x^{2}+3\right ) y^{\prime }-2 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.141 |
|
|
\[
{}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.624 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.911 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-7 y^{\prime \prime }-y^{\prime }+6 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.150 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.218 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.855 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.233 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.182 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+7 y^{\prime }-5 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.123 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.140 |
|
|
\[
{}y^{\prime \prime \prime \prime }+8 y^{\prime \prime }-9 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.122 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+16 y^{\prime }-16 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.112 |
|
|
\[
{}2 y^{\prime \prime \prime }+3 y^{\prime \prime }-2 y^{\prime }-3 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.107 |
|
|
\[
{}y^{\prime \prime \prime }+5 y^{\prime \prime }+9 y^{\prime }+5 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.120 |
|
|
\[
{}4 y^{\prime \prime \prime }-8 y^{\prime \prime }+5 y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.823 |
|
|
\[
{}27 y^{\prime \prime \prime }+27 y^{\prime \prime }+9 y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.110 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.125 |
|
|
\[
{}y^{\prime \prime \prime \prime }+12 y^{\prime \prime }+36 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.141 |
|
|
\[
{}16 y^{\prime \prime \prime \prime }-72 y^{\prime \prime }+81 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.137 |
|
|
\[
{}6 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+7 y^{\prime \prime }+5 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.128 |
|
|
\[
{}4 y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+3 y^{\prime \prime }-13 y^{\prime }-6 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.119 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.131 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.135 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.860 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime }-4 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.145 |
|
|
\[
{}3 y^{\prime \prime \prime }-y^{\prime \prime }-7 y^{\prime }+5 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.135 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.142 |
|
|
\[
{}2 y^{\prime \prime \prime }-11 y^{\prime \prime }+12 y^{\prime }+9 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.145 |
|
|
\[
{}8 y^{\prime \prime \prime }-4 y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.826 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.139 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+7 y^{\prime \prime }+6 y^{\prime }-8 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.170 |
|
|
\[
{}4 y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+9 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.146 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-8 y^{\prime }-8 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.141 |
|
|
\[
{}4 y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+19 y^{\prime \prime }+32 y^{\prime }+12 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.140 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.117 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.130 |
|
|
\[
{}y^{\prime \prime \prime \prime }+64 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.129 |
|
|
\[
{}y^{\left (6\right )}-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.154 |
|
|
\[
{}y^{\prime \prime \prime \prime }+64 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.950 |
|
|
\[
{}y^{\left (5\right )}+y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.180 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = -{\mathrm e}^{x} \left (-24 x^{2}+76 x +4\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.206 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{-3 x} \left (6 x^{2}-23 x +32\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.207 |
|
|
\[
{}4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y = -{\mathrm e}^{x} \left (6 x^{2}+45 x +4\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.185 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y = {\mathrm e}^{-2 x} \left (3 x^{2}-17 x +2\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.212 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y = {\mathrm e}^{x} \left (16 x^{3}+24 x^{2}+2 x -1\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.207 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-2 y = {\mathrm e}^{x} \left (15 x^{2}+34 x +14\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.181 |
|
|
\[
{}4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y = -{\mathrm e}^{-2 x} \left (1-15 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.218 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = -{\mathrm e}^{x} \left (7+6 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.181 |
|
|
\[
{}2 y^{\prime \prime \prime }-7 y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{2 x} \left (17+30 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.191 |
|
|
\[
{}y^{\prime \prime \prime }-5 y^{\prime \prime }+3 y^{\prime }+9 y = 2 \,{\mathrm e}^{3 x} \left (11-24 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.210 |
|
|
\[
{}y^{\prime \prime \prime }-7 y^{\prime \prime }+8 y^{\prime }+16 y = 2 \,{\mathrm e}^{4 x} \left (13+15 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.191 |
|
|
\[
{}8 y^{\prime \prime \prime }-12 y^{\prime \prime }+6 y^{\prime }-y = {\mathrm e}^{\frac {x}{2}} \left (1+4 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.189 |
|
|
\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }-7 y^{\prime }+6 y = -3 \,{\mathrm e}^{-x} \left (-8 x^{2}+8 x +12\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.200 |
|
|
\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-2 y = -3 \,{\mathrm e}^{2 x} \left (11+12 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.895 |
|
|
\[
{}y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime } = -16 \,{\mathrm e}^{-2 x} \left (-x^{3}+x^{2}+x +1\right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.213 |
|
|
\[
{}4 y^{\prime \prime \prime \prime }-11 y^{\prime \prime }-9 y^{\prime }-2 y = -{\mathrm e}^{x} \left (1-6 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.208 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x} \left (x^{2}+4 x +3\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.231 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+2 y = {\mathrm e}^{2 x} \left (x^{4}+x +24\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.246 |
|
|
\[
{}2 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-5 y^{\prime }-2 y = 18 \,{\mathrm e}^{x} \left (5+2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.186 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }-4 y = -{\mathrm e}^{2 x} \left (15 x^{2}+28 x +4\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.217 |
|
|
\[
{}2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime }-y = 3 \,{\mathrm e}^{-\frac {x}{2}} \left (1-6 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.206 |
|
|
\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = {\mathrm e}^{x} \left (-3 x^{2}+x +3\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.198 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{2 x} \left (18 x^{2}+33 x +13\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.246 |
|
|
\[
{}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime } = {\mathrm e}^{2 x} \left (12 x^{2}+26 x +15\right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.214 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y = {\mathrm e}^{x} \left (x +1\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.185 |
|
|
\[
{}2 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-y = {\mathrm e}^{x} \left (11+12 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.200 |
|
|
\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime } = {\mathrm e}^{-x} \left (10 x^{2}-24 x +5\right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.211 |
|
|
\[
{}y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+18 y^{\prime \prime }-20 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (-5 x^{2}-8 x +3\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.217 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (\left (16+10 x \right ) \cos \left (x \right )+\left (30-10 x \right ) \sin \left (x \right )\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.263 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y = {\mathrm e}^{-x} \left (\left (1-22 x \right ) \cos \left (2 x \right )-\left (1+6 x \right ) \sin \left (2 x \right )\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.315 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }-2 y = {\mathrm e}^{2 x} \left (\left (-x^{2}+5 x +27\right ) \cos \left (x \right )+\left (9 x^{2}+13 x +2\right ) \sin \left (x \right )\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.337 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y = -{\mathrm e}^{x} \left (\left (4 x^{2}+5 x +9\right ) \cos \left (2 x \right )-\left (-3 x^{2}-5 x +6\right ) \sin \left (2 x \right )\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
1.378 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }+12 y = 8 \cos \left (2 x \right )-16 \sin \left (2 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.606 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+2 y = {\mathrm e}^{x} \left (\left (20+4 x \right ) \cos \left (x \right )-\left (12+12 x \right ) \sin \left (x \right )\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.921 |
|
|
\[
{}y^{\prime \prime \prime }-7 y^{\prime \prime }+20 y^{\prime }-24 y = -{\mathrm e}^{2 x} \left (\left (13-8 x \right ) \cos \left (2 x \right )-\left (8-4 x \right ) \sin \left (2 x \right )\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.814 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+18 y^{\prime } = -{\mathrm e}^{3 x} \left (\left (2-3 x \right ) \cos \left (3 x \right )-\left (3+3 x \right ) \sin \left (3 x \right )\right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
1.659 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-8 y^{\prime }-8 y = {\mathrm e}^{x} \left (8 \cos \left (x \right )+16 \sin \left (x \right )\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.259 |
|
|
\[
{}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }-4 y = {\mathrm e}^{x} \left (2 \cos \left (2 x \right )-\sin \left (2 x \right )\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.217 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+15 y = {\mathrm e}^{2 x} \left (15 x \cos \left (2 x \right )+32 \sin \left (2 x \right )\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.253 |
|
|
\[
{}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+13 y^{\prime \prime }+12 y^{\prime }+4 y = {\mathrm e}^{-x} \left (\left (4-x \right ) \cos \left (x \right )-\left (5+x \right ) \sin \left (x \right )\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.247 |
|
|
\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }-4 y = -{\mathrm e}^{-x} \left (\cos \left (x \right )-\sin \left (x \right )\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.803 |
|
|
\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y = {\mathrm e}^{x} \left (\cos \left (2 x \right )+\sin \left (2 x \right )\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.645 |
|
|
\[
{}y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+32 y^{\prime \prime }+64 y^{\prime }+39 y = {\mathrm e}^{-2 x} \left (\left (4-15 x \right ) \cos \left (3 x \right )-\left (4+15 x \right ) \sin \left (3 x \right )\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.021 |
|
|
\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y = {\mathrm e}^{x} \left (\left (7+8 x \right ) \cos \left (2 x \right )+\left (8-4 x \right ) \sin \left (2 x \right )\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.924 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+8 y^{\prime \prime }+8 y^{\prime }+4 y = -2 \,{\mathrm e}^{x} \left (\cos \left (x \right )-\sin \left (x \right )\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.250 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+32 y^{\prime \prime }-64 y^{\prime }+64 y = {\mathrm e}^{2 x} \left (\cos \left (2 x \right )-\sin \left (2 x \right )\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.128 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+26 y^{\prime \prime }-40 y^{\prime }+25 y = {\mathrm e}^{2 x} \left (3 \cos \left (x \right )-\left (1+3 x \right ) \sin \left (x \right )\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.394 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = {\mathrm e}^{2 x}-4 \,{\mathrm e}^{x}-2 \cos \left (x \right )+4 \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.257 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 5 \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{x}-4 \cos \left (x \right )+4 \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.869 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = -2 x -2+4 \,{\mathrm e}^{x}-6 \,{\mathrm e}^{-x}+96 \,{\mathrm e}^{3 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.223 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+9 y^{\prime }-10 y = 10 \,{\mathrm e}^{2 x}+20 \,{\mathrm e}^{x} \sin \left (2 x \right )-10
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.783 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 12 \,{\mathrm e}^{-x}+9 \cos \left (2 x \right )-13 \sin \left (2 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.257 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 4 \,{\mathrm e}^{-x} \left (1-6 x \right )-2 x \cos \left (x \right )+2 \left (x +1\right ) \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.642 |
|