# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y = {\mathrm e}^{-2 x} \left (3 x^{2}-17 x +2\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.215 |
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y = {\mathrm e}^{x} \left (16 x^{3}+24 x^{2}+2 x -1\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.003 |
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-2 y = {\mathrm e}^{x} \left (15 x^{2}+34 x +14\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.596 |
|
\[ {}4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y = -{\mathrm e}^{-2 x} \left (1-15 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.04 |
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = -{\mathrm e}^{x} \left (7+6 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.951 |
|
\[ {}2 y^{\prime \prime \prime }-7 y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{2 x} \left (17+30 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.122 |
|
\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+3 y^{\prime }+9 y = 2 \,{\mathrm e}^{3 x} \left (11-24 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.094 |
|
\[ {}y^{\prime \prime \prime }-7 y^{\prime \prime }+8 y^{\prime }+16 y = 2 \,{\mathrm e}^{4 x} \left (13+15 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.06 |
|
\[ {}8 y^{\prime \prime \prime }-12 y^{\prime \prime }+6 y^{\prime }-y = {\mathrm e}^{\frac {x}{2}} \left (1+4 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.35 |
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }-7 y^{\prime }+6 y = -3 \,{\mathrm e}^{-x} \left (-8 x^{2}+8 x +12\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.706 |
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-2 y = -3 \,{\mathrm e}^{2 x} \left (11+12 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.387 |
|
\[ {}y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime } = -16 \,{\mathrm e}^{-2 x} \left (-x^{3}+x^{2}+x +1\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_y]] |
✓ |
✓ |
4.398 |
|
\[ {}4 y^{\prime \prime \prime \prime }-11 y^{\prime \prime }-9 y^{\prime }-2 y = -{\mathrm e}^{x} \left (1-6 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.614 |
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x} \left (x^{2}+4 x +3\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
63.285 |
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+2 y = {\mathrm e}^{2 x} \left (x^{4}+x +24\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
11.03 |
|
\[ {}2 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-5 y^{\prime }-2 y = 18 \,{\mathrm e}^{x} \left (5+2 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.367 |
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }-4 y = -{\mathrm e}^{2 x} \left (15 x^{2}+28 x +4\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.969 |
|
\[ {}2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime }-y = 3 \,{\mathrm e}^{-\frac {x}{2}} \left (1-6 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.747 |
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = {\mathrm e}^{x} \left (-3 x^{2}+x +3\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.535 |
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{2 x} \left (18 x^{2}+33 x +13\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.428 |
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime } = {\mathrm e}^{2 x} \left (12 x^{2}+26 x +15\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_y]] |
✓ |
✓ |
0.41 |
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y = {\mathrm e}^{x} \left (1+x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.381 |
|
\[ {}2 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-y = {\mathrm e}^{x} \left (11+12 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.385 |
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime } = {\mathrm e}^{-x} \left (10 x^{2}-24 x +5\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_y]] |
✓ |
✓ |
0.417 |
|
\[ {}y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+18 y^{\prime \prime }-20 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (-5 x^{2}-8 x +3\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.433 |
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (\left (16+10 x \right ) \cos \left (x \right )+\left (30-10 x \right ) \sin \left (x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.293 |
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y = {\mathrm e}^{-x} \left (\left (1-22 x \right ) \cos \left (2 x \right )-\left (6 x +1\right ) \sin \left (2 x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.531 |
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }-2 y = {\mathrm e}^{2 x} \left (\left (-x^{2}+5 x +27\right ) \cos \left (x \right )+\left (9 x^{2}+13 x +2\right ) \sin \left (x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
16.825 |
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y = -{\mathrm e}^{x} \left (\left (4 x^{2}+5 x +9\right ) \cos \left (2 x \right )-\left (-3 x^{2}-5 x +6\right ) \sin \left (2 x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
13.105 |
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }+12 y = 8 \cos \left (2 x \right )-16 \sin \left (2 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
5.253 |
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+2 y = {\mathrm e}^{x} \left (\left (20+4 x \right ) \cos \left (x \right )-\left (12+12 x \right ) \sin \left (x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
7.104 |
|
\[ {}y^{\prime \prime \prime }-7 y^{\prime \prime }+20 y^{\prime }-24 y = -{\mathrm e}^{2 x} \left (\left (13-8 x \right ) \cos \left (2 x \right )-\left (8-4 x \right ) \sin \left (2 x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
12.679 |
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+18 y^{\prime } = -{\mathrm e}^{3 x} \left (\left (2-3 x \right ) \cos \left (3 x \right )-\left (3+3 x \right ) \sin \left (3 x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
5.123 |
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-8 y^{\prime }-8 y = {\mathrm e}^{x} \left (8 \cos \left (x \right )+16 \sin \left (x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
9.607 |
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }-4 y = {\mathrm e}^{x} \left (2 \cos \left (2 x \right )-\sin \left (2 x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
11.234 |
|
\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+15 y = {\mathrm e}^{2 x} \left (15 x \cos \left (2 x \right )+32 \sin \left (2 x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
13.16 |
|
\[ {}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+13 y^{\prime \prime }+12 y^{\prime }+4 y = {\mathrm e}^{-x} \left (\left (4-x \right ) \cos \left (x \right )-\left (x +5\right ) \sin \left (x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.553 |
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }-4 y = -{\mathrm e}^{-x} \left (\cos \left (x \right )-\sin \left (x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
10.404 |
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y = {\mathrm e}^{x} \left (\cos \left (2 x \right )+\sin \left (2 x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
10.407 |
|
\[ {}y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+32 y^{\prime \prime }+64 y^{\prime }+39 y = {\mathrm e}^{-2 x} \left (\left (4-15 x \right ) \cos \left (3 x \right )-\left (4+15 x \right ) \sin \left (3 x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
20.096 |
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y = {\mathrm e}^{x} \left (\left (7+8 x \right ) \cos \left (2 x \right )+\left (8-4 x \right ) \sin \left (2 x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
18.985 |
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+8 y^{\prime \prime }+8 y^{\prime }+4 y = -2 \,{\mathrm e}^{x} \left (\cos \left (x \right )-\sin \left (x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.466 |
|
\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+32 y^{\prime \prime }-64 y^{\prime }+64 y = {\mathrm e}^{2 x} \left (\cos \left (2 x \right )-\sin \left (2 x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.51 |
|
\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+26 y^{\prime \prime }-40 y^{\prime }+25 y = {\mathrm e}^{2 x} \left (3 \cos \left (x \right )-\left (1+3 x \right ) \sin \left (x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.118 |
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = {\mathrm e}^{2 x}-4 \,{\mathrm e}^{x}-2 \cos \left (x \right )+4 \sin \left (x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.951 |
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 5 \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{x}-4 \cos \left (x \right )+4 \sin \left (x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.99 |
|
\[ {}y^{\prime \prime \prime }-y^{\prime } = -2 x -2+4 \,{\mathrm e}^{x}-6 \,{\mathrm e}^{-x}+96 \,{\mathrm e}^{3 x} \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
1.115 |
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+9 y^{\prime }-10 y = 10 \,{\mathrm e}^{2 x}+20 \,{\mathrm e}^{x} \sin \left (2 x \right )-10 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
7.984 |
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 12 \,{\mathrm e}^{-x}+9 \cos \left (2 x \right )-13 \sin \left (2 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.533 |
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 4 \,{\mathrm e}^{-x} \left (1-6 x \right )-2 x \cos \left (x \right )+2 \left (1+x \right ) \sin \left (x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.883 |
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = -12 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x}+10 \cos \left (x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.194 |
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+11 y^{\prime \prime }-14 y^{\prime }+10 y = -{\mathrm e}^{x} \left (\sin \left (x \right )+2 \cos \left (2 x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
16.946 |
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{x} \left (1+x \right )+{\mathrm e}^{-2 x} \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.485 |
|
\[ {}y^{\prime \prime \prime \prime }+4 y = \sinh \left (x \right ) \cos \left (x \right )-\cosh \left (x \right ) \sin \left (x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
11.277 |
|
\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+9 y^{\prime \prime }+7 y^{\prime }+2 y = {\mathrm e}^{-x} \left (30+24 x \right )-{\mathrm e}^{-2 x} \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.486 |
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y = {\mathrm e}^{x} \left (12 x -2 \cos \left (x \right )+2 \sin \left (x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.671 |
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = {\mathrm e}^{2 x} \left (10+3 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.952 |
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-2 y = -{\mathrm e}^{3 x} \left (17 x^{2}+67 x +9\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.8 |
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = {\mathrm e}^{2 x} \left (-3 x^{2}-4 x +5\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.112 |
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = -2 \,{\mathrm e}^{-x} \left (6 x^{2}-18 x +7\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.387 |
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x} \left (1+x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.345 |
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = -{\mathrm e}^{-x} \left (3 x^{2}-9 x +4\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.411 |
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{-2 x} \left (\left (23-2 x \right ) \cos \left (x \right )+\left (8-9 x \right ) \sin \left (x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.282 |
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{x} \left (\left (28+6 x \right ) \cos \left (2 x \right )+\left (11-12 x \right ) \sin \left (2 x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_y]] |
✓ |
✓ |
6.084 |
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y = {\mathrm e}^{x} \left (\left (6 x +2\right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.115 |
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{x} \left (1-6 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.519 |
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = -{\mathrm e}^{-x} \left (4-8 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.483 |
|
\[ {}4 y^{\prime \prime \prime }-3 y^{\prime }-y = {\mathrm e}^{-\frac {x}{2}} \left (2-3 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.491 |
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \left (20-12 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.042 |
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y = 30 \cos \left (x \right )-10 \sin \left (x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
5.213 |
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+5 y^{\prime \prime }-2 y^{\prime } = -2 \,{\mathrm e}^{x} \left (\cos \left (x \right )-\sin \left (x \right )\right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_y]] |
✓ |
✓ |
88.982 |
|
\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 2 x \] |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.556 |
|
\[ {}4 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-5 x y^{\prime }+2 y = 30 x^{2} \] |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.631 |
|
\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2} \] |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.553 |
|
\[ {}16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 x y^{\prime }+9 y = 96 x^{\frac {5}{2}} \] |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
0.769 |
|
\[ {}x^{4} y^{\prime \prime \prime \prime }-4 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }-24 x y^{\prime }+24 y = x^{4} \] |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
0.695 |
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = 12 x^{2} \] |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.737 |
|
\[ {}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 4 x \] |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.31 |
|
\[ {}x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 x y^{\prime }-18 y = x^{3} \] |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.283 |
|
\[ {}x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+16 x y^{\prime }-16 y = 9 x^{4} \] |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.198 |
|
\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = \left (1+x \right ) x \] |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.092 |
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 9 x^{2} \] |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.356 |
|
\[ {}4 x^{4} y^{\prime \prime \prime \prime }+24 x^{3} y^{\prime \prime \prime }+23 x^{2} y^{\prime \prime }-x y^{\prime }+y = 6 x \] |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.06 |
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-6 x y^{\prime }+6 y = 40 x^{3} \] |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.34 |
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = F \left (x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.537 |
|
\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = F \left (x \right ) \] |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.614 |
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = F \left (x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.59 |
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = F \left (x \right ) \] |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.754 |
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+2 y_{2} \\ y_{2}^{\prime }=2 y_{1}+y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.524 |
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-\frac {5 y_{1}}{4}+\frac {3 y_{2}}{4} \\ y_{2}^{\prime }=\frac {3 y_{1}}{4}-\frac {5 y_{2}}{4} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.56 |
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-\frac {4 y_{1}}{5}+\frac {3 y_{2}}{5} \\ y_{2}^{\prime }=-\frac {2 y_{1}}{5}-\frac {11 y_{2}}{5} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.634 |
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}-4 y_{2} \\ y_{2}^{\prime }=-y_{1}-y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.597 |
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-4 y_{2} \\ y_{2}^{\prime }=-y_{1}-y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.61 |
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}-3 y_{2} \\ y_{2}^{\prime }=2 y_{1}-y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.583 |
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-6 y_{1}-3 y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.597 |
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}-y_{2}-2 y_{3} \\ y_{2}^{\prime }=y_{1}-2 y_{2}-3 y_{3} \\ y_{3}^{\prime }=-4 y_{1}+y_{2}-y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.138 |
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-6 y_{1}-4 y_{2}-8 y_{3} \\ y_{2}^{\prime }=-4 y_{1}-4 y_{3} \\ y_{3}^{\prime }=-8 y_{1}-4 y_{2}-6 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.02 |
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+5 y_{2}+8 y_{3} \\ y_{2}^{\prime }=y_{1}-y_{2}-2 y_{3} \\ y_{3}^{\prime }=-y_{1}-y_{2}-y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.181 |
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}-y_{2}+2 y_{3} \\ y_{2}^{\prime }=12 y_{1}-4 y_{2}+10 y_{3} \\ y_{3}^{\prime }=-6 y_{1}+y_{2}-7 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.054 |
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}-y_{2}-4 y_{3} \\ y_{2}^{\prime }=4 y_{1}-3 y_{2}-2 y_{3} \\ y_{3}^{\prime }=y_{1}-y_{2}-y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.065 |
|
|
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