Number of problems in this table is 331
Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.656 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.564 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.575 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.679 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.696 |
|
|
\[ {}y^{\prime \prime }+\omega ^{2} y = \cos \left (2 t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.008 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.82 |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.557 |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.522 |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t <\infty \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.308 |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <3 \pi \\ 0 & 3 \pi \le t <\infty \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.123 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & \pi \le t <2 \pi \\ 0 & \operatorname {otherwise} \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.998 |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.614 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & \operatorname {otherwise} \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.308 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.156 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \operatorname {otherwise} \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
5.484 |
|
|
\[ {}y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.079 |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = k \left (\operatorname {Heaviside}\left (t -\frac {3}{2}\right )-\operatorname {Heaviside}\left (t -\frac {5}{2}\right )\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
10.746 |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -\frac {3}{2}\right )}{2}-\frac {\operatorname {Heaviside}\left (t -\frac {5}{2}\right )}{2} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
5.13 |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )-\operatorname {Heaviside}\left (t -5-k \right ) \left (t -5-k \right )}{k} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
10.247 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.436 |
|
|
\[ {}y^{\prime \prime }+4 y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.982 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \delta \left (t -5\right )+\operatorname {Heaviside}\left (t -10\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.079 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = \sin \left (t \right )+\delta \left (t -3 \pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.706 |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \cos \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.864 |
|
|
\[ {}y^{\prime \prime }+4 y = 2 \delta \left (t -\frac {\pi }{4}\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.983 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.102 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{2}+y = \delta \left (-1+t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.325 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{4}+y = \delta \left (-1+t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.22 |
|
|
\[ {}y^{\prime \prime }+y = \frac {\operatorname {Heaviside}\left (t -4+k \right )-\operatorname {Heaviside}\left (t -4-k \right )}{2 k} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.893 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.774 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.362 |
|
|
\[ {}y^{\prime \prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.313 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 4 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.366 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-12 y = 36 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.35 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 10 \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.391 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 4 \,{\mathrm e}^{3 t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.377 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 30 \,{\mathrm e}^{-3 t} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.413 |
|
|
\[ {}y^{\prime \prime }-y = 12 \,{\mathrm e}^{2 t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.38 |
|
|
\[ {}y^{\prime \prime }+4 y = 10 \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.425 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = -6 \,{\mathrm e}^{t}+12 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.469 |
|
|
\[ {}y^{\prime \prime }-y = 6 \cos \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.478 |
|
|
\[ {}y^{\prime \prime }-9 y = 13 \sin \left (2 t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.551 |
|
|
\[ {}y^{\prime \prime }-y = 8 \sin \left (t \right )-6 \cos \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.747 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 10 \cos \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.477 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.529 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.438 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 3 \cos \left (t \right )+\sin \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.553 |
|
|
\[ {}y^{\prime \prime }+4 y = 9 \sin \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.64 |
|
|
\[ {}y^{\prime \prime }+y = 6 \cos \left (2 t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.542 |
|
|
\[ {}y^{\prime \prime }+9 y = 7 \sin \left (4 t \right )+14 \cos \left (4 t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.015 |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.282 |
|
|
\[ {}y^{\prime \prime }-y = \operatorname {Heaviside}\left (-1+t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.826 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 1-3 \operatorname {Heaviside}\left (t -2\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.349 |
|
|
\[ {}y^{\prime \prime }-4 y = \operatorname {Heaviside}\left (-1+t \right )-\operatorname {Heaviside}\left (t -2\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.668 |
|
|
\[ {}y^{\prime \prime }+y = t -\operatorname {Heaviside}\left (-1+t \right ) \left (-1+t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.913 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = -10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.341 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 30 \operatorname {Heaviside}\left (-1+t \right ) {\mathrm e}^{1-t} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.366 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 5 \operatorname {Heaviside}\left (t -3\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.24 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \sin \left (t \right )+\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (1+\cos \left (t \right )\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.093 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \delta \left (-1+t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.901 |
|
|
\[ {}y^{\prime \prime }-4 y = \delta \left (t -3\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.839 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -\frac {\pi }{2}\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.927 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.868 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = \delta \left (t -2\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.972 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.152 |
|
|
\[ {}y^{\prime \prime }+9 y = 15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.599 |
|
|
\[ {}y^{\prime \prime }+16 y = 4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.829 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.188 |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.29 |
|
|
\[ {}y^{\prime \prime }-y = \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.505 |
|
|
\[ {}y^{\prime \prime }-y = {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.409 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = \sin \left (2 x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.608 |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.548 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.583 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-2 x} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.521 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }-3 y = \operatorname {Heaviside}\left (x -4\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.669 |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.375 |
|
|
\[ {}q^{\prime \prime }+9 q^{\prime }+14 q = \frac {\sin \left (t \right )}{2} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.678 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.342 |
|
|
\[ {}y^{\prime \prime }+9 y = 10 \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.495 |
|
|
\[ {}y^{\prime \prime }-\frac {y}{4} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.32 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+5 y = 29 \cos \left (2 t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.524 |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 21 \,{\mathrm e}^{3 t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.473 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.358 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 6 t -8 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.401 |
|
|
\[ {}y^{\prime \prime }+\frac {y}{25} = \frac {t^{2}}{50} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.47 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4} = 9 t^{3}+64 \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.49 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.662 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 50 t -100 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.718 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -3} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.599 |
|
|
\[ {}9 y^{\prime \prime }-6 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.313 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-3 t}-{\mathrm e}^{-5 t} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.449 |
|
|
\[ {}y^{\prime \prime }+10 y^{\prime }+24 y = 144 t^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.414 |
|
|
\[
{}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0 |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.729 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 4 t & 0 |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
5.199 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = \left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0 |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
8.507 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0 |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.619 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0 |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.387 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0 |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.86 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t^{2} & 0 |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.085 |
|
|
\[ {}y^{\prime \prime }+4 y = \delta \left (t -\pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.691 |
|
|
\[ {}y^{\prime \prime }+16 y = 4 \delta \left (t -3 \pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.795 |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.767 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (-1+t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.085 |
|
|
\[ {}4 y^{\prime \prime }+24 y^{\prime }+37 y = 17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.625 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 10 \sin \left (t \right )+10 \delta \left (-1+t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.142 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.918 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = \delta \left (t -\frac {\pi }{2}\right )+\operatorname {Heaviside}\left (t -\pi \right ) \cos \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.856 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = \operatorname {Heaviside}\left (-1+t \right )+\delta \left (t -2\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.821 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 25 t -100 \delta \left (t -\pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.044 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 5 \,{\mathrm e}^{3 t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.156 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = t \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.085 |
|
|
\[ {}y^{\prime \prime }-y = t^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.032 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-5 y = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.069 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-2 y = -6 \,{\mathrm e}^{\pi -t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.226 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-y = t \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.172 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+y = 3 \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.142 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.611 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+3 y = 2 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.135 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+2 y = t \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.145 |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = t \,{\mathrm e}^{2 t} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.486 |
|
|
\[
{}i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0 |
1 |
1 |
0 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
31.611 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.44 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = 6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.589 |
|
|
\[ {}y^{\prime \prime }+y = \sqrt {2}\, \sin \left (\sqrt {2}\, t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.984 |
|
|
\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.589 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.471 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.439 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3} {\mathrm e}^{2 t} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.516 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = t \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.543 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.547 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.441 |
|
|
\[ {}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.586 |
|
|
\[ {}y^{\prime \prime }-y = {\mathrm e}^{t} \cos \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.731 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = t +1 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.689 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.467 |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+20 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.286 |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.783 |
|
|
\[ {}y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.107 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = \operatorname {Heaviside}\left (-1+t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.99 |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.503 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.454 |
|
|
\[ {}y^{\prime \prime }+9 y = \cos \left (3 t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.723 |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.665 |
|
|
\[ {}y^{\prime \prime }+16 y = \left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.734 |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \frac {\pi }{2}\le t \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.712 |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (t \right )+t \sin \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.809 |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.537 |
|
|
\[ {}y^{\prime \prime }+16 y = \delta \left (t -2 \pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.519 |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -\frac {\pi }{2}\right )+\delta \left (t -\frac {3 \pi }{2}\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.66 |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.652 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = \delta \left (-1+t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.613 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 1+\delta \left (t -2\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.87 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -2 \pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.724 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = \delta \left (-1+t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.547 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = \delta \left (t -\pi \right )+\delta \left (t -3 \pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.013 |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.358 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.475 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = \delta \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.496 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.359 |
|
|
\[ {}x^{\prime \prime }-x^{\prime }-6 x = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.468 |
|
|
\[ {}x^{\prime \prime }-2 x^{\prime }+2 x = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.418 |
|
|
\[ {}x^{\prime \prime }-2 x^{\prime }+2 x = {\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.635 |
|
|
\[ {}x^{\prime \prime }-x^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.295 |
|
|
\[ {}x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x = 1-\operatorname {Heaviside}\left (t -5\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.307 |
|
|
\[ {}x^{\prime \prime }+9 x = \sin \left (3 t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.835 |
|
|
\[ {}x^{\prime \prime }-2 x = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.495 |
|
|
\[ {}x^{\prime \prime }+4 x = \cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right ) \] |
1 |
1 |
0 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.539 |
|
|
\[ {}x^{\prime \prime }+\pi ^{2} x = \pi ^{2} \operatorname {Heaviside}\left (1-t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.653 |
|
|
\[ {}x^{\prime \prime }-4 x = 1-\operatorname {Heaviside}\left (-1+t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.645 |
|
|
\[ {}x^{\prime \prime }+3 x^{\prime }+2 x = {\mathrm e}^{-4 t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.51 |
|
|
\[ {}x^{\prime \prime }-x = \delta \left (t -5\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.088 |
|
|
\[ {}x^{\prime \prime }+x = \delta \left (t -2\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.172 |
|
|
\[ {}x^{\prime \prime }+4 x = \delta \left (t -2\right )-\delta \left (t -5\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.515 |
|
|
\[ {}x^{\prime \prime }+x = 3 \delta \left (t -2 \pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.002 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \delta \left (-1+t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.922 |
|
|
\[ {}x^{\prime \prime }+4 x = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.441 |
|
|
\[ {}y^{\prime \prime }+9 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.398 |
|
|
\[ {}4 y^{\prime \prime }-4 y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.424 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.37 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.409 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.377 |
|
|
\[ {}4 y^{\prime \prime }-4 y^{\prime }+37 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.427 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.365 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.388 |
|
|
\[ {}4 y^{\prime \prime }-12 y^{\prime }+13 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.4 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.452 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.356 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.408 |
|
|
\[ {}y^{\prime \prime }-20 y^{\prime }+51 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.389 |
|
|
\[ {}2 y^{\prime \prime }+3 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.391 |
|
|
\[ {}3 y^{\prime \prime }+8 y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.401 |
|
|
\[ {}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.446 |
|
|
\[ {}4 y^{\prime \prime }+40 y^{\prime }+101 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.393 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+34 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.42 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = 9 t \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.537 |
|
|
\[ {}4 y^{\prime \prime }+16 y^{\prime }+17 y = 17 t -1 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.532 |
|
|
\[ {}4 y^{\prime \prime }+5 y^{\prime }+4 y = 3 \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.654 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t^{2} {\mathrm e}^{2 t} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.447 |
|
|
\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{-2 t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.475 |
|
|
\[ {}2 y^{\prime \prime }-3 y^{\prime }+17 y = 17 t -1 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.635 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.431 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 2+t \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.51 |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+20 y = \sin \left (2 t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.599 |
|
|
\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = t^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.453 |
|
|
\[ {}2 y^{\prime \prime }+y^{\prime }-y = 4 \sin \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.592 |
|
|
\[ {}3 y^{\prime \prime }+5 y^{\prime }-2 y = 7 \,{\mathrm e}^{-2 t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.447 |
|
|
\[ {}y^{\prime \prime }+9 y = 24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.84 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-1+t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.198 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.081 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-1+t \right )\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.909 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 39 \operatorname {Heaviside}\left (t \right )-507 \left (t -2\right ) \operatorname {Heaviside}\left (t -2\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.249 |
|
|
\[ {}y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (t -4\right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (t -4\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.873 |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+5 y = 25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.298 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-1+t \right )+\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -3\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.49 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.482 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.882 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.442 |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \pi \le t \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.574 |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\le t \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.757 |
|
|
\[ {}y^{\prime \prime }+4 \pi ^{2} y = 3 \delta \left (t -\frac {1}{3}\right )-\delta \left (-1+t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.138 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 3 \delta \left (-1+t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.684 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+29 y = 5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.166 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 1-\delta \left (-1+t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.707 |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}} \delta \left (-1+t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.546 |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \delta \left (-1+t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.575 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.265 |
|
|
\[ {}y^{\prime \prime }-9 y = 2 \sin \left (3 x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.509 |
|
|
\[ {}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.52 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{x}-3 x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.407 |
|
|
\[ {}y^{\prime \prime }-9 y = 2+x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.457 |
|
|
\[ {}y^{\prime \prime }+9 y = 2+x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.603 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+6 y = -2 \sin \left (3 x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.189 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = -x^{2}+1 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.54 |
|
|
\[ {}y^{\prime \prime }+9 y = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.447 |
|
|
\[ {}y^{\prime \prime }+9 y = 18 \,{\mathrm e}^{3 x} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.52 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.37 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.44 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.49 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.85 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (-1+x \right )^{2} & 1\le x \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.462 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.473 |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.03 |
|
|
\[ {}y^{\prime \prime }-4 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.082 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.207 |
|
|
\[ {}y^{\prime \prime }+9 y = \delta \left (x -\pi \right )+\delta \left (x -3 \pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.817 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \delta \left (-1+x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.796 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = \cos \left (x \right )+2 \delta \left (x -\pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.654 |
|
|
\[ {}y^{\prime \prime }+4 y = \cos \left (x \right ) \delta \left (x -\pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.614 |
|
|
\[ {}y^{\prime \prime }+a^{2} y = \delta \left (x -\pi \right ) f \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.027 |
|
|
\[ {}y^{\prime \prime }+4 y = 8 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.468 |
|
|
\[ {}y^{\prime \prime }-4 y = {\mathrm e}^{2 t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.497 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 2 \,{\mathrm e}^{t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.613 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 13 \operatorname {Heaviside}\left (t -4\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.898 |
|
|
\[ {}y^{\prime \prime }+4 y = \cos \left (2 t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.609 |
|
|
\[ {}y^{\prime \prime }+3 y = \operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.593 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+9 y = 20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.691 |
|
|
\[ {}y^{\prime \prime }+3 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right . \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.58 |
|
|
\[ {}y^{\prime \prime }+3 y = 5 \delta \left (t -2\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.171 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -3\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.632 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = -2 \delta \left (t -2\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.563 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = \delta \left (-1+t \right )-3 \delta \left (t -4\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
5.292 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \sin \left (4 t \right ) {\mathrm e}^{-2 t} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.986 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+5 y = \operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.886 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.871 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+3 y = \left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.797 |
|
|
\[ {}y^{\prime \prime }+16 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.408 |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (2 t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.676 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.38 |
|
|
\[ {}y^{\prime \prime }+16 y = t \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.548 |
|
|
\[ {}y^{\prime \prime }-4 y = t^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.528 |
|
|
\[ {}y^{\prime \prime }+4 y = 20 \,{\mathrm e}^{4 t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.656 |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (2 t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.783 |
|
|
\[ {}y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t -2\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.299 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{4 t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.568 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = t^{2} {\mathrm e}^{4 t} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.594 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 7 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.512 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.938 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.158 |
|
|
\[ {}y^{\prime \prime }-9 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.419 |
|
|
\[ {}y^{\prime \prime }+9 y = 27 t^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.719 |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+7 y = 165 \,{\mathrm e}^{4 t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.57 |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+17 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.472 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t} t^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.522 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.504 |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+17 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.457 |
|
|
\[ {}y^{\prime \prime } = {\mathrm e}^{t} \sin \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.699 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+40 y = 122 \,{\mathrm e}^{-3 t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.789 |
|
|
\[ {}y^{\prime \prime }-9 y = 24 \,{\mathrm e}^{-3 t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.559 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.546 |
|
|
\[ {}y^{\prime \prime }+4 y = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.49 |
|
|
\[ {}y^{\prime \prime }+4 y = t \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.644 |
|
|
\[ {}y^{\prime \prime }+4 y = {\mathrm e}^{3 t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.594 |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (2 t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.449 |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.926 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.493 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = t \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.581 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.477 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{-3 t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.564 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.558 |
|
|
\[ {}y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.45 |
|
|
\[ {}y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.489 |
|
|
\[ {}y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -10\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.137 |
|
|
\[
{}y^{\prime \prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1 |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.521 |
|
|
\[
{}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1 |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.169 |
|
|
\[ {}y^{\prime \prime } = \delta \left (t -3\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.433 |
|
|
\[ {}y^{\prime \prime } = \delta \left (-1+t \right )-\delta \left (t -4\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.514 |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t \right )+\delta \left (t -\pi \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.799 |
|
|
\[ {}y^{\prime \prime }+y = -2 \delta \left (t -\frac {\pi }{2}\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.83 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = \delta \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.398 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = \delta \left (-1+t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.04 |
|
|
\[ {}y^{\prime \prime }+16 y = \delta \left (t -2\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.061 |
|
|
\[ {}y^{\prime \prime }-16 y = \delta \left (t -10\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.053 |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
0.733 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
0.936 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t -3\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.296 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \delta \left (t -4\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.979 |
|
|
\[ {}y^{\prime \prime }-12 y^{\prime }+45 y = \delta \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
0.967 |
|
|
\[ {}x^{\prime \prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.21 |
|
|
\[ {}x^{\prime \prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.259 |
|
|
\[ {}x^{\prime \prime } = \cos \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.361 |
|
|
\[ {}x^{\prime \prime }+x^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.23 |
|
|
\[ {}x^{\prime \prime }+x^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.222 |
|
|
\[ {}x^{\prime \prime }-x^{\prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.283 |
|
|
\[ {}x^{\prime \prime }+x = t \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.284 |
|
|
\[ {}x^{\prime \prime }+6 x^{\prime } = 12 t +2 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.303 |
|
|
\[ {}x^{\prime \prime }-2 x^{\prime }+2 x = 2 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.335 |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 4 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.359 |
|
|
\[ {}2 x^{\prime \prime }-2 x^{\prime } = \left (t +1\right ) {\mathrm e}^{t} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.398 |
|
|
\[ {}x^{\prime \prime }+x = 2 \cos \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.482 |
|
|
|
||||||||
|
|
||||||||
|
|