Number of problems in this table is 77
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) |
|
\[ {}y^{\prime }-2 y = 6 \,{\mathrm e}^{5 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.441 |
|
|
\[ {}y^{\prime }+y = 8 \,{\mathrm e}^{3 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.39 |
|
|
\[ {}y^{\prime }+3 y = 2 \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.418 |
|
|
\[ {}y^{\prime }+2 y = 4 t \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.377 |
|
|
\[ {}y^{\prime }-y = 6 \cos \left (t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.501 |
|
|
\[ {}y^{\prime }-y = 5 \sin \left (2 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.529 |
|
|
\[ {}y^{\prime }+y = 5 \,{\mathrm e}^{t} \sin \left (t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.586 |
|
|
\[ {}y^{\prime }+2 y = 2 \operatorname {Heaviside}\left (-1+t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.896 |
|
|
\[ {}y^{\prime }-2 y = \operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{t -2} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.053 |
|
|
\[ {}y^{\prime }-y = 4 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \sin \left (t +\frac {\pi }{4}\right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.749 |
|
|
\[ {}y^{\prime }+2 y = \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.399 |
|
|
\[ {}y^{\prime }+3 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.232 |
|
|
\[ {}y^{\prime }-3 y = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 1 & \frac {\pi }{2}\le t \end {array}\right . \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.909 |
|
|
\[ {}y^{\prime }-3 y = -10 \,{\mathrm e}^{-t +a} \sin \left (-2 t +2 a \right ) \operatorname {Heaviside}\left (t -a \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
13.737 |
|
|
\[ {}y^{\prime }-y = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.273 |
|
|
\[ {}y^{\prime }+y = \delta \left (t -5\right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.756 |
|
|
\[ {}y^{\prime }-2 y = \delta \left (t -2\right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.748 |
|
|
\[ {}y^{\prime }+4 y = 3 \delta \left (-1+t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.836 |
|
|
\[ {}y^{\prime }-5 y = 2 \,{\mathrm e}^{-t}+\delta \left (t -3\right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.939 |
|
|
\[ {}y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[_quadrature] |
✓ |
✓ |
0.33 |
|
|
\[ {}y^{\prime }+2 y = 2 \] |
1 |
1 |
1 |
[_quadrature] |
✓ |
✓ |
0.278 |
|
|
\[ {}y^{\prime }+2 y = {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.431 |
|
|
\[ {}y^{\prime }+\frac {26 y}{5} = \frac {97 \sin \left (2 t \right )}{5} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.677 |
|
|
\[ {}y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[_quadrature] |
✓ |
✓ |
0.308 |
|
|
\[ {}y^{\prime }-6 y = 0 \] |
1 |
1 |
1 |
[_quadrature] |
✓ |
✓ |
0.323 |
|
|
\[ {}L i^{\prime }+R i = E_{0} \operatorname {Heaviside}\left (t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
3.074 |
|
|
\[ {}L i^{\prime }+R i = E_{0} \delta \left (t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
3.217 |
|
|
\[ {}L i^{\prime }+R i = E_{0} \sin \left (\omega t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.338 |
|
|
\[ {}y^{\prime }-y = 1 \] |
1 |
1 |
1 |
[_quadrature] |
✓ |
✓ |
0.418 |
|
|
\[ {}2 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[_quadrature] |
✓ |
✓ |
0.335 |
|
|
\[ {}y^{\prime }+6 y = {\mathrm e}^{4 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.526 |
|
|
\[ {}y^{\prime }-y = 2 \cos \left (5 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.654 |
|
|
\[ {}y^{\prime }+y = {\mathrm e}^{-3 t} \cos \left (2 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.837 |
|
|
\[ {}y^{\prime }+4 y = {\mathrm e}^{-4 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.501 |
|
|
\[ {}y^{\prime }-y = 1+t \,{\mathrm e}^{t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.519 |
|
|
\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.691 |
|
|
\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.87 |
|
|
\[ {}y^{\prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.791 |
|
|
\[ {}y^{\prime }+y = t \sin \left (t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.716 |
|
|
\[ {}y^{\prime }-y = t \,{\mathrm e}^{t} \sin \left (t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.717 |
|
|
\[ {}y^{\prime }-3 y = \delta \left (t -2\right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.638 |
|
|
\[ {}y^{\prime }+y = \delta \left (-1+t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.637 |
|
|
\[ {}x^{\prime }+5 x = \operatorname {Heaviside}\left (t -2\right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.759 |
|
|
\[ {}x^{\prime }+x = \sin \left (2 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.836 |
|
|
\[ {}x^{\prime } = 2 x+\operatorname {Heaviside}\left (-1+t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.455 |
|
|
\[ {}x^{\prime } = x-2 \operatorname {Heaviside}\left (-1+t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.955 |
|
|
\[ {}x^{\prime } = -x+\operatorname {Heaviside}\left (-1+t \right )-\operatorname {Heaviside}\left (t -2\right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.234 |
|
|
\[ {}x^{\prime }+3 x = \delta \left (-1+t \right )+\operatorname {Heaviside}\left (t -4\right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.467 |
|
|
\[ {}2 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.454 |
|
|
\[ {}y^{\prime }-y = {\mathrm e}^{2 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.408 |
|
|
\[ {}y^{\prime }+y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.832 |
|
|
\[ {}y^{\prime }-2 y = 4 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right )\right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.905 |
|
|
\[ {}10 Q^{\prime }+100 Q = \operatorname {Heaviside}\left (-1+t \right )-\operatorname {Heaviside}\left (t -2\right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.082 |
|
|
\[ {}y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[_quadrature] |
✓ |
✓ |
0.23 |
|
|
\[ {}y^{\prime }+2 y = 4 \] |
1 |
1 |
1 |
[_quadrature] |
✓ |
✓ |
0.267 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x} \] |
1 |
1 |
1 |
[_quadrature] |
✓ |
✓ |
0.257 |
|
|
\[ {}y^{\prime }-y = 2 \,{\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.475 |
|
|
\[ {}y^{\prime }-2 y = 6 \] |
1 |
1 |
1 |
[_quadrature] |
✓ |
✓ |
0.413 |
|
|
\[ {}y^{\prime }+y = {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.473 |
|
|
\[ {}y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.227 |
|
|
\[ {}y^{\prime }+3 y = \delta \left (-2+x \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.819 |
|
|
\[ {}y^{\prime }-3 y = \delta \left (-1+x \right )+2 \operatorname {Heaviside}\left (-2+x \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.398 |
|
|
\[ {}y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[_quadrature] |
✓ |
✓ |
0.461 |
|
|
\[ {}y^{\prime }-2 y = t^{3} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.671 |
|
|
\[ {}y^{\prime }+3 y = \operatorname {Heaviside}\left (t -4\right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.297 |
|
|
\[ {}y^{\prime } = \operatorname {Heaviside}\left (t -3\right ) \] |
1 |
1 |
1 |
[_quadrature] |
✓ |
✓ |
0.345 |
|
|
\[ {}y^{\prime } = \operatorname {Heaviside}\left (t -3\right ) \] |
1 |
1 |
1 |
[_quadrature] |
✓ |
✓ |
0.336 |
|
|
\[
{}y^{\prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1 |
1 |
1 |
1 |
[_quadrature] |
✓ |
✓ |
0.509 |
|
|
\[ {}y^{\prime } = 3 \delta \left (t -2\right ) \] |
1 |
1 |
1 |
[_quadrature] |
✓ |
✓ |
0.337 |
|
|
\[ {}y^{\prime } = \delta \left (t -2\right )-\delta \left (t -4\right ) \] |
1 |
1 |
1 |
[_quadrature] |
✓ |
✓ |
0.356 |
|
|
\[ {}y^{\prime }+2 y = 4 \delta \left (-1+t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.068 |
|
|
\[ {}y^{\prime }+3 y = \delta \left (t -2\right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.099 |
|
|
\[ {}x^{\prime }+3 x = {\mathrm e}^{-2 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.407 |
|
|
\[ {}x^{\prime }-3 x = 3 t^{3}+3 t^{2}+2 t +1 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.382 |
|
|
\[ {}x^{\prime }-x = \cos \left (t \right )-\sin \left (t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.471 |
|
|
\[ {}2 x^{\prime }+6 x = t \,{\mathrm e}^{-3 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.428 |
|
|
\[ {}x^{\prime }+x = 2 \sin \left (t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.45 |
|
|
|
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