|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.469 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.935 |
|
|
\[
{}y^{\prime \prime }-y = \frac {1}{\sqrt {1-{\mathrm e}^{2 x}}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.694 |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{-2 x} \sin \left ({\mathrm e}^{-x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.933 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 15 \,{\mathrm e}^{-x} \sqrt {x +1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.204 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.495 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{2 x}}{\left (1+{\mathrm e}^{x}\right )^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.932 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \frac {1}{1+{\mathrm e}^{x}}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.613 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.874 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = \frac {5 \ln \left (x \right )}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
17.988 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 9 x^{2} \ln \left (x \right )
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.275 |
|
|
\[
{}\left (-2+x \right )^{2} y^{\prime \prime }-3 \left (-2+x \right ) y^{\prime }+4 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.536 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
1.314 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 60 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.364 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 9 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.274 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 2 t^{2}+1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.276 |
|
|
\[
{}y^{\prime \prime }+4 y = 8 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.343 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.293 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 8 \,{\mathrm e}^{-t} \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.465 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 8 \,{\mathrm e}^{t} \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.336 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 54 t \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.289 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 9 \,{\mathrm e}^{2 t} \operatorname {Heaviside}\left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.598 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.778 |
|
|
\[
{}y^{\prime \prime }+4 y = 8 \sin \left (2 t \right ) \operatorname {Heaviside}\left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.601 |
|
|
\[
{}y^{\prime \prime }+4 y = 8 \left (t^{2}+t -1\right ) \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.189 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{t} \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.553 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.503 |
|
|
\[
{}y^{\prime \prime }+4 y = 4 \operatorname {Heaviside}\left (t -\pi \right )+2 \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.803 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 10 \,{\mathrm e}^{-t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.379 |
|
|
\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 120 \,{\mathrm e}^{3 t} \operatorname {Heaviside}\left (t -1\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
7.901 |
|
|
\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = 40 t^{2} \operatorname {Heaviside}\left (t -2\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
7.991 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y = \left (2 t^{2}+t +1\right ) \delta \left (t -1\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
3.273 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 x-y=0 \\ x+y^{\prime }-2 y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.448 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+x-5 y^{\prime }-4 y=0 \\ -y^{\prime }-2 x+y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.333 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+3 y=0 \\ 3 x-y^{\prime }+y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.365 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y=0 \\ x^{\prime }+x-y^{\prime }=0 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.047 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }-3 x-4 y=0 \\ x+y^{\prime \prime }+y=0 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.049 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }-y_{2}=0 \\ 4 y_{1}+y_{2}^{\prime }-4 y_{2}-2 y_{3}=0 \\ -2 y_{1}+y_{2}+y_{3}^{\prime }+y_{3}=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.470 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }-2 y_{1}+3 y_{2}-3 y_{3}=0 \\ -4 y_{1}+y_{2}^{\prime }+5 y_{2}-3 y_{3}=0 \\ -4 y_{1}+4 y_{2}+y_{3}^{\prime }-2 y_{3}=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.473 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+x+2 y=8 \\ 2 x+y^{\prime }-2 y=2 \,{\mathrm e}^{-t}-8 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.529 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-3 y+t \,{\mathrm e}^{-t} \\ y^{\prime }=2 x-3 y+{\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.492 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x-2 y={\mathrm e}^{t} \\ -4 x+y^{\prime }-3 y=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.513 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-4 x+3 y=\sin \left (t \right ) \\ -2 x+y^{\prime }+y=-2 \cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.593 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-y=0 \\ -x+y^{\prime }={\mathrm e}^{t}+{\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.476 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 x+5 y=0 \\ -x+y^{\prime }-2 y=\sin \left (2 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.631 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-2 x+2 y^{\prime }=-4 \,{\mathrm e}^{2 t} \\ 2 x^{\prime }-3 x+3 y^{\prime }-y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.515 |
|
|
\[
{}\left [\begin {array}{c} 3 x^{\prime }+2 x+y^{\prime }-6 y=5 \,{\mathrm e}^{t} \\ 4 x^{\prime }+2 x+y^{\prime }-8 y=5 \,{\mathrm e}^{t}+2 t -3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.669 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-5 x+3 y=2 \,{\mathrm e}^{3 t} \\ -x+y^{\prime }-y=5 \,{\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.547 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-2 x+y=0 \\ x+y^{\prime }-2 y=-5 \,{\mathrm e}^{t} \sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.564 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+4 x+2 y=\frac {2}{{\mathrm e}^{t}-1} \\ 6 x-y^{\prime }+3 y=\frac {3}{{\mathrm e}^{t}-1} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.061 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+y=\sec \left (t \right ) \\ -2 x+y^{\prime }+y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.787 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x-2 y=16 t \,{\mathrm e}^{t} \\ 2 x-y^{\prime }-2 y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.285 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-2 x+y=5 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x+y^{\prime }-2 y=10 \,{\mathrm e}^{t} \sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.356 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-4 x+3 y=\sin \left (t \right ) \\ 2 x+y^{\prime }-y=2 \cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.280 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-2 x-y=2 \,{\mathrm e}^{t} \\ x-y^{\prime }+2 y=3 \,{\mathrm e}^{4 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.223 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y=40 \,{\mathrm e}^{3 t} \\ x^{\prime }+x-y^{\prime }=36 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.001 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-2 x-y=2 \,{\mathrm e}^{t} \\ y^{\prime }-2 y-4 z=4 \,{\mathrm e}^{2 t} \\ x-z^{\prime }-z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.235 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }+2 x-2 y^{\prime }=0 \\ 3 x^{\prime }+y^{\prime \prime }-8 y=240 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.001 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x-2 y=0 \\ x-y^{\prime }=15 \cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.326 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+y=2 \sin \left (t \right ) \left (1-\operatorname {Heaviside}\left (t -\pi \right )\right ) \\ 2 x-y^{\prime }-y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.491 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+x-5 y^{\prime }-4 y=28 \,{\mathrm e}^{t} \operatorname {Heaviside}\left (t -2\right ) \\ 3 x^{\prime }-2 x-4 y^{\prime }+y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.400 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=-4 x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.342 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2} \\ x_{2}^{\prime }=3 x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.375 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}+3 x_{2} \\ x_{2}^{\prime }=-3 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.435 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}+2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.457 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }=4 x_{1}-x_{2}+4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.509 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2}-x_{3} \\ x_{3}^{\prime }=-x_{1}+2 x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.686 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2}-x_{3} \\ x_{2}^{\prime }=3 x_{1}-4 x_{2}-3 x_{3} \\ x_{3}^{\prime }=2 x_{1}-4 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.490 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-2 x_{2}+2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.450 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{2}-2 x_{3} \\ x_{2}^{\prime }=4 x_{1}+x_{2} \\ x_{3}^{\prime }=2 x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.464 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+26 \sin \left (t \right ) \\ x_{2}^{\prime }=3 x_{1}+4 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.602 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+8 x_{2}+9 t \\ x_{2}^{\prime }=x_{1}+x_{2}+3 \,{\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.544 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+2 x_{2} \\ x_{2}^{\prime }=-3 x_{1}+4 x_{2}+\frac {{\mathrm e}^{3 t}}{1+{\mathrm e}^{2 t}} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.064 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}-2 x_{2}+\frac {2}{{\mathrm e}^{t}-1} \\ x_{2}^{\prime }=6 x_{1}+3 x_{2}-\frac {3}{{\mathrm e}^{t}-1} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.061 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }=-2 x_{1}+3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.638 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}+x_{2}+\frac {4}{\sin \left (2 t \right )} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.968 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+27 t \\ x_{2}^{\prime }=-x_{1}+4 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.401 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=4 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.472 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}-x_{2}+35 \,{\mathrm e}^{t} t^{{3}/{2}} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.507 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}-x_{3}+6 \,{\mathrm e}^{-t} \\ x_{3}^{\prime }=2 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.728 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-2 x_{2}-x_{3} \\ x_{2}^{\prime }=-x_{1}+x_{2}+x_{3}+12 t \\ x_{3}^{\prime }=x_{1}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.750 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+4 x_{2}-2 x_{3}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}+x_{2} \\ x_{3}^{\prime }=6 x_{1}-6 x_{2}+5 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
153.299 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}-x_{3}+4 \,{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}+x_{2} \\ x_{3}^{\prime }=3 x_{1}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.962 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+2 x_{3} \\ x_{2}^{\prime }=x_{1}+2 x_{3} \\ x_{3}^{\prime }=-2 x_{1}+x_{2}-x_{3}+4 \sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.290 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-x_{2}-x_{3}+{\mathrm e}^{3 t} \\ x_{2}^{\prime }=x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2}+2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.916 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}-x_{3}+2 \,{\mathrm e}^{2 t} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2}-3 x_{3} \\ x_{3}^{\prime }=-x_{1}+x_{2}+2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.564 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{3}+24 t \\ x_{2}^{\prime }=x_{1}-x_{2} \\ x_{3}^{\prime }=3 x_{1}-x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.558 |
|
|
\[
{}y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.466 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.597 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.463 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+y = 0
\] |
[_Gegenbauer] |
✓ |
0.584 |
|
|
\[
{}y^{\prime \prime }-2 x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.464 |
|
|
\[
{}y^{\prime \prime }-2 x^{2} y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.519 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+\left (4 x -1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.673 |
|
|
\[
{}y^{\prime \prime }+\left (\cos \left (x \right )+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.657 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } \sin \left (x \right )+y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.858 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.613 |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+k y = 0
\] |
[_Laguerre] |
✓ |
0.912 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-2 x^{2}+x \right ) y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.796 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.261 |
|