|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=4 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.565 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.487 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.484 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=\frac {9 x_{1}}{5}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.605 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.511 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2} \\ x_{2}^{\prime }=-5 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.494 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=3 x_{1}+2 x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.555 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{3} \\ x_{2}^{\prime }=x_{1}-x_{2} \\ x_{3}^{\prime }=-2 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.098 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.628 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }=-x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.617 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {3 x_{1}}{4}-2 x_{2} \\ x_{2}^{\prime }=x_{1}-\frac {5 x_{2}}{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.503 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {4 x_{1}}{5}+2 x_{2} \\ x_{2}^{\prime }=-x_{1}+\frac {6 x_{2}}{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.512 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{4}+x_{2} \\ x_{2}^{\prime }=-x_{1}-\frac {x_{2}}{4} \\ x_{3}^{\prime }=-\frac {x_{3}}{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.486 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{4}+x_{2} \\ x_{2}^{\prime }=-x_{1}-\frac {x_{2}}{4} \\ x_{3}^{\prime }=\frac {x_{3}}{10} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.504 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{2}-\frac {x_{2}}{8} \\ x_{2}^{\prime }=2 x_{1}-\frac {x_{2}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.499 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.408 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-2 x_{2} \\ x_{2}^{\prime }=8 x_{1}-4 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.353 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {3 x_{1}}{2}+x_{2} \\ x_{2}^{\prime }=-\frac {x_{1}}{4}-\frac {x_{2}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.401 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=-\frac {5 x_{1}}{2}+2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.398 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.480 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.348 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}-7 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.513 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {5 x_{1}}{2}+\frac {3 x_{2}}{2} \\ x_{2}^{\prime }=-\frac {3 x_{1}}{2}+\frac {x_{2}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.582 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+\frac {3 x_{2}}{2} \\ x_{2}^{\prime }=-\frac {3 x_{1}}{2}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.589 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+9 x_{2} \\ x_{2}^{\prime }=-x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.463 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=-4 x_{1}+x_{2} \\ x_{3}^{\prime }=3 x_{1}+6 x_{2}+2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.483 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {5 x_{1}}{2}+x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}-\frac {5 x_{2}}{2}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2}-\frac {5 x_{3}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.444 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2}+t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.517 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+\sqrt {3}\, x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=\sqrt {3}\, x_{1}-x_{2}+\sqrt {3}\, {\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.603 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2}-\cos \left (t \right ) \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.826 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+{\mathrm e}^{-2 t} \\ x_{2}^{\prime }=4 x_{1}-2 x_{2}-2 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.552 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-2 x_{2}+\frac {1}{t^{3}} \\ x_{2}^{\prime }=8 x_{1}-4 x_{2}-\frac {1}{t^{2}} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.457 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}+2 x_{2}+\frac {1}{t} \\ x_{2}^{\prime }=2 x_{1}-x_{2}+\frac {2}{t}+4 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.527 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+2 \,{\mathrm e}^{t} \\ x_{2}^{\prime }=4 x_{1}+x_{2}-{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.503 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2}-{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.500 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {5 x_{1}}{4}+\frac {3 x_{2}}{4}+2 t \\ x_{2}^{\prime }=\frac {3 x_{1}}{4}-\frac {5 x_{2}}{4}+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.515 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+\sqrt {2}\, x_{2}+{\mathrm e}^{-t} \\ x_{2}^{\prime }=\sqrt {2}\, x_{1}-2 x_{2}-{\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.584 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.898 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2}+\csc \left (t \right ) \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\sec \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.133 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{2}-\frac {x_{2}}{8}+\frac {{\mathrm e}^{-\frac {t}{2}}}{2} \\ x_{2}^{\prime }=2 x_{1}-\frac {x_{2}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.615 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2}+2 \,{\mathrm e}^{-t} \\ x_{2}^{\prime }=x_{1}-2 x_{2}+3 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.539 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.439 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.449 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.415 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}-7 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.398 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.489 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.461 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=4 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.506 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2} \\ x_{2}^{\prime }=-\frac {5 x_{2}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.407 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.392 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2} \\ x_{2}^{\prime }=-5 x_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.719 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1} \\ x_{2}^{\prime }=-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.315 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=\frac {9 x_{1}}{5}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.614 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}-2 \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.766 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2}-2 \\ x_{2}^{\prime }=x_{1}-2 x_{2}+1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.602 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2}-1 \\ x_{2}^{\prime }=2 x_{1}-x_{2}+5 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.894 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.488 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.481 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.493 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.490 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.490 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y = t
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.168 |
|
|
\[
{}t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.070 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.074 |
|
|
\[
{}x y^{\prime \prime \prime }-y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.161 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.130 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-3 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.123 |
|
|
\[
{}t y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }+t y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.059 |
|
|
\[
{}\left (2-t \right ) y^{\prime \prime \prime }+\left (2 t -3\right ) y^{\prime \prime }-t y^{\prime }+y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.059 |
|
|
\[
{}t^{2} \left (t +3\right ) y^{\prime \prime \prime }-3 t \left (t +2\right ) y^{\prime \prime }+6 \left (1+t \right ) y^{\prime }-6 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.066 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.095 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+4 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\left (6\right )}+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.115 |
|
|
\[
{}y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}y^{\left (6\right )}-y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.081 |
|
|
\[
{}y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.082 |
|
|
\[
{}y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.108 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.093 |
|
|
\[
{}y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+6 y^{\prime \prime }+30 y^{\prime }-36 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.254 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.251 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.315 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.461 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.319 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.305 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.507 |
|
|
\[
{}y^{\prime \prime }+\omega ^{2} y = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.289 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.321 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.332 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.587 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t <\infty \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.724 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <3 \pi \\ 0 & 3 \pi \le t <\infty \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.439 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & \pi \le t <2 \pi \\ 0 & \operatorname {otherwise} \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.386 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.524 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & \operatorname {otherwise} \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.727 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.526 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \operatorname {otherwise} \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.640 |
|