| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x_{1}^{\prime }&=-4 x_{1} \\
x_{2}^{\prime }&=2 x_{1}+5 x_{2}-9 x_{3} \\
x_{3}^{\prime }&=5 x_{2}-x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-2 x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}-4 x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{1}+2 x_{2}-3 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2}+3 x_{3} \\
x_{2}^{\prime }&=-9 x_{1}-3 x_{2}-9 x_{3} \\
x_{3}^{\prime }&=4 x_{1}+4 x_{2}+3 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
x_{1}^{\prime }&=-17 x_{1}-42 x_{3} \\
x_{2}^{\prime }&=-7 x_{1}+4 x_{2}-14 x_{3} \\
x_{3}^{\prime }&=7 x_{1}+18 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.656 |
|
| \begin{align*}
x_{1}^{\prime }&=-16 x_{1}+30 x_{2}-18 x_{3} \\
x_{2}^{\prime }&=-8 x_{1}+8 x_{2}+16 x_{3} \\
x_{3}^{\prime }&=8 x_{1}-15 x_{2}+9 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.641 |
|
| \begin{align*}
x_{1}^{\prime }&=-7 x_{1}-6 x_{2}-7 x_{3} \\
x_{2}^{\prime }&=-3 x_{1}-3 x_{2}-3 x_{3} \\
x_{3}^{\prime }&=7 x_{1}+6 x_{2}+7 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2}-2 x_{3} \\
x_{2}^{\prime }&=x_{1}+6 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+6 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}-4 x_{2}-2 x_{3} \\
x_{2}^{\prime }&=-4 x_{1}-5 x_{2}-6 x_{3} \\
x_{3}^{\prime }&=4 x_{1}+8 x_{2}+7 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| \begin{align*}
x_{1}^{\prime }&=7 x_{1}-2 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=4 x_{2}-x_{3} \\
x_{3}^{\prime }&=-x_{1}+x_{2}+4 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.621 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}-x_{2}-2 x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{3} \\
x_{3}^{\prime }&=x_{1} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}-x_{3} \\
x_{2}^{\prime }&=-x_{2} \\
x_{3}^{\prime }&=x_{1} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+13 x_{2} \\
x_{2}^{\prime }&=-x_{1}-2 x_{2} \\
x_{3}^{\prime }&=2 x_{3}+4 x_{4} \\
x_{4}^{\prime }&=2 x_{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| \begin{align*}
x_{1}^{\prime }&=7 x_{1}-x_{4} \\
x_{2}^{\prime }&=6 x_{2} \\
x_{3}^{\prime }&=-x_{3} \\
x_{4}^{\prime }&=2 x_{1}+5 x_{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.228 |
|
| \begin{align*}
x_{1}^{\prime }&=-6 x_{1}+x_{2}+1 \\
x_{2}^{\prime }&=6 x_{1}-5 x_{2}+{\mathrm e}^{-t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.752 |
|
| \begin{align*}
x_{1}^{\prime }&=9 x_{1}-2 x_{2}+9 t \\
x_{2}^{\prime }&=5 x_{1}-2 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.894 |
|
| \begin{align*}
x_{1}^{\prime }&=10 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=4 x_{1}+2 x_{2}+\frac {{\mathrm e}^{6 t}}{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2}+3 x_{3}+{\mathrm e}^{6 t} \\
x_{2}^{\prime }&=-9 x_{1}-3 x_{2}-9 x_{3}+1 \\
x_{3}^{\prime }&=4 x_{1}+4 x_{2}+3 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.375 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-2 x_{2}+x_{3}+t \\
x_{2}^{\prime }&=x_{1}-4 x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{1}+2 x_{2}-3 x_{3}+1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.302 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=8 x_{1}+x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| \begin{align*}
x_{1}^{\prime }&=-6 x_{2} \\
x_{2}^{\prime }&=x_{1}-5 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}+9 x_{2} \\
x_{2}^{\prime }&=-2 x_{1}-x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \begin{align*}
x_{1}^{\prime }&=-4 x_{1} \\
x_{2}^{\prime }&=-4 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.271 |
|
| \begin{align*}
x_{1}^{\prime }&=7 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=x_{1}+4 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-7 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}-x_{2} \\
x_{2}^{\prime }&=x_{1}-4 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
x_{1}^{\prime }&=10 x_{1}-8 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
-2 y+y^{\prime }&=6 \,{\mathrm e}^{5 t} \\
y \left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \begin{align*}
y+y^{\prime }&=8 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.221 |
|
| \begin{align*}
3 y+y^{\prime }&=2 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.289 |
|
| \begin{align*}
y^{\prime }+2 y&=4 t \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
-y+y^{\prime }&=6 \cos \left (t \right ) \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.356 |
|
| \begin{align*}
-y+y^{\prime }&=5 \sin \left (2 t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
y+y^{\prime }&=5 \,{\mathrm e}^{t} \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.184 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=0 \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.191 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=4 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.217 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-12 y&=36 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 12 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.194 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=10 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.227 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=4 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.211 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=30 \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.217 |
|
| \begin{align*}
y^{\prime \prime }-y&=12 \,{\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.227 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=10 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.244 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=12-6 \,{\mathrm e}^{t} \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.241 |
|
| \begin{align*}
y^{\prime \prime }-y&=6 \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.252 |
|
| \begin{align*}
y^{\prime \prime }-9 y&=13 \sin \left (2 t \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.250 |
|
| \begin{align*}
y^{\prime \prime }-y&=8 \sin \left (t \right )-6 \cos \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.253 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=10 \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.263 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+4 y&=20 \sin \left (2 t \right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.259 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+4 y&=20 \sin \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.252 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=3 \cos \left (t \right )+\sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.269 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=9 \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.258 |
|
| \begin{align*}
y^{\prime \prime }+y&=6 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.247 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=7 \sin \left (4 t \right )+14 \cos \left (4 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= A \\
y^{\prime }\left (0\right ) &= B \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \begin{align*}
y^{\prime }+2 y&=2 \operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.882 |
|
| \begin{align*}
-2 y+y^{\prime }&=\operatorname {Heaviside}\left (-2+t \right ) {\mathrm e}^{-2+t} \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.991 |
|
| \begin{align*}
-y+y^{\prime }&=4 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \sin \left (t +\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.322 |
|
| \begin{align*}
y^{\prime }+2 y&=\operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \\
y \left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| \begin{align*}
3 y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
1.540 |
|
| \begin{align*}
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 . \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
1.689 |
|
| \begin{align*}
y^{\prime }-3 y&=-10 \,{\mathrm e}^{-t +a} \sin \left (-2 t +2 a \right ) \operatorname {Heaviside}\left (t -a \right ) \\
y \left (0\right ) &= 5 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.599 |
|
| \begin{align*}
y^{\prime \prime }-y&=\operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=1-3 \operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.864 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.168 |
|
| \begin{align*}
y^{\prime \prime }+y&=t -\operatorname {Heaviside}\left (t -1\right ) \left (t -1\right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=-10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.563 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=30 \operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{1-t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.395 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=5 \operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.832 |
|
| \begin{align*}
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 ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.234 |
|
| \begin{align*}
-y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
1.118 |
|
| \begin{align*}
-y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
1.959 |
|
| \begin{align*}
y+y^{\prime }&=\delta \left (t -5\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| \begin{align*}
-2 y+y^{\prime }&=\delta \left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| \begin{align*}
y^{\prime }+4 y&=3 \delta \left (t -1\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| \begin{align*}
y^{\prime }-5 y&=2 \,{\mathrm e}^{-t}+\delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.929 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.596 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=\delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=\delta \left (t -\frac {\pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.132 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=\delta \left (t -\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.528 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=\delta \left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.790 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&=\delta \left (t -\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.190 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.948 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.297 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.913 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_erf] |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.384 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.307 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.399 |
|
| \begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \begin{align*}
y^{\prime \prime }+2 x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
\left (x^{2}-3\right ) y^{\prime \prime }-3 y^{\prime } x -5 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.463 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 y^{\prime } x -16 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.485 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
y^{\prime \prime }-{\mathrm e}^{x} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.509 |
|
| \begin{align*}
y^{\prime \prime } x -\left (x -1\right ) y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.661 |
|