| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime } t&=y+\sqrt {t^{2}+y^{2}} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.758 |
|
| \begin{align*}
2 t y y^{\prime }&=3 y^{2}-t^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
133.092 |
|
| \begin{align*}
\left (t -\sqrt {t y}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.656 |
|
| \begin{align*}
y^{\prime }&=\frac {y+t}{t -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.661 |
|
| \begin{align*}
{\mathrm e}^{\frac {t}{y}} \left (-t +y\right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.460 |
|
| \begin{align*}
y^{\prime }&=\frac {t +y+1}{t -y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.881 |
|
| \begin{align*}
1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.217 |
|
| \begin{align*}
t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.276 |
|
| \begin{align*}
2 t \sin \left (y\right )+{\mathrm e}^{t} y^{3}+\left (\cos \left (y\right ) t^{2}+3 \,{\mathrm e}^{t} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.670 |
|
| \begin{align*}
1+{\mathrm e}^{t y} \left (t y+1\right )+\left (1+{\mathrm e}^{t y} t^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
2.271 |
|
| \begin{align*}
\sec \left (t \right ) \tan \left (t \right )+\sec \left (t \right )^{2} y+\left (\tan \left (t \right )+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
8.715 |
|
| \begin{align*}
\frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.543 |
|
| \begin{align*}
2 t y^{3}+3 t^{2} y^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.116 |
|
| \begin{align*}
2 t \cos \left (y\right )+3 t^{2} y+\left (2 y+2 t^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
✗ |
62.806 |
|
| \begin{align*}
3 t^{2}+4 t y+\left (2 y+2 t^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
1.516 |
|
| \begin{align*}
2 t -2 \,{\mathrm e}^{t y} \sin \left (2 t \right )+{\mathrm e}^{t y} \cos \left (2 t \right ) y+\left (-3+{\mathrm e}^{t y} t \cos \left (2 t \right )\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
4.029 |
|
| \begin{align*}
3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
7.533 |
|
| \begin{align*}
y^{\prime }&=2 t \left (1+y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.678 |
|
| \begin{align*}
y^{\prime }&=t^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✗ |
✓ |
✓ |
✗ |
7.855 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{t}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
8.205 |
|
| \begin{align*}
y^{\prime }&=y^{2}+\cos \left (t \right )^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
133.378 |
|
| \begin{align*}
y^{\prime }&=1+y+y^{2} \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✓ |
✗ |
✗ |
10.286 |
|
| \begin{align*}
y^{\prime }&=t +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
5.366 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
✗ |
70.018 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
✗ |
80.147 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
✗ |
67.868 |
|
| \begin{align*}
y^{\prime }&=y+{\mathrm e}^{-y}+{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
0.835 |
|
| \begin{align*}
y^{\prime }&=y^{3}+{\mathrm e}^{-5 t} \\
y \left (0\right ) &= {\frac {2}{5}} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
✗ |
0.868 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\left (-t +y\right )^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.204 |
|
| \begin{align*}
y^{\prime }&=\left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
1.020 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-t}+\ln \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
1.059 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \\
y \left (0\right ) &= 100 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.372 |
|
| \begin{align*}
y^{\prime }&=t^{2}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
11.307 |
|
| \begin{align*}
y^{\prime }&=t \left (1+y\right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.677 |
|
| \begin{align*}
y^{\prime }&=t y^{a} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
63.347 |
|
| \begin{align*}
y^{\prime }&=t \sqrt {1-y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.954 |
|
| \begin{align*}
y^{\prime }&=y+{\mathrm e}^{-y}+2 t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
5.077 |
|
| \begin{align*}
y^{\prime }&=1-t +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
3.208 |
|
| \begin{align*}
y^{\prime }&=\frac {t^{2}+y^{2}}{1+t +y^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
✗ |
1.670 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{t} y^{2}-2 y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.651 |
|
| \begin{align*}
y^{\prime }&=t y^{3}-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.109 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }+3 y^{\prime } t -y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.823 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } t +y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.835 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.587 |
|
| \begin{align*}
6 y^{\prime \prime }-7 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.694 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.782 |
|
| \begin{align*}
3 y^{\prime \prime }+6 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.957 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.583 |
|
| \begin{align*}
2 y^{\prime \prime }+y^{\prime }-10 y&=0 \\
y \left (1\right ) &= 5 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.629 |
|
| \begin{align*}
5 y^{\prime \prime }+5 y^{\prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.682 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+y&=0 \\
y \left (2\right ) &= 1 \\
y^{\prime }\left (2\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.343 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= v \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.504 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+5 y^{\prime } t -2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
9.439 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
11.148 |
|
| \begin{align*}
2 y^{\prime \prime }+3 y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
9.881 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+3 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
10.053 |
|
| \begin{align*}
4 y^{\prime \prime }-y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
10.808 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.968 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.384 |
|
| \begin{align*}
2 y^{\prime \prime }-y^{\prime }+3 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.631 |
|
| \begin{align*}
3 y^{\prime \prime }-2 y^{\prime }+4 y&=0 \\
y \left (2\right ) &= 1 \\
y^{\prime }\left (2\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
6.393 |
|
| \begin{align*}
y^{\prime \prime }+w^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.467 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.151 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+2 y^{\prime } t +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.360 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.328 |
|
| \begin{align*}
4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.763 |
|
| \begin{align*}
9 y^{\prime \prime }+6 y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.938 |
|
| \begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.806 |
|
| \begin{align*}
6 y^{\prime \prime }+2 y^{\prime }+y&=0 \\
y \left (2\right ) &= 1 \\
y^{\prime }\left (2\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
9.751 |
|
| \begin{align*}
9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\
y \left (\pi \right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.280 |
|
| \begin{align*}
y^{\prime \prime }-\frac {2 \left (1+t \right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.117 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime } t +\left (4 t^{2}-2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.112 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.112 |
|
| \begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.099 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +6 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.123 |
|
| \begin{align*}
\left (2 t +1\right ) y^{\prime \prime }-4 \left (1+t \right ) y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.109 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \begin{align*}
t y^{\prime \prime }-\left (1+3 t \right ) y^{\prime }+3 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.109 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.442 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-y^{\prime } t +y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.119 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 t} t \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
18.870 |
|
| \begin{align*}
2 y^{\prime \prime }-3 y^{\prime }+y&=\left (t^{2}+1\right ) {\mathrm e}^{t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
69.980 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=t \,{\mathrm e}^{3 t}+1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
69.242 |
|
| \begin{align*}
3 y^{\prime \prime }+4 y^{\prime }+y&=\sin \left (t \right ) {\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.525 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=t^{{5}/{2}} {\mathrm e}^{-2 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
145.310 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\sqrt {1+t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.689 |
|
| \begin{align*}
y^{\prime \prime }-y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
7.839 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-2 y&=t^{2} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.924 |
|
| \begin{align*}
y^{\prime \prime }+p \left (t \right ) y^{\prime }+q \left (t \right ) y&=1+t \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
1.151 |
|
| \begin{align*}
y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1}&=t^{2}+1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
7.401 |
|
| \begin{align*}
y^{\prime \prime }+3 y&=t^{3}-1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
47.620 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=t \,{\mathrm e}^{\alpha t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
25.727 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{t} t^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
60.088 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=t^{2}+t +1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
86.059 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
24.323 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+4 y&=t^{2} {\mathrm e}^{7 t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
80.162 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=t \sin \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
71.013 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=\left (3 t^{7}-5 t^{4}\right ) {\mathrm e}^{3 t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
83.047 |
|