| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
{\mathrm e}^{x} \left (y-3 \left (1+{\mathrm e}^{x}\right )^{2}\right )+\left (1+{\mathrm e}^{x}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.740 |
|
| \begin{align*}
2 x \left (y+1\right )-\left (x^{2}+1\right ) y^{\prime }&=0 \\
y \left (1\right ) &= -5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.355 |
|
| \begin{align*}
r^{\prime }+r \tan \left (t \right )&=\cos \left (t \right )^{2} \\
r \left (\frac {\pi }{4}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.994 |
|
| \begin{align*}
x^{\prime }-x&=\sin \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.050 |
|
| \begin{align*}
y^{\prime }+\frac {y}{2 x}&=\frac {x}{y^{3}} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.752 |
|
| \begin{align*}
x y^{\prime }+y&=\left (y x \right )^{{3}/{2}} \\
y \left (1\right ) &= 4 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
22.630 |
|
| \begin{align*}
y^{\prime }+y&=\left \{\begin {array}{cc} 2 & 0\le x <1 \\ 0 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
3.534 |
|
| \begin{align*}
y^{\prime }+y&=\left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right . \\
y \left (0\right ) &= 6 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
6.660 |
|
| \begin{align*}
y^{\prime }+y&=\left \{\begin {array}{cc} {\mathrm e}^{-x} & 0\le x <2 \\ {\mathrm e}^{-2} & 2\le x \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
3.909 |
|
| \begin{align*}
\left (x +2\right ) y^{\prime }+y&=\left \{\begin {array}{cc} 2 x & 0\le x <2 \\ 4 & 2\le x \end {array}\right . \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.254 |
|
| \begin{align*}
a y^{\prime }+b y&=k \,{\mathrm e}^{-\lambda x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.646 |
|
| \begin{align*}
y^{\prime }+y&=2 \sin \left (x \right )+5 \sin \left (2 x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.639 |
|
| \begin{align*}
\cos \left (y\right ) y^{\prime }+\frac {\sin \left (y\right )}{x}&=1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
5.192 |
|
| \begin{align*}
\left (y+1\right ) y^{\prime }+x \left (y^{2}+2 y\right )&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.825 |
|
| \begin{align*}
y^{\prime }&=\left (1-x \right ) y^{2}+\left (2 x -1\right ) y-x \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✓ |
8.241 |
|
| \begin{align*}
y^{\prime }&=-y^{2}+y x +1 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
4.886 |
|
| \begin{align*}
y^{\prime }&=-8 x y^{2}+4 x \left (1+4 x \right ) y-8 x^{3}-4 x^{2}+1 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
12.453 |
|
| \begin{align*}
6 x^{2} y-\left (x^{3}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.363 |
|
| \begin{align*}
\left (3 x^{2} y^{2}-x \right ) y^{\prime }+2 x y^{3}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
11.136 |
|
| \begin{align*}
y-1+x \left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.804 |
|
| \begin{align*}
x^{2}-2 y+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.492 |
|
| \begin{align*}
3 x -5 y+\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
113.406 |
|
| \begin{align*}
y^{2} {\mathrm e}^{2 x}+\left (y \,{\mathrm e}^{2 x}-2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.607 |
|
| \begin{align*}
8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.787 |
|
| \begin{align*}
2 x^{2}+y x +y^{2}+2 x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
66.481 |
|
| \begin{align*}
y^{\prime }&=\frac {4 x^{3} y^{2}-3 x^{2} y}{x^{3}-2 x^{4} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
24.229 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+y x&={\mathrm e}^{-x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.536 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -7 y}{3 y-8 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
113.792 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
31.299 |
|
| \begin{align*}
\left (x^{3}+1\right ) y^{\prime }+6 x^{2} y&=6 x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.537 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x^{2}+y^{2}}{2 y x -x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
54.047 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
35.500 |
|
| \begin{align*}
8+2 y^{2}+\left (-x^{2}+1\right ) y y^{\prime }&=0 \\
y \left (3\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
10.054 |
|
| \begin{align*}
y^{2} {\mathrm e}^{2 x}-2 x +y \,{\mathrm e}^{2 x} y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.650 |
|
| \begin{align*}
3 x^{2}+2 x y^{2}+\left (2 x^{2} y+6 y^{2}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
25.248 |
|
| \begin{align*}
4 x y y^{\prime }&=1+y^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.404 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +7 y}{2 x -2 y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
65.532 |
|
| \begin{align*}
y^{\prime }&=\frac {x y}{x^{2}+1} \\
y \left (\sqrt {15}\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.770 |
|
| \begin{align*}
y^{\prime }+y&=\left \{\begin {array}{cc} 1 & 0\le x <2 \\ 0 & 0<x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.759 |
|
| \begin{align*}
\left (x +2\right ) y^{\prime }+y&=\left \{\begin {array}{cc} 2 x & 0\le x \le 2 \\ 4 & 2<x \end {array}\right . \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.931 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=\frac {y^{3}}{x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
204.229 |
|
| \begin{align*}
5 y x +4 y^{2}+1+\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
9.868 |
|
| \begin{align*}
2 x +\tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.778 |
|
| \begin{align*}
\left (x +1\right ) y^{2}+y+\left (1+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
10.463 |
|
| \begin{align*}
2 x y^{2}+y+\left (2 y^{3}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✓ |
6.932 |
|
| \begin{align*}
4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
77.136 |
|
| \begin{align*}
8 x^{2} y^{3}-2 y^{4}+\left (5 x^{3} y^{2}-8 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
198.453 |
|
| \begin{align*}
5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.212 |
|
| \begin{align*}
3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.336 |
|
| \begin{align*}
x -2 y-3+\left (2 x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
36.794 |
|
| \begin{align*}
10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
56.347 |
|
| \begin{align*}
6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime }&=0 \\
y \left (\frac {1}{2}\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.226 |
|
| \begin{align*}
3 x -y-6+\left (x +y+2\right ) y^{\prime }&=0 \\
y \left (2\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
88.581 |
|
| \begin{align*}
2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime }&=0 \\
y \left (-2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.925 |
|
| \begin{align*}
\left (x +y+1\right ) y^{\prime }+1+4 x +3 y&=0 \\
y \left (3\right ) &= -4 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
50.408 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{x} \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{x} \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (1\right ) &= 7 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
3.460 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.862 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.766 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=0 \\
y \left (2\right ) &= 3 \\
y^{\prime }\left (2\right ) &= -1 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.011 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.112 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 x y^{\prime }-8 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.228 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }-3 \left (x +1\right ) y^{\prime }+3 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.244 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.231 |
|
| \begin{align*}
\left (x^{2}-x +1\right ) y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.243 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime \prime }-4 \left (x +1\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.258 |
|
| \begin{align*}
\left (x^{3}-x^{2}\right ) y^{\prime \prime }-\left (x^{3}+2 x^{2}-2 x \right ) y^{\prime }+\left (2 x^{2}+2 x -2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.275 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=4 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=2-12 x +6 \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
4 y^{\prime \prime }-12 y^{\prime }+5 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.462 |
|
| \begin{align*}
3 y^{\prime \prime }-14 y^{\prime }-5 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.113 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.110 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+16 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.578 |
|
| \begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+25 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.645 |
|
| \begin{align*}
4 y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.516 |
|
| \begin{align*}
y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.117 |
|
| \begin{align*}
4 y^{\prime \prime \prime }+4 y^{\prime \prime }-7 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.116 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.123 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.135 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.139 |
|
| \begin{align*}
y^{\left (5\right )}-2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.145 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime }+2 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.131 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime }+12 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.136 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+15 y^{\prime \prime }+20 y^{\prime }+12 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.146 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.104 |
|
| \begin{align*}
y^{\left (5\right )}&=0 \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.093 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-12 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.637 |
|
| \begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&=0 \\
y \left (0\right ) &= -4 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.647 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+8 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.648 |
|