| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y \left (\left (b x +a y\right )^{3}+b \,x^{3}\right ) y^{\prime }+x \left (\left (b x +a y\right )^{3}+a y^{3}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
35.790 |
|
| \begin{align*}
y+x y^{2}-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.335 |
|
| \begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.127 |
|
| \begin{align*}
\left (x -1\right ) \left (y^{2}-y+1\right )&=\left (y+1\right ) \left (x^{2}+x +1\right ) y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.067 |
|
| \begin{align*}
\left (x -2 y x -y^{2}\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
3.922 |
|
| \begin{align*}
\cos \left (x \right ) y+\left (2 y-\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.767 |
|
| \begin{align*}
y^{\prime }-1&={\mathrm e}^{x +2 y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.080 |
|
| \begin{align*}
2 x^{5}+4 x^{3} y-2 x y^{2}+\left (y^{2}+2 x^{2} y-x^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
6.375 |
|
| \begin{align*}
x^{2} y^{n} y^{\prime }&=2 x y^{\prime }-y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
7.619 |
|
| \begin{align*}
\sqrt {x^{2}+1}+n y+\left (\sqrt {1+y^{2}}+n x \right ) y^{\prime }&=0 \\
y \left (0\right ) &= n \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
27.114 |
|
| \begin{align*}
\left (3 x +3 y+a^{2}\right ) y^{\prime }&=4 x +4 y+b^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.464 |
|
| \begin{align*}
a x y {y^{\prime }}^{2}+\left (x^{2}-a y^{2}-b \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
101.651 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+8 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| \begin{align*}
y^{\prime \prime }+y&=2 \cos \left (x \right )+2 \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.646 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| \begin{align*}
x y^{\prime \prime \prime }&=2 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.237 |
|
| \begin{align*}
y^{\prime } y^{\prime \prime \prime }&=3 {y^{\prime \prime }}^{2} \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✗ |
1.206 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \begin{align*}
-{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
2.052 |
|
| \begin{align*}
x y^{\prime \prime }+\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.703 |
|
| \begin{align*}
x^{2} \ln \left (x \right )^{2} y^{\prime \prime }-x \ln \left (x \right ) y^{\prime }+\left (1+\ln \left (x \right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.808 |
|
| \begin{align*}
y^{\prime \prime } \left (1+2 \ln \left (y^{\prime }\right )\right )&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear]] |
✓ |
✓ |
✓ |
✓ |
2.919 |
|
| \begin{align*}
y^{\prime \prime } {\mathrm e}^{y^{\prime }} \left (y^{\prime }+2\right )&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear]] |
✓ |
✓ |
✓ |
✓ |
3.434 |
|
| \begin{align*}
2 \left (1-y\right ) y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
2.722 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}-2 y^{\prime } y^{\prime \prime }+3&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
106.714 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.259 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| \begin{align*}
x^{2} \left (1-\ln \left (x \right )\right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.769 |
|
| \begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
2.876 |
|
| \begin{align*}
y^{\prime \prime }+6 y {y^{\prime }}^{3}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
0.401 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime } \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.715 |
|
| \begin{align*}
x \sin \left (x \right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.568 |
|
| \begin{align*}
y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
6.124 |
|
| \begin{align*}
y^{3} y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
2.663 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime } \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.137 |
|
| \begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2}+y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.728 |
|
| \begin{align*}
y \left (1+\ln \left (y\right )\right ) y^{\prime \prime }+{y^{\prime }}^{2}&=2 x y \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.749 |
|
| \begin{align*}
y^{\prime \prime \prime }&=x \,{\mathrm e}^{x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.158 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }&=x \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.121 |
|
| \begin{align*}
y^{\prime \prime \prime }&=x \ln \left (x \right ) \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 1 \\
y^{\prime \prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.268 |
|
| \begin{align*}
y^{\prime \prime \prime }&=x +\cos \left (x \right ) \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.162 |
|
| \begin{align*}
y^{\prime \prime \prime }&=\frac {x}{\left (x +2\right )^{5}} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
y^{\prime \prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.284 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}-5 y^{\prime }+6&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.892 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}-2 y^{\prime } y^{\prime \prime }+3&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
104.589 |
|
| \begin{align*}
x y^{\prime \prime }&=y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}+{y^{\prime }}^{2}&={y^{\prime }}^{4} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
36.618 |
|
| \begin{align*}
{y^{\prime \prime \prime }}^{2}+{y^{\prime \prime }}^{2}&=1 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✓ |
✗ |
1.775 |
|
| \begin{align*}
y^{\prime \prime } \left (1+2 \ln \left (y^{\prime }\right )\right )&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear]] |
✓ |
✓ |
✓ |
✓ |
2.326 |
|
| \begin{align*}
x&=1+{y^{\prime \prime }}^{2} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \begin{align*}
4 y^{\prime }+{y^{\prime \prime }}^{2}&=4 x y^{\prime \prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}-y^{\prime } y^{\prime \prime \prime }&=\frac {{y^{\prime }}^{2}}{x^{2}} \\
\end{align*} |
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.293 |
|
| \begin{align*}
y^{\prime \prime } {\mathrm e}^{y^{\prime }} \left (y^{\prime }+2\right )&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear]] |
✓ |
✓ |
✓ |
✓ |
2.967 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {y^{\prime }}{x}+\frac {x^{2}}{y^{\prime }} \\
y \left (2\right ) &= 0 \\
y^{\prime }\left (2\right ) &= 4 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✗ |
0.479 |
|
| \begin{align*}
x y^{\prime \prime \prime }+y^{\prime \prime }-x -1&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.084 |
|
| \begin{align*}
y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✗ |
1.212 |
|
| \begin{align*}
x {y^{\prime }}^{2} y^{\prime \prime }-{y^{\prime }}^{3}&=\frac {x^{4}}{3} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✗ |
1.415 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime }+2 x^{3} y^{\prime \prime }&=1 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.374 |
|
| \begin{align*}
\sqrt {-x^{2}+1}\, y^{\prime \prime }+\sqrt {1-{y^{\prime }}^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✗ |
✓ |
✗ |
0.827 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime \prime }+2 y^{\prime \prime }&=\frac {x +1}{2 x^{2}} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.286 |
|
| \begin{align*}
y^{3} y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
2.279 |
|
| \begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}-1&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
3.457 |
|
| \begin{align*}
2 y^{2} y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
2.427 |
|
| \begin{align*}
2 y^{\prime \prime }&=a \,{\mathrm e}^{y} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
8.805 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {1}{4 \sqrt {y}} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
1.259 |
|
| \begin{align*}
3 y^{\prime \prime }&=\frac {1}{y^{{5}/{3}}} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
1.698 |
|
| \begin{align*}
1+{y^{\prime }}^{2}&=2 y y^{\prime \prime } \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
1.954 |
|
| \begin{align*}
y^{3} y^{\prime \prime }&=-1 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✗ |
✓ |
✗ |
1.083 |
|
| \begin{align*}
y^{4}-y^{3} y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
9.175 |
|
| \begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=y^{2} y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.748 |
|
| \begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.717 |
|
| \begin{align*}
y^{\prime \prime }&={\mathrm e}^{2 y} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
0.856 |
|
| \begin{align*}
2 y y^{\prime \prime }-3 {y^{\prime }}^{2}&=4 y^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
2.595 |
|
| \begin{align*}
y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
5.820 |
|
| \begin{align*}
x y^{\prime } \left (y y^{\prime \prime }-{y^{\prime }}^{2}\right )-y {y^{\prime }}^{2}&=x^{4} y^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]] |
✗ |
✓ |
✓ |
✗ |
1.356 |
|
| \begin{align*}
x^{4} y^{\prime \prime }&=\left (-x y^{\prime }+y\right )^{3} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
1.578 |
|
| \begin{align*}
y^{2} y^{\prime \prime \prime }-3 y y^{\prime } y^{\prime \prime }+2 {y^{\prime }}^{3}+\frac {y \left (y y^{\prime \prime }-{y^{\prime }}^{2}\right )}{x}&=\frac {y^{3}}{x^{2}} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
0.062 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.614 |
|
| \begin{align*}
3 y^{\prime \prime }-2 y^{\prime }-8 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
y^{\prime \prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.356 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 10 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.413 |
|
| \begin{align*}
y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.054 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \begin{align*}
y^{\left (6\right )}+2 y^{\left (5\right )}+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.068 |
|
| \begin{align*}
4 y^{\prime \prime }-8 y^{\prime }+5 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
y^{\prime \prime \prime }-8 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+10 y^{\prime \prime }+12 y^{\prime }+5 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.070 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }-5 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.069 |
|
| \begin{align*}
y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-6 y^{\prime }-4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.076 |
|
| \begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.054 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.059 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| \begin{align*}
y^{\left (10\right )}&=0 \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.071 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime }-2 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| \begin{align*}
2 y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.056 |
|