| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
2.481 |
|
| \begin{align*}
\left (y^{2} x^{2}-1\right ) y^{\prime }+2 x y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
2.844 |
|
| \begin{align*}
a x y^{\prime }+b y+x^{m} y^{n} \left (\alpha x y^{\prime }+\beta y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
6.739 |
|
| \begin{align*}
2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
1.631 |
|
| \begin{align*}
y^{\prime }&=2 y x -x^{3}+x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.782 |
|
| \begin{align*}
y-x y^{2} \ln \left (x \right )+y^{\prime } x&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.828 |
|
| \begin{align*}
\left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3}&=0 \\
\end{align*} |
[_rational] |
✗ |
✓ |
✓ |
✗ |
4.044 |
|
| \begin{align*}
y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.294 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-2 x y^{\prime } y+y^{2}&=y^{2} x^{2}+x^{4} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
18.423 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.223 |
|
| \begin{align*}
x {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.583 |
|
| \begin{align*}
x {y^{\prime }}^{3}&=1+y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| \begin{align*}
{y^{\prime }}^{3}-x^{3} \left (1-y^{\prime }\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
33.165 |
|
| \begin{align*}
{y^{\prime }}^{3}+y^{3}-3 y^{\prime } y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
71.784 |
|
| \begin{align*}
y&={y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.518 |
|
| \begin{align*}
y^{2} \left (y^{\prime }-1\right )&=\left (2-y^{\prime }\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.639 |
|
| \begin{align*}
y \left (1+{y^{\prime }}^{2}\right )&=2 \alpha \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \begin{align*}
{y^{\prime }}^{4}&=4 y \left (y^{\prime } x -2 y\right )^{2} \\
\end{align*} | [[_homogeneous, ‘class G‘]] | ✓ | ✓ | ✓ | ✗ | 41.967 |
|
| \begin{align*}
y&=2 y^{\prime } x +\frac {x^{2}}{2}+{y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✗ |
✓ |
0.602 |
|
| \begin{align*}
y&=\frac {k \left (y^{\prime } y+x \right )}{\sqrt {1+{y^{\prime }}^{2}}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✗ |
97.827 |
|
| \begin{align*}
x&=y^{\prime } y+a {y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
28.454 |
|
| \begin{align*}
y&=x {y^{\prime }}^{2}+{y^{\prime }}^{3} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.441 |
|
| \begin{align*}
y&=y^{\prime } x +y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.196 |
|
| \begin{align*}
y&=2 y^{\prime } x +y^{2} {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.429 |
|
| \begin{align*}
{y^{\prime }}^{2} \left (x^{2}-1\right )-2 x y^{\prime } y+y^{2}-1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.239 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.654 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y-x} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.883 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y-x}+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.523 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.087 |
|
| \begin{align*}
y^{\prime }&=y \ln \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.659 |
|
| \begin{align*}
y^{\prime }&=y \ln \left (y\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.683 |
|
| \begin{align*}
y^{\prime }&=-x +\sqrt {x^{2}+2 y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
3.449 |
|
| \begin{align*}
y^{\prime }&=-x -\sqrt {x^{2}+2 y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
3.352 |
|
| \begin{align*}
4 x -2 y^{\prime } y+x {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \begin{align*}
x {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} | [[_homogeneous, ‘class A‘], _rational, _dAlembert] | ✓ | ✓ | ✓ | ✓ | 0.698 |
|
| \begin{align*}
y^{2} \left (y^{\prime }-1\right )&=\left (2-y^{\prime }\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.489 |
|
| \begin{align*}
{y^{\prime }}^{4}&=4 y \left (y^{\prime } x -2 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
35.919 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-2 x y^{\prime } y+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| \begin{align*}
y&={y^{\prime }}^{2}-y^{\prime } x +\frac {x^{3}}{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
17.542 |
|
| \begin{align*}
y&=2 y^{\prime } x +\frac {x^{2}}{2}+{y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✗ |
✓ |
0.570 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime } y+{\mathrm e}^{x}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.359 |
|
| \begin{align*}
{y^{\prime \prime \prime }}^{2}+x^{2}&=1 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1651.873 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {1}{\sqrt {y}} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
4.243 |
|
| \begin{align*}
a^{3} y^{\prime \prime \prime } y^{\prime \prime }&=\sqrt {1+c^{2} {y^{\prime \prime }}^{2}} \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✓ |
✗ |
29.674 |
|
| \begin{align*}
y^{\prime \prime \prime }&=\sqrt {1+{y^{\prime \prime }}^{2}} \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✓ |
✓ |
6.599 |
|
| \begin{align*}
2 \left (2 a -y\right ) y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
7.795 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime \prime \prime }+{y^{\prime \prime \prime }}^{3}&=0 \\
\end{align*} |
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]] |
✓ |
✗ |
✓ |
✗ |
1.681 |
|
| \begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.965 |
|
| \begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} | [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] | ✓ | ✓ | ✓ | ✗ | 1.415 |
|
| \begin{align*}
x y y^{\prime \prime }+x {y^{\prime }}^{2}-y^{\prime } y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
2.546 |
|
| \begin{align*}
n \,x^{3} y^{\prime \prime }&=\left (y-y^{\prime } x \right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.753 |
|
| \begin{align*}
y^{2} \left (x^{2} y^{\prime \prime }-y^{\prime } x +y\right )&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.622 |
|
| \begin{align*}
x^{2} y^{2} y^{\prime \prime }-3 y^{2} y^{\prime } x +4 y^{3}+x^{6}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.641 |
|
| \begin{align*}
y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✗ |
✗ |
✗ |
✗ |
38.043 |
|
| \begin{align*}
x \left (x^{2} y^{\prime }+2 y x \right ) y^{\prime \prime }+4 x {y^{\prime }}^{2}+8 x y^{\prime } y+4 y^{2}-1&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.291 |
|
| \begin{align*}
x \left (y x +1\right ) y^{\prime \prime }+x^{2} {y^{\prime }}^{2}+\left (4 y x +2\right ) y^{\prime }+y^{2}+1&=0 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.435 |
|
| \begin{align*}
a^{2} y^{\prime \prime }&=2 x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✗ |
✓ |
✗ |
2.365 |
|
| \begin{align*}
x^{2} y y^{\prime \prime }+x^{2} {y^{\prime }}^{2}-5 x y^{\prime } y&=4 y^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.533 |
|
| \begin{align*}
\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \\
\end{align*} | [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] | ✓ | ✓ | ✓ | ✗ | 2.167 |
|
| \begin{align*}
5 {y^{\prime \prime \prime }}^{2}-3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✗ |
4.155 |
|
| \begin{align*}
40 {y^{\prime \prime \prime }}^{3}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+9 {y^{\prime \prime }}^{2} y^{\left (5\right )}&=0 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.200 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}+2 y^{\prime \prime } x -y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.381 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}-2 y^{\prime \prime } x -y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.765 |
|
| \begin{align*}
2 x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+12 y^{\prime } x -12 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.226 |
|
| \begin{align*}
y^{\prime \prime \prime }-\frac {3 y^{\prime \prime }}{x}+\frac {6 y^{\prime }}{x^{2}}-\frac {6 y}{x^{3}}&=0 \\
\end{align*} |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
✓ |
✓ |
✓ |
0.227 |
|
| \begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✗ |
✓ |
✓ |
✗ |
78.434 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| \begin{align*}
\sin \left (x \right )^{2} y^{\prime \prime }&=2 y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.398 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.218 |
|
| \begin{align*}
-y+y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.056 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime \prime }-y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.477 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=2 x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.245 |
|
| \begin{align*}
y^{\prime \prime }+\frac {x y^{\prime }}{1-x}-\frac {y}{1-x}&=x -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.534 |
|
| \begin{align*}
-2 y x +\left (x^{2}+2\right ) y^{\prime }-2 y^{\prime \prime } x +\left (x^{2}+2\right ) y^{\prime \prime \prime }&=x^{4}+12 \\
\end{align*} | [[_3rd_order, _linear, _nonhomogeneous]] | ✗ | ✓ | ✓ | ✗ | 0.068 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.024 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y}{\ln \left (x \right ) x^{2}}&={\mathrm e}^{x} \left (\frac {2}{x}+\ln \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
1.721 |
|
| \begin{align*}
y^{\prime \prime }+p_{1} y^{\prime }+p_{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.263 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.904 |
|
| \begin{align*}
\sin \left (x \right )^{2} y^{\prime \prime }+\cos \left (x \right ) \sin \left (x \right ) y^{\prime }&=y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
8.439 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.092 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.084 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.070 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.067 |
|
| \begin{align*}
2 y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.250 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+8 y&={\mathrm e}^{x}+{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=x \,{\mathrm e}^{x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.163 |
|
| \begin{align*}
y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{x} \left (x +1\right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.246 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\sin \left (2 x \right ) x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.811 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| \begin{align*}
y^{\prime \prime }-y&=\frac {{\mathrm e}^{x}-{\mathrm e}^{-x}}{{\mathrm e}^{x}+{\mathrm e}^{-x}} \\
\end{align*} | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.635 |
|
| \begin{align*}
y^{\prime \prime }-2 y&=4 x^{2} {\mathrm e}^{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.506 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (2 x \right ) \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.219 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\ln \left (2 \sin \left (\frac {x}{2}\right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.880 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {n \left (n +1\right ) y}{x^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.471 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.770 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=x \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.002 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y&=x^{2}+\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.175 |
|