| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
2 \left (1-y\right ) y y^{\prime \prime }-\left (1-2 y\right ) {y^{\prime }}^{2}+f \left (x \right ) \left (1-y\right ) y y^{\prime }&=0 \\
\end{align*} |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
47.070 |
|
| \begin{align*}
2 \left (1-y\right ) y y^{\prime \prime }-\left (1-3 y\right ) {y^{\prime }}^{2}+h \left (y\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
2.626 |
|
| \begin{align*}
3 \left (1-y\right ) y y^{\prime \prime }-2 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
2.584 |
|
| \begin{align*}
\left (1-y\right ) y^{\prime \prime }-3 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
2.864 |
|
| \begin{align*}
a y \left (-1+y\right ) y^{\prime \prime }+\left (b y+c \right ) {y^{\prime }}^{2}+h \left (y\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
5.194 |
|
| \begin{align*}
a y \left (-1+y\right ) y^{\prime \prime }-\left (-1+a \right ) \left (-1+2 y\right ) {y^{\prime }}^{2}+f y \left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.599 |
|
| \begin{align*}
a b y \left (-1+y\right ) y^{\prime \prime }-\left (\left (2 a b -a -b \right ) y+\left (1-a \right ) b \right ) {y^{\prime }}^{2}+f y \left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.663 |
|
| \begin{align*}
x y^{2} y^{\prime \prime }-a&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
4.533 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) \left (a^{2}-y^{2}\right ) y^{\prime \prime }+\left (a^{2}-x^{2}\right ) y {y^{\prime }}^{2}-x \left (a^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
35.170 |
|
| \begin{align*}
2 x^{2} y \left (-1+y\right ) y^{\prime \prime }-x^{2} \left (3 y-1\right ) {y^{\prime }}^{2}+2 x y \left (-1+y\right ) y^{\prime }+\left (a y^{2}+b \right ) \left (-1+y\right )^{3}+c x y^{2} \left (-1+y\right )+d \,x^{2} y^{2} \left (1+y\right )&=0 \\
\end{align*} |
[[_Painleve, ‘5th‘]] |
✗ |
✗ |
✗ |
✗ |
53.074 |
|
| \begin{align*}
\left (x +y\right ) \left (-y+y^{\prime } x \right )^{3}+x^{3} y^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
17.924 |
|
| \begin{align*}
y^{3} y^{\prime \prime }-a&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
2.493 |
|
| \begin{align*}
\left (1-3 y^{2}\right ) {y^{\prime }}^{2}+y \left (1+y^{2}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.838 |
|
| \begin{align*}
2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
1.102 |
|
| \begin{align*}
2 y^{3} y^{\prime \prime }+y^{2} {y^{\prime }}^{2}-a \,x^{2}-b x -c&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
1.194 |
|
| \begin{align*}
2 \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) y^{\prime \prime }-\left (\left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )+\left (y-b \right ) \left (y-c \right )\right ) {y^{\prime }}^{2}+\left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} \left (A_{0} +\frac {B_{0}}{\left (y-a \right )^{2}}+\frac {C_{1}}{\left (y-b \right )^{2}}+\frac {D_{0}}{\left (y-c \right )^{2}}\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
8.142 |
|
| \begin{align*}
\left (4 y^{3}-a y-b \right ) y^{\prime \prime }-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.753 |
|
| \begin{align*}
\left (4 y^{3}-a y-b \right ) \left (y^{\prime \prime }+f y^{\prime }\right )-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.198 |
|
| \begin{align*}
\left (-1+y^{2}\right ) \left (y^{2} a^{2}-1\right ) y^{\prime \prime }+b \sqrt {\left (1-y^{2}\right ) \left (1-y^{2} a^{2}\right )}\, {y^{\prime }}^{2}+\left (1+a^{2}-2 y^{2} a^{2}\right ) y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✗ |
✓ |
✗ |
4.458 |
|
| \begin{align*}
\left (c +2 b x +a \,x^{2}+y^{2}\right )^{2} y^{\prime \prime }+d y&=0 \\
\end{align*} |
[NONE] |
✗ |
✓ |
✓ |
✗ |
1.693 |
|
| \begin{align*}
\sqrt {y}\, y^{\prime \prime }-a&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
1.479 |
|
| \begin{align*}
\sqrt {x^{2}+y^{2}}\, y^{\prime \prime }-a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
47.503 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.742 |
|
| \begin{align*}
\left (b +a \sin \left (y\right )^{2}\right ) y^{\prime \prime }+a {y^{\prime }}^{2} \cos \left (y\right ) \sin \left (y\right )+A y \left (c +a \sin \left (y\right )^{2}\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
6.709 |
|
| \begin{align*}
h \left (y\right ) y^{\prime \prime }+a h \left (y\right ) {y^{\prime }}^{2}+j \left (y\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.028 |
|
| \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]] |
✗ |
✗ |
✗ |
✗ |
244.703 |
|
| \begin{align*}
\left (-y+y^{\prime } x \right ) y^{\prime \prime }+4 {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
8.965 |
|
| \begin{align*}
\left (-y+y^{\prime } x \right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
25.309 |
|
| \begin{align*}
a \,x^{3} y^{\prime } y^{\prime \prime }+b y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
52.390 |
|
| \begin{align*}
\left ({y^{\prime }}^{2}+a \left (-y+y^{\prime } x \right )\right ) y^{\prime \prime }-b&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
63.348 |
|
| \begin{align*}
\left (a \sqrt {1+{y^{\prime }}^{2}}-y^{\prime } x \right ) y^{\prime \prime }-{y^{\prime }}^{2}-1&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✗ |
✓ |
✓ |
✗ |
524.511 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}-a y-b&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
✓ |
✓ |
✗ |
0.063 |
|
| \begin{align*}
a^{2} {y^{\prime \prime }}^{2}-2 a x y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
✗ |
1.086 |
|
| \begin{align*}
2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2}-x \left (x +4 y^{\prime }\right ) y^{\prime \prime }+2 \left (x +y^{\prime }\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[NONE] |
✗ |
✓ |
✓ |
✗ |
0.055 |
|
| \begin{align*}
4 {y^{\prime }}^{2}-2 \left (y+3 y^{\prime } x \right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
7.612 |
|
| \begin{align*}
\left (2-9 x \right ) x^{2} {y^{\prime \prime }}^{2}-6 \left (1-6 x \right ) x y^{\prime } y^{\prime \prime }+6 y y^{\prime \prime }-36 x {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
41.745 |
|
| \begin{align*}
y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
2.725 |
|
| \begin{align*}
\left (y^{2} a^{2}-b^{2}\right ) {y^{\prime \prime }}^{2}-2 a^{2} y {y^{\prime }}^{2} y^{\prime \prime }+\left (a^{2} {y^{\prime }}^{2}-1\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
1.954 |
|
| \begin{align*}
\left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2}-4 x y \left (-y+y^{\prime } x \right )^{3}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.068 |
|
| \begin{align*}
\sqrt {a {y^{\prime \prime }}^{2}+b {y^{\prime }}^{2}}+c y y^{\prime \prime }+d {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✗ |
✗ |
✗ |
196.883 |
|
| \begin{align*}
y^{\prime \prime \prime }-a^{2} \left ({y^{\prime }}^{5}+2 {y^{\prime }}^{3}+y^{\prime }\right )&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✓ |
✗ |
1.985 |
|
| \begin{align*}
y^{\prime \prime \prime }+y y^{\prime \prime }-{y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.033 |
|
| \begin{align*}
y^{\prime \prime \prime }-y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.035 |
|
| \begin{align*}
a y y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.029 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime }+y^{\prime \prime } x +\left (2 y x -1\right ) y^{\prime }+y^{2}-f \left (x \right )&=0 \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear]] |
✗ |
✗ |
✗ |
✗ |
0.035 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime }+x \left (-1+y\right ) y^{\prime \prime }+x {y^{\prime }}^{2}+\left (1-y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✗ |
✓ |
✗ |
✗ |
0.040 |
|
| \begin{align*}
y^{3} y^{\prime }-y^{\prime } y^{\prime \prime }+y y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
0.036 |
|
| \begin{align*}
15 {y^{\prime }}^{3}-18 y y^{\prime } y^{\prime \prime }+4 y^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.038 |
|
| \begin{align*}
40 {y^{\prime }}^{3}-45 y y^{\prime } y^{\prime \prime }+9 y^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| \begin{align*}
2 y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.138 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }-3 y^{\prime } {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]] |
✓ |
✓ |
✓ |
✗ |
0.707 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }-\left (a +3 y^{\prime }\right ) {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]] |
✓ |
✓ |
✓ |
✗ |
8.686 |
|
| \begin{align*}
y^{\prime \prime } y^{\prime \prime \prime }-a \sqrt {1+b^{2} {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]] |
✓ |
✓ |
✓ |
✗ |
13.599 |
|
| \begin{align*}
y^{\prime } y^{\prime \prime \prime \prime }-y^{\prime \prime } y^{\prime \prime \prime }+{y^{\prime }}^{3} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.076 |
|
| \begin{align*}
3 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2}&=0 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✗ |
1.188 |
|
| \begin{align*}
9 {y^{\prime \prime }}^{2} y^{\left (5\right )}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+40 y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.099 |
|
| \begin{align*}
y^{\prime \prime }-f \left (y\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
1.748 |
|
| \begin{align*}
y^{\prime \prime \prime }&=f \left (y\right ) \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.023 |
|
| \begin{align*}
x^{\prime }&=a x \\
y^{\prime }&=b \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
x^{\prime }&=a y \\
y^{\prime }&=-a x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.373 |
|
| \begin{align*}
x^{\prime }&=a y \\
y^{\prime }&=b x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \begin{align*}
x^{\prime }&=a x-y \\
y^{\prime }&=x+a y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
x^{\prime }&=a x+b y \\
y^{\prime }&=c x+b y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.884 |
|
| \begin{align*}
a x^{\prime }+b y^{\prime }&=\alpha x+\beta y \\
b x^{\prime }-a y^{\prime }&=\beta x-\alpha y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=2 x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| \begin{align*}
x^{\prime }+3 x+4 y&=0 \\
y^{\prime }+2 x+5 y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
x^{\prime }&=-5 x-2 y \\
y^{\prime }&=x-7 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.479 |
|
| \begin{align*}
x^{\prime }&=a_{1} x+b_{1} y+c_{1} \\
y^{\prime }&=a_{2} x+b_{2} y+c_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.789 |
|
| \begin{align*}
x^{\prime }+2 y&=3 t \\
y^{\prime }-2 x&=4 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.577 |
|
| \begin{align*}
x^{\prime }+y-t^{2}+6 t +1&=0 \\
-x+y^{\prime }&=-3 t^{2}+3 t +1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.657 |
|
| \begin{align*}
x^{\prime }+3 x-y&={\mathrm e}^{2 t} \\
y^{\prime }+x+5 y&={\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| \begin{align*}
x^{\prime }+2 x+y^{\prime }+y&={\mathrm e}^{2 t}+t \\
x^{\prime }-x+y^{\prime }+3 y&={\mathrm e}^{t}-1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.192 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-y&={\mathrm e}^{t} \\
2 x^{\prime }+y^{\prime }+2 y&=\cos \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| \begin{align*}
4 x^{\prime }+9 y^{\prime }+2 x+31 y&={\mathrm e}^{t} \\
3 x^{\prime }+7 y^{\prime }+x+24 y&=3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| \begin{align*}
4 x^{\prime }+9 y^{\prime }+11 x+31 y&={\mathrm e}^{t} \\
3 x^{\prime }+7 y^{\prime }+8 x+24 y&={\mathrm e}^{2 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.574 |
|
| \begin{align*}
4 x^{\prime }+9 y^{\prime }+44 x+49 y&=t \\
3 x^{\prime }+7 y^{\prime }+34 x+38 y&={\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.657 |
|
| \begin{align*}
x^{\prime }&=x f \left (t \right )+y g \left (t \right ) \\
y^{\prime }&=-x g \left (t \right )+y f \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.032 |
|
| \begin{align*}
x^{\prime }+\left (a x+b y\right ) f \left (t \right )&=g \left (t \right ) \\
y^{\prime }+\left (c x+d y\right ) f \left (t \right )&=h \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.045 |
|
| \begin{align*}
x^{\prime }&=x \cos \left (t \right ) \\
y^{\prime }&=x \,{\mathrm e}^{-\sin \left (t \right )} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.035 |
|
| \begin{align*}
t x^{\prime }+y&=0 \\
y^{\prime } t +x&=0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.026 |
|
| \begin{align*}
t x^{\prime }+2 x&=t \\
y^{\prime } t -\left (t +2\right ) x-t y&=-t \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| \begin{align*}
t x^{\prime }+2 x-2 y&=t \\
y^{\prime } t +x+5 y&=t^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.032 |
|
| \begin{align*}
t^{2} \left (1-\sin \left (t \right )\right ) x^{\prime }&=t \left (1-2 \sin \left (t \right )\right ) x+t^{2} y \\
t^{2} \left (1-\sin \left (t \right )\right ) y^{\prime }&=\left (t \cos \left (t \right )-\sin \left (t \right )\right ) x+t \left (1-t \cos \left (t \right )\right ) y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.048 |
|
| \begin{align*}
x^{\prime }+y^{\prime }+y&=f \left (t \right ) \\
x^{\prime \prime }+y^{\prime \prime }+y^{\prime }+x+y&=g \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.037 |
|
| \begin{align*}
2 x^{\prime }+y^{\prime }-3 x&=0 \\
x^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{2 t} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| \begin{align*}
x^{\prime }+x-y^{\prime }&=2 t \\
x^{\prime \prime }+y^{\prime }-9 x+3 y&=\sin \left (2 t \right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.036 |
|
| \begin{align*}
x^{\prime }-x+2 y&=0 \\
x^{\prime \prime }-2 y^{\prime }&=2 t -\cos \left (2 t \right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.042 |
|
| \begin{align*}
t x^{\prime }-y^{\prime } t -2 y&=0 \\
t x^{\prime \prime }+2 x^{\prime }+t x&=0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.034 |
|
| \begin{align*}
x^{\prime \prime }+a y&=0 \\
y^{\prime \prime }-a^{2} y&=0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.025 |
|
| \begin{align*}
x^{\prime \prime }&=a x+b y \\
y^{\prime \prime }&=c x+d y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.037 |
|
| \begin{align*}
x^{\prime \prime }&=a_{1} x+b_{1} y+c_{1} \\
y^{\prime \prime }&=a_{2} x+b_{2} y+c_{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.025 |
|
| \begin{align*}
x^{\prime \prime }+x+y&=-5 \\
y^{\prime \prime }-4 x-3 y&=-3 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.036 |
|
| \begin{align*}
x^{\prime \prime }&=\left (3 \cos \left (a t +b \right )^{2}-1\right ) c^{2} x+\frac {3 c^{2} y \sin \left (2 a t b \right )}{2} \\
y^{\prime \prime }&=\left (3 \sin \left (a t +b \right )^{2}-1\right ) c^{2} y+\frac {3 c^{2} x \sin \left (2 a t b \right )}{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.036 |
|
| \begin{align*}
x^{\prime \prime }+6 x+7 y&=0 \\
y^{\prime \prime }+3 x+2 y&=2 t \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.027 |
|
| \begin{align*}
x^{\prime \prime }-a y^{\prime }+b x&=0 \\
y^{\prime \prime }+a x^{\prime }+b y&=0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.042 |
|
| \begin{align*}
a_{1} x^{\prime \prime }+b_{1} x^{\prime }+c_{1} x-A y^{\prime }&=B \,{\mathrm e}^{i \omega t} \\
a_{2} y^{\prime \prime }+b_{2} y^{\prime }+c_{2} y+A x^{\prime }&=0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.057 |
|
| \begin{align*}
x^{\prime \prime }+a \left (x^{\prime }-y^{\prime }\right )+b_{1} x&=c_{1} {\mathrm e}^{i \omega t} \\
y^{\prime \prime }+a \left (y^{\prime }-x^{\prime }\right )+b_{2} y&=c_{2} {\mathrm e}^{i \omega t} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.048 |
|
| \begin{align*}
\operatorname {a11} x^{\prime \prime }+\operatorname {b11} x^{\prime }+\operatorname {c11} x+\operatorname {a12} y^{\prime \prime }+\operatorname {b12} y^{\prime }+\operatorname {c12} y&=0 \\
\operatorname {a21} x^{\prime \prime }+\operatorname {b21} x^{\prime }+\operatorname {c21} x+\operatorname {a22} y^{\prime \prime }+\operatorname {b22} y^{\prime }+\operatorname {c22} y&=0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.063 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }-y^{\prime }+y&=0 \\
y^{\prime \prime \prime }-y^{\prime \prime }+2 x^{\prime }-x&=t \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.038 |
|
| \begin{align*}
x^{\prime \prime }+y^{\prime \prime }+y^{\prime }&=\sinh \left (2 t \right ) \\
2 x^{\prime \prime }+y^{\prime \prime }&=2 t \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.035 |
|