| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y y^{\prime }+x&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.740 |
|
| \begin{align*}
r^{\prime }&=r \tan \left (t \right ) \\
r \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.696 |
|
| \begin{align*}
{\mathrm e}^{x} \sec \left (y\right )+\left ({\mathrm e}^{x}+1\right ) \sec \left (y\right ) \tan \left (y\right ) y^{\prime }&=0 \\
y \left (3\right ) &= \frac {\pi }{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
0.656 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=-x +y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.163 |
|
| \begin{align*}
y&=y^{\prime } x -\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.273 |
|
| \begin{align*}
x^{3}-y^{3}+y^{\prime } y^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.774 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\csc \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.561 |
|
| \begin{align*}
3 x^{2}+2 y x +4 y^{2}+\left (20 x^{2}+6 y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
20.475 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
48.709 |
|
| \begin{align*}
x^{2}+2 y x -2 y^{2}+\left (y^{2}+2 y x -2 x^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.609 |
|
| \begin{align*}
a x -b y+\left (b x -a y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
16.321 |
|
| \begin{align*}
2 x^{2}+5 x y^{2}+\left (5 x^{2} y-2 y^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
3.135 |
|
| \begin{align*}
a \,x^{2}+2 b x y+c y^{2}+\left (b \,x^{2}+2 c x y+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
95.858 |
|
| \begin{align*}
\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
28.642 |
|
| \begin{align*}
x^{2}+y \,{\mathrm e}^{2 y}+\left (2 y x +x \right ) {\mathrm e}^{2 y} y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✓ |
3.256 |
|
| \begin{align*}
\sin \left (x \right )+\sin \left (y\right )+\left (x \cos \left (y\right )+\cos \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✓ |
29.079 |
|
| \begin{align*}
4 x -2 y+3+\left (5 y-2 x +7\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.056 |
|
| \begin{align*}
2 x \sin \left (y\right )+2 x +3 \cos \left (x \right ) y+\left (\cos \left (y\right ) x^{2}+3 \sin \left (x \right )\right ) y^{\prime }&=0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
40.104 |
|
| \begin{align*}
y \,{\mathrm e}^{2 x}-3 x \,{\mathrm e}^{2 y}+\left (\frac {{\mathrm e}^{2 x}}{2}-3 x^{2} {\mathrm e}^{2 y}-{\mathrm e}^{y}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
6.076 |
|
| \begin{align*}
-y+y^{\prime } x&=x^{2} y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
12.055 |
|
| \begin{align*}
x^{3} y^{\prime }-x^{2} y&=x^{5} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.408 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) \left (y^{\prime } x +y\right )&=x y \left (-y+y^{\prime } x \right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
68.625 |
|
| \begin{align*}
3 y+2 y^{\prime } x +4 x y^{2}+3 x^{2} y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.174 |
|
| \begin{align*}
-y+y^{\prime } x&=x^{2} \sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
37.740 |
|
| \begin{align*}
y^{\prime } x +y&=3 x^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.528 |
|
| \begin{align*}
x^{2} y^{\prime }-y x&=x^{2}-y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
18.475 |
|
| \begin{align*}
y&=\left (2 x^{2} y^{3}-x \right ) y^{\prime } \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✗ |
✗ |
✗ |
16.588 |
|
| \begin{align*}
y^{\prime }+4 y&=x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.365 |
|
| \begin{align*}
y^{\prime }+\sin \left (x \right ) y&=2 x \,{\mathrm e}^{\cos \left (x \right )} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.773 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=8 x^{2} \cos \left (x \right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.558 |
|
| \begin{align*}
2 y+y^{\prime }&=\sin \left (3 x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.219 |
|
| \begin{align*}
1-y^{\prime } x&=\ln \left (y\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.893 |
|
| \begin{align*}
2-x -y+\left (x +y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.280 |
|
| \begin{align*}
2+3 x -5 y+7 y^{\prime }&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.757 |
|
| \begin{align*}
4 x +3 y+2+\left (5 x +4 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.204 |
|
| \begin{align*}
x -y-3+\left (3 x -3 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.550 |
|
| \begin{align*}
2 x -y-1+\left (3 x +2 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
39.501 |
|
| \begin{align*}
x y \left (y^{\prime } x +y\right )&=4 x^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.432 |
|
| \begin{align*}
y^{3} \left (y y^{\prime }+x \right )&=\left (x^{2}+y^{2}\right )^{3} y^{\prime } \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
✗ |
4.284 |
|
| \begin{align*}
\left (1+{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.555 |
|
| \begin{align*}
y y^{\prime }+y^{2} \tan \left (x \right )&=\cos \left (x \right )^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.887 |
|
| \begin{align*}
-y+y^{\prime } x&=y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.220 |
|
| \begin{align*}
y^{\prime }+3 x^{2} y&=3 x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.127 |
|
| \begin{align*}
4 x^{2} y^{2} y^{\prime }-3 x y^{3}&=x^{2} y^{3}+2 x^{2} y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.089 |
|
| \begin{align*}
\sin \left (x \right )+\cos \left (y\right )+\cos \left (x \right )-y^{\prime } \sin \left (y\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
5.635 |
|
| \begin{align*}
y^{\prime } x +y&=y^{2} x^{3} \sin \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.175 |
|
| \begin{align*}
R q^{\prime }+\frac {q}{c}&=E \\
q \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.168 |
|
| \begin{align*}
\left (y^{2} x^{2}-y x -2\right ) x y^{\prime }+y \left (y^{2} x^{2}-1\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| \begin{align*}
3 x^{2}-2 y x +\left (4 y^{3}-x^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✗ |
✗ |
2.626 |
|
| \begin{align*}
3 x^{2}+2 y x -2 y^{2}+\left (2 x^{2}+6 y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.904 |
|
| \begin{align*}
2 x -y+1+\left (x -2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
32.470 |
|
| \begin{align*}
3 x +3 y-2+\left (2 x +2 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.198 |
|
| \begin{align*}
a x y-b +\left (c x y-d \right ) x y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
27.579 |
|
| \begin{align*}
{y^{\prime }}^{2}-3&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.353 |
|
| \begin{align*}
{y^{\prime }}^{2}-4 y^{\prime }+2&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.383 |
|
| \begin{align*}
x y^{2} {y^{\prime }}^{2}+\left (x^{3}+x y^{2}-y^{3}\right ) y^{\prime }+x^{3}-y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
2 {y^{\prime }}^{3}+3 {y^{\prime }}^{2}&=x +y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
1.036 |
|
| \begin{align*}
2 y a \,x^{3}-a \,x^{2} y^{\prime }+c {y^{\prime }}^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
7.177 |
|
| \begin{align*}
y^{2}-2 y y^{\prime } x +x^{2} {y^{\prime }}^{2}-{y^{\prime }}^{3}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.343 |
|
| \begin{align*}
x +y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.979 |
|
| \begin{align*}
2 x +y y^{\prime } \left (4 {y^{\prime }}^{2}+6\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
3.748 |
|
| \begin{align*}
2 {y^{\prime }}^{2}+y y^{\prime }-y^{4}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.570 |
|
| \begin{align*}
y&=4 x {y^{\prime }}^{2}+2 y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.325 |
|
| \begin{align*}
\left (x^{2}-2 y x \right ) {y^{\prime }}^{2}-\left (3 x^{2}+2 y\right ) \left (x -2 y\right ) y^{\prime }+6 x y \left (x -2 y\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.224 |
|
| \begin{align*}
{y^{\prime }}^{2}+y&=y^{\prime } x +1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.286 |
|
| \begin{align*}
y y^{\prime }&=-x {y^{\prime }}^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.168 |
|
| \begin{align*}
\left (-y^{\prime } x +y\right )^{2}&=y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✓ |
1.451 |
|
| \begin{align*}
y-{y^{\prime }}^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.376 |
|
| \begin{align*}
x -x {y^{\prime }}^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.295 |
|
| \begin{align*}
{y^{\prime }}^{3}+y {y^{\prime }}^{2}-x^{2} y^{\prime }-x^{2} y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| \begin{align*}
y&=y^{\prime } x +\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
6.221 |
|
| \begin{align*}
x {y^{\prime }}^{2}&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.681 |
|
| \begin{align*}
y^{\prime \prime }-12 y^{\prime }+35 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
6.020 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.793 |
|
| \begin{align*}
9 y^{\prime \prime }-30 y^{\prime }+25 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
7.931 |
|
| \begin{align*}
3 y^{\prime \prime }-4 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
15.892 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+7 y^{\prime \prime }+6 y^{\prime }-8 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.078 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }+3 y^{\prime }-6 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.075 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+5 y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.087 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+42 y^{\prime \prime }-104 y^{\prime }+169 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.096 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=2 x^{2}-3 x -17 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.172 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y+8 \,{\mathrm e}^{-x}+3 x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
33.215 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=2 \tan \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
27.438 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&=6 x^{5} {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
6.602 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=x \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
28.152 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=4 \cos \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.322 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=x^{3}+{\mathrm e}^{x} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.189 |
|
| \begin{align*}
y^{\prime \prime }+2 a y^{\prime }+a^{2} y&=x^{2} {\mathrm e}^{-a x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
28.728 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }&=x \,{\mathrm e}^{x} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.201 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=2 \sin \left (x \right ) {\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
23.404 |
|
| \begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=\sin \left (x \right ) {\mathrm e}^{-x} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.162 |
|
| \begin{align*}
x^{\prime }+x+y^{\prime }+y&=0 \\
x^{\prime }-y^{\prime }-y&=t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| \begin{align*}
y^{\prime }-3 z&=5 \\
y-z^{\prime }-x&=3-2 t \\
z+x^{\prime }&=-1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.211 |
|
| \begin{align*}
x^{\prime \prime }-x+y&={\mathrm e}^{t} \\
x^{\prime }+x-y^{\prime }-y&=3 \,{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.052 |
|
| \begin{align*}
x^{\prime }-2 x+y^{\prime }-2 y&=1 \\
y^{\prime }+z^{\prime }+z&=2 \\
3 x+z^{\prime }+z&=3 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.119 |
|
| \begin{align*}
x^{\prime }+3 x-y&=0 \\
y^{\prime }+y-3 x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
x^{\prime }-x-2 y&=0 \\
y^{\prime }-2 y-3 x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \begin{align*}
y^{\prime }+y-x^{\prime \prime }+x&={\mathrm e}^{t} \\
y^{\prime }-x^{\prime }+x&={\mathrm e}^{-t} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.046 |
|
| \begin{align*}
2 y^{\prime \prime \prime }+y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= -1 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.043 |
|