| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x y^{\prime }-4 \sqrt {y^{2}-x^{2}}&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
48.076 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{4}+2 x y^{3}-3 x^{2} y^{2}-2 x^{3} y}{2 x^{2} y^{2}-2 x^{3} y-2 x^{4}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
127.954 |
|
| \begin{align*}
\left (y+x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime }&={\mathrm e}^{\frac {x}{y}} y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.769 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}+y^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
32.776 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
y \left (5\right ) &= 8 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
83.207 |
|
| \begin{align*}
t y^{\prime }+y&=y^{2} t^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.494 |
|
| \begin{align*}
y^{\prime }&=y \left (t y^{3}-1\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.304 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{t}&=y^{2} t^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.220 |
|
| \begin{align*}
t^{2} y^{\prime }+2 y t -y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
32.563 |
|
| \begin{align*}
5 \left (t^{2}+1\right ) y^{\prime }&=4 t y \left (y^{3}-1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
21.014 |
|
| \begin{align*}
3 t y^{\prime }+9 y&=2 t y^{{5}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.161 |
|
| \begin{align*}
y^{\prime }&=y+\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.015 |
|
| \begin{align*}
y^{\prime }&=r y-k^{2} y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.880 |
|
| \begin{align*}
y^{\prime }&=a y+b y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
25.325 |
|
| \begin{align*}
y^{\prime }+3 y t&=4-4 t^{2}+y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
6.642 |
|
| \begin{align*}
\left (3 x-y \right ) x^{\prime }+9 y -2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
39.157 |
|
| \begin{align*}
1&=\left (3 \,{\mathrm e}^{y}-2 x \right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.189 |
|
| \begin{align*}
y^{\prime }-4 y^{2} {\mathrm e}^{x}&=y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.176 |
|
| \begin{align*}
x y^{\prime }+\left (x +1\right ) y&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.904 |
|
| \begin{align*}
y^{\prime }&=\frac {x y^{2}-\frac {\sin \left (2 x \right )}{2}}{\left (-x^{2}+1\right ) y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.568 |
|
| \begin{align*}
\frac {\sqrt {x}\, y^{\prime }}{y}&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.043 |
|
| \begin{align*}
5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.270 |
|
| \begin{align*}
2 x y y^{\prime }+\ln \left (x \right )&=-1-y^{2} \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.530 |
|
| \begin{align*}
\left (2-x \right ) y^{\prime }&=y+2 \left (2-x \right )^{5} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.840 |
|
| \begin{align*}
x y^{\prime }&=-\frac {1}{\ln \left (x \right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x y +x^{2}}{3 y^{2}+2 x y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
24.655 |
|
| \begin{align*}
4 x y y^{\prime }&=8 x^{2}+5 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
36.504 |
|
| \begin{align*}
y^{\prime }+y-y^{{1}/{4}}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
9.157 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=4+x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| \begin{align*}
x^{\prime }&=x+2 y+\sin \left (t \right ) \\
y^{\prime }&=-x+y-\cos \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.971 |
|
| \begin{align*}
x^{\prime }&=-2 x t +y \\
y^{\prime }&=3 x-y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.044 |
|
| \begin{align*}
x^{\prime }&=x+2 y+4 \\
y^{\prime }&=-2 x+y-3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.023 |
|
| \begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.368 |
|
| \begin{align*}
x^{\prime }&=-x+y t \\
y^{\prime }&=x t -y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.043 |
|
| \begin{align*}
x^{\prime }&=x+y+4 \\
y^{\prime }&=-2 x+\sin \left (t \right ) y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✗ |
✗ |
0.042 |
|
| \begin{align*}
x^{\prime }&=3 x-4 y \\
y^{\prime }&=x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.731 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=3 x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=-2 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+2 \sin \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.014 |
|
| \begin{align*}
x^{\prime }&=x-4 y+2 t \\
y^{\prime }&=x-3 y-3 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| \begin{align*}
x^{\prime }&=-x+y+1 \\
y^{\prime }&=x+y-3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.193 |
|
| \begin{align*}
x^{\prime }&=-x-4 y-4 \\
y^{\prime }&=x-y-6 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| \begin{align*}
x^{\prime }&=-\frac {x}{4}-\frac {3 y}{4}+8 \\
y^{\prime }&=\frac {x}{2}+y-\frac {23}{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.174 |
|
| \begin{align*}
x^{\prime }&=-2 x+y-11 \\
y^{\prime }&=-5 x+4 y-35 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.955 |
|
| \begin{align*}
x^{\prime }&=x+y-3 \\
y^{\prime }&=-x+y+1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| \begin{align*}
x^{\prime }&=-5 x+4 y-35 \\
y^{\prime }&=-2 x+y-11 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.982 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=2 x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=3 x-4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=3 x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=4 x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \begin{align*}
x^{\prime }&=4 x-3 y \\
y^{\prime }&=8 x-6 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| \begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=\frac {3 x}{4}+\frac {5 y}{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
x^{\prime }&=-\frac {3 x}{4}-\frac {7 y}{4} \\
y^{\prime }&=\frac {x}{4}+\frac {5 y}{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| \begin{align*}
x^{\prime }&=-\frac {x}{4}-\frac {3 y}{4} \\
y^{\prime }&=\frac {x}{2}+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| \begin{align*}
x^{\prime }&=5 x-y \\
y^{\prime }&=3 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-5 x+4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \begin{align*}
x^{\prime }&=3 x+6 y \\
y^{\prime }&=-x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=3 x-4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.652 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=3 x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 5 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
x^{\prime }&=5 x-y \\
y^{\prime }&=3 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-5 x+4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.650 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=4 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.862 |
|
| \begin{align*}
x^{\prime }&=-x-4 y \\
y^{\prime }&=x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| \begin{align*}
x^{\prime }&=2 x-\frac {5 y}{2} \\
y^{\prime }&=\frac {9 x}{5}-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=5 x-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.859 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=-5 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
x^{\prime }&=-x-4 y \\
y^{\prime }&=x-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= -3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| \begin{align*}
x^{\prime }&=x-5 y \\
y^{\prime }&=x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| \begin{align*}
x^{\prime }&=-3 x+2 y \\
y^{\prime }&=-x-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| \begin{align*}
x^{\prime }&=\frac {3 x}{4}-2 y \\
y^{\prime }&=x-\frac {5 y}{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| \begin{align*}
x^{\prime }&=-\frac {4 x}{5}+2 y \\
y^{\prime }&=-x+\frac {6 y}{5} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.864 |
|
| \begin{align*}
x^{\prime }&=a x+y \\
y^{\prime }&=-x+a y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| \begin{align*}
x^{\prime }&=-5 y \\
y^{\prime }&=x+a y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.599 |
|
| \begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=a x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=a x+\frac {5 y}{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| \begin{align*}
x^{\prime }&=-x+a y \\
y^{\prime }&=-x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| \begin{align*}
x^{\prime }&=3 x+a y \\
y^{\prime }&=-6 x-4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| \begin{align*}
x^{\prime }&=a x+10 y \\
y^{\prime }&=-x-4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.563 |
|
| \begin{align*}
x^{\prime }&=4 x+a y \\
y^{\prime }&=8 x-6 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.955 |
|
| \begin{align*}
i^{\prime }&=\frac {i}{2}-\frac {v}{8} \\
v^{\prime }&=2 i-\frac {v}{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| \begin{align*}
x^{\prime }&=3 x-4 y \\
y^{\prime }&=x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=-\frac {3 x}{4}-\frac {y}{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \begin{align*}
x^{\prime }&=-\frac {3 x}{2}+y \\
y^{\prime }&=-\frac {x}{4}-\frac {y}{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
x^{\prime }&=-3 x+\frac {5 y}{2} \\
y^{\prime }&=-\frac {5 x}{2}+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| \begin{align*}
x^{\prime }&=-x-\frac {y}{2} \\
y^{\prime }&=2 x-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
x^{\prime }&=2 x+\frac {y}{2} \\
y^{\prime }&=-\frac {x}{2}+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \begin{align*}
x^{\prime }&=x-4 y \\
y^{\prime }&=4 x-7 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| \begin{align*}
x^{\prime }&=-\frac {5 x}{2}+\frac {3 y}{2} \\
y^{\prime }&=-\frac {3 x}{2}+\frac {y}{2} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
x^{\prime }&=2 x+\frac {3 y}{2} \\
y^{\prime }&=-\frac {3 x}{2}-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= -2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=-\frac {3 x}{4}-\frac {y}{4} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| \begin{align*}
x^{\prime }&=-3 x+\frac {5 y}{2} \\
y^{\prime }&=-\frac {5 x}{2}+2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.509 |
|
| \begin{align*}
x^{\prime }&=2 x+\frac {y}{2} \\
y^{\prime }&=-\frac {x}{2}+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.463 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.456 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=8 x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=8 x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.691 |
|