| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 101 |
\begin{align*}
\left (t^{2}+1\right ) x^{\prime }&=-t x+y \\
\left (t^{2}+1\right ) y^{\prime }&=-x-t y \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.029 |
|
| 102 |
\begin{align*}
x^{\prime }&=1+5 y \\
y^{\prime }&=1-6 x^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.029 |
|
| 103 |
\begin{align*}
x^{\prime \prime }-3 x-4 y&=0 \\
x+y^{\prime \prime }+y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.029 |
|
| 104 |
\begin{align*}
w^{\prime \prime }-2 z&=0 \\
w^{\prime }+y^{\prime }-z&=2 t \\
w^{\prime }-2 y+z^{\prime \prime }&=0 \\
\end{align*} With initial conditions \begin{align*}
w \left (0\right ) &= 0 \\
w^{\prime }\left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
z^{\prime }\left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.029 |
|
| 105 |
\begin{align*}
x^{\prime }&=y z \\
y^{\prime }&=x z \\
z^{\prime }&=x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.029 |
|
| 106 |
\begin{align*}
x^{\prime }&=x y \\
y^{\prime }&=1+y^{2} \\
z^{\prime }&=z \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.029 |
|
| 107 |
\begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.029 |
|
| 108 |
\begin{align*}
x^{{5}/{2}} y^{\left (5\right )}-a y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.030 |
|
| 109 |
\begin{align*}
y^{3} y^{\prime }-y^{\prime } y^{\prime \prime }+y y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.030 |
|
| 110 |
\begin{align*}
15 {y^{\prime }}^{3}-18 y y^{\prime } y^{\prime \prime }+4 y^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.030 |
|
| 111 |
\begin{align*}
40 {y^{\prime }}^{3}-45 y y^{\prime } y^{\prime \prime }+9 y^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.030 |
|
| 112 |
\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*} |
✗ |
✗ |
✗ |
✗ |
0.030 |
|
| 113 |
\begin{align*}
\sin \left (y^{\prime \prime }\right )+y y^{\prime \prime \prime \prime }&=1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.030 |
|
| 114 |
\begin{align*}
x^{\prime }&=\frac {y}{x-y} \\
y^{\prime }&=\frac {x}{x-y} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.030 |
|
| 115 |
\begin{align*}
x^{\prime }&=3 x-x^{2} \\
y^{\prime }&=2 x y-3 y+2 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.030 |
|
| 116 |
\begin{align*}
x^{\prime }&=\left (2+x\right ) \left (-x+y\right ) \\
y^{\prime }&=y-x^{2}-y^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.030 |
|
| 117 |
\begin{align*}
x^{\prime }&=x+4 y-y^{2} \\
y^{\prime }&=6 x-y+2 x y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.030 |
|
| 118 |
\begin{align*}
x^{\prime }&=\sin \left (x\right )-4 y \\
y^{\prime }&=\sin \left (2 x\right )-5 y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.030 |
|
| 119 |
\begin{align*}
y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.030 |
|
| 120 |
\begin{align*}
y^{\prime \prime \prime }+x^{2} y&={\mathrm e}^{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.030 |
|
| 121 |
\begin{align*}
y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.030 |
|
| 122 |
\begin{align*}
x^{\prime }&=-x+x^{2} \\
y^{\prime }&=-3 y+x y \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.030 |
|
| 123 |
\begin{align*}
x^{\prime }&=-x+x y \\
y^{\prime }&=y+\left (x^{2}+y^{2}\right )^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.030 |
|
| 124 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y&=40 \,{\mathrm e}^{3 t} \\
x^{\prime }+x-y^{\prime }&=36 \,{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 3 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.031 |
|
| 125 |
\begin{align*}
-x^{2} y+3 y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.031 |
|
| 126 |
\begin{align*}
y^{2}-2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=x^{3} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.031 |
|
| 127 |
\begin{align*}
t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
0.031 |
|
| 128 |
\begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime } x +4 x^{2} y^{\prime }+8 x^{3} y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.031 |
|
| 129 |
\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*} |
✗ |
✗ |
✗ |
✗ |
0.031 |
|
| 130 |
\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*} |
✗ |
✓ |
✓ |
✓ |
0.031 |
|
| 131 |
\begin{align*}
x^{\prime }&=x \left (y-z\right ) \\
y^{\prime }&=y \left (z-x\right ) \\
z^{\prime }&=z \left (x-y\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.031 |
|
| 132 |
\begin{align*}
x^{\prime }&=x \left (y^{2}-z^{2}\right ) \\
y^{\prime }&=y \left (z^{2}-x^{2}\right ) \\
z^{\prime }&=z \left (x^{2}-y^{2}\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.031 |
|
| 133 |
\begin{align*}
x^{\prime }&=-x \,y^{2}+x+y \\
y^{\prime }&=y \,x^{2}-x-y \\
z^{\prime }&=y^{2}-x^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.031 |
|
| 134 |
\begin{align*}
y^{\prime \prime \prime }+y x&=\cosh \left (x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.031 |
|
| 135 |
\begin{align*}
x_{1}^{\prime }&=\frac {x_{1}^{2}}{x_{2}} \\
x_{2}^{\prime }&=x_{2}-x_{1} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.031 |
|
| 136 |
\begin{align*}
x^{\prime }&=\frac {y+t}{x+y} \\
y^{\prime }&=\frac {t +x}{x+y} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.031 |
|
| 137 |
\begin{align*}
x^{\prime }&=y \left (2-x-y\right ) \\
y^{\prime }&=-x-y-2 x y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.031 |
|
| 138 |
\begin{align*}
y^{\prime }+\frac {2 z}{x^{2}}&=1 \\
z^{\prime }+y&=x \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.031 |
|
| 139 |
\begin{align*}
x y^{\prime }+y x^{\prime }&=t^{2} \\
2 x^{\prime \prime }-y^{\prime }&=5 t \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.031 |
|
| 140 |
\begin{align*}
x y^{\prime \prime \prime }+4 y^{\prime \prime } x -y x&=1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.031 |
|
| 141 |
\begin{align*}
y-y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.032 |
|
| 142 |
\begin{align*}
a y y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.032 |
|
| 143 |
\begin{align*}
y^{3} y^{\prime }-y^{\prime } y^{\prime \prime }+y y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.032 |
|
| 144 |
\begin{align*}
\left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 y^{\prime } x -4 y&=8 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.032 |
|
| 145 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✓ |
✓ |
✗ |
0.032 |
|
| 146 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+\left (2 x^{3}-x^{2}\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✓ |
✓ |
✗ |
0.032 |
|
| 147 |
\begin{align*}
a y+2 a x y^{\prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.032 |
|
| 148 |
\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*} |
✗ |
✓ |
✗ |
✗ |
0.032 |
|
| 149 |
\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*} |
✗ |
✓ |
✓ |
✓ |
0.032 |
|
| 150 |
\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*} |
✗ |
✓ |
✓ |
✓ |
0.032 |
|
| 151 |
\begin{align*}
x^{\prime }&=\frac {x^{2}}{2}-\frac {y}{24} \\
y^{\prime }&=2 x y-3 z \\
z^{\prime }&=3 x z-\frac {y^{2}}{6} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.032 |
|
| 152 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.032 |
|
| 153 |
\begin{align*}
{y^{\prime \prime \prime }}^{2}+\sqrt {y}&=\sin \left (x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.032 |
|
| 154 |
\begin{align*}
x^{\prime }&=\frac {y+t}{x+y} \\
y^{\prime }&=\frac {x-t}{x+y} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.032 |
|
| 155 |
\begin{align*}
x^{\prime }&=\frac {t -y}{-x+y} \\
y^{\prime }&=\frac {x-t}{-x+y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.032 |
|
| 156 |
\begin{align*}
x^{\prime }&=\sin \left (x\right ) \cos \left (y\right ) \\
y^{\prime }&=\cos \left (x\right ) \sin \left (y\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.032 |
|
| 157 |
\begin{align*}
x^{\prime }&=-x+2 x y \\
y^{\prime }&=y-x^{2}-y^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.032 |
|
| 158 |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{z} \\
z^{\prime }&=\frac {y}{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.032 |
|
| 159 |
\begin{align*}
t x^{\prime }&=t -2 x \\
y^{\prime } t&=t x+t y+2 x-t \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.032 |
|
| 160 |
\begin{align*}
w^{\prime \prime }-y+2 z&=3 \,{\mathrm e}^{-t} \\
-2 w^{\prime }+2 y^{\prime }+z&=0 \\
2 w^{\prime }-2 y+z^{\prime }+2 z^{\prime \prime }&=0 \\
\end{align*} With initial conditions \begin{align*}
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 2 \\
z^{\prime }\left (0\right ) &= -2 \\
w \left (0\right ) &= 1 \\
w^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.032 |
|
| 161 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-\sin \left (x\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.032 |
|
| 162 |
\begin{align*}
x^{\prime }&=5 x-6 y+x y \\
y^{\prime }&=6 x-7 y-x y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.032 |
|
| 163 |
\begin{align*}
x^{\prime }&=y+x^{2}-x y \\
y^{\prime }&=-2 x+3 y+y^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.032 |
|
| 164 |
\begin{align*}
t y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }+t y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| 165 |
\begin{align*}
y^{\prime \prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.033 |
|
| 166 |
\begin{align*}
-y y^{\prime }+{y^{\prime }}^{2}+y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.033 |
|
| 167 |
\begin{align*}
x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| 168 |
\begin{align*}
x y^{\prime \prime \prime }+3 y^{\prime \prime }+y x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| 169 |
\begin{align*}
a \,x^{2} y-6 y^{\prime }+x^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| 170 |
\begin{align*}
x^{6} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| 171 |
\begin{align*}
f y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.033 |
|
| 172 |
\begin{align*}
\left (x^{2}+y^{2}-t^{2}\right ) x^{\prime }&=-2 t x \\
\left (x^{2}+y^{2}-t^{2}\right ) y^{\prime }&=-2 t y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| 173 |
\begin{align*}
x^{\prime \prime }&=a \,{\mathrm e}^{2 x}-{\mathrm e}^{-x}+{\mathrm e}^{-2 x} \cos \left (y\right )^{2} \\
y^{\prime \prime }&={\mathrm e}^{-2 x} \sin \left (y\right ) \cos \left (y\right )-\frac {\sin \left (y\right )}{\cos \left (y\right )^{3}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.033 |
|
| 174 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.033 |
|
| 175 |
\begin{align*}
-2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+\left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| 176 |
\begin{align*}
x^{\prime \prime \prime }+x^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.033 |
|
| 177 |
\begin{align*}
{\mathrm e}^{t} x^{\prime }&=\frac {1}{y} \\
{\mathrm e}^{t} y^{\prime }&=\frac {1}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| 178 |
\begin{align*}
x^{\prime }&=2 y \,x^{2}-3 x^{2}-4 y \\
y^{\prime }&=-2 x \,y^{2}+6 x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| 179 |
\begin{align*}
x^{\prime }&=-2 y+x y \\
y^{\prime }&=x+4 x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| 180 |
\begin{align*}
t x^{\prime }+y&=0 \\
y^{\prime } t +x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| 181 |
\begin{align*}
x^{\prime }&=2 x-7 x y-a x \\
y^{\prime }&=-y+4 x y-a y \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.033 |
|
| 182 |
\begin{align*}
x^{\prime }&=2 x-2 x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| 183 |
\begin{align*}
y^{\prime }&=-\sqrt {1-y^{2}} \\
x^{\prime }&=x+2 y \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| 184 |
\begin{align*}
x^{\prime }+3 y^{\prime }&=x y \\
3 x^{\prime }-y^{\prime }&=\sin \left (t \right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.033 |
|
| 185 |
\begin{align*}
y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.033 |
|
| 186 |
\begin{align*}
y^{\prime }&=-2 \\
z^{\prime }&=x \,{\mathrm e}^{2 x +y} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| 187 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✓ |
✓ |
✗ |
0.034 |
|
| 188 |
\begin{align*}
\left (2 x -1\right ) y^{\prime \prime \prime }-8 y^{\prime } x +8 y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.034 |
|
| 189 |
\begin{align*}
x^{2} y^{\prime \prime \prime }-5 y^{\prime \prime } x +\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.034 |
|
| 190 |
\begin{align*}
y^{\prime \prime \prime }+y x&=\sin \left (x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.034 |
|
| 191 |
\begin{align*}
y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x} \\
y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.034 |
|
| 192 |
\begin{align*}
y^{\left (5\right )}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.034 |
|
| 193 |
\begin{align*}
x_{1}^{\prime }&={\mathrm e}^{t -x_{1}} \\
x_{2}^{\prime }&=2 \,{\mathrm e}^{x_{1}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.034 |
|
| 194 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.034 |
|
| 195 |
\begin{align*}
x^{\prime }&=x-x^{2}-x y \\
y^{\prime }&=\frac {y}{2}-\frac {y^{2}}{4}-\frac {3 x y}{4} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.034 |
|
| 196 |
\begin{align*}
x^{\prime }&=x \left (1-x-y\right ) \\
y^{\prime }&=y \left (\frac {3}{4}-y-\frac {x}{2}\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.034 |
|
| 197 |
\begin{align*}
t x^{\prime }-x-3 y&=t \\
y^{\prime } t -x+y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.034 |
|
| 198 |
\begin{align*}
x^{\prime }&=3 x-2 y+\left (x^{2}+y^{2}\right )^{2} \\
y^{\prime }&=4 x-y+\left (x^{2}-y^{2}\right )^{5} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.034 |
|
| 199 |
\begin{align*}
y_{1}^{\prime }&=\sin \left (t \right ) y_{1} \\
y_{2}^{\prime }&=y_{1}+\cos \left (t \right ) y_{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.034 |
|
| 200 |
\begin{align*}
x^{3} \left (x +1\right ) y^{\prime \prime \prime }-\left (2+4 x \right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✓ |
✓ |
✗ |
0.035 |
|