| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 201 |
\begin{align*}
2 x^{3} y y^{\prime \prime \prime }+6 x^{3} y^{\prime } y^{\prime \prime }+18 x^{2} y y^{\prime \prime }+18 {y^{\prime }}^{2} x^{2}+36 x y y^{\prime }+6 y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.044 |
|
| 202 |
\begin{align*}
x^{\prime } t +2 x&=15 y \\
t y^{\prime }&=x \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.044 |
|
| 203 |
\begin{align*}
x^{\prime }&=-2 x t +y \\
y^{\prime }&=3 x-y \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.044 |
|
| 204 |
\begin{align*}
x^{\prime }&=-x+y+y^{2} \\
y^{\prime }&=-2 y-x^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.044 |
|
| 205 |
\begin{align*}
y^{\prime \prime }&=x-2 \\
x^{\prime \prime }&=y+2 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.044 |
|
| 206 |
\begin{align*}
x^{\prime }+y^{\prime }&=\cos \left (t \right ) \\
x+y^{\prime \prime }&=2 \\
\end{align*}
With initial conditions \begin{align*}
x \left (\pi \right ) &= 2 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.044 |
|
| 207 |
\begin{align*}
3 x y^{\prime \prime \prime }-4 y x&=\cos \left (y\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.044 |
|
| 208 |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{4}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.044 |
|
| 209 |
\begin{align*}
y^{\left (5\right )}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.044 |
|
| 210 |
\begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.045 |
|
| 211 |
\begin{align*}
y^{\prime \prime \prime }-7 y^{\prime }+6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.045 |
|
| 212 |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.045 |
|
| 213 |
\begin{align*}
t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
0.045 |
|
| 214 |
\begin{align*}
-2 y x +y^{\prime } \left (x^{2}+2\right )-2 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.045 |
|
| 215 |
\begin{align*}
y^{\prime \prime \prime \prime }+\left (a \,x^{2}+b \lambda +c \right ) y^{\prime \prime }+\left (a \,x^{2}+\beta \lambda +\gamma \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.045 |
|
| 216 |
\begin{align*}
x^{2} y^{\prime \prime \prime }+x \left (-1+y\right ) y^{\prime \prime }+{y^{\prime }}^{2} x +\left (1-y\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.045 |
|
| 217 |
\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*} |
✗ |
✓ |
✓ |
✓ |
0.045 |
|
| 218 |
\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*} |
✗ |
✗ |
✗ |
✗ |
0.045 |
|
| 219 |
\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*} |
✗ |
✓ |
✗ |
✗ |
0.045 |
|
| 220 |
\begin{align*}
y_{1}^{\prime }&={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2} \\
y_{2}^{\prime }&=\frac {y_{1}}{\left (x -2\right )^{2}} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (3\right ) &= 1 \\
y_{2} \left (3\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.045 |
|
| 221 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.045 |
|
| 222 |
\begin{align*}
x^{\prime }&=-10 x+4 \,{\mathrm e}^{y}-4 \cos \left (y^{2}\right ) \\
y^{\prime }&=2 \,{\mathrm e}^{x}-2-y+x^{4} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.045 |
|
| 223 |
\begin{align*}
9 y^{\prime \prime \prime }+12 y^{\prime \prime }+4 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 224 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 225 |
\begin{align*}
3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 226 |
\begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 227 |
\begin{align*}
x^{\prime }&=1+y t \\
y^{\prime }&=-x t +y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.046 |
|
| 228 |
\begin{align*}
f^{\prime }\left (x \right ) y+2 f \left (x \right ) y^{\prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.046 |
|
| 229 |
\begin{align*}
x y^{\prime \prime \prime }+3 y^{\prime \prime }-a \,x^{2} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| 230 |
\begin{align*}
x^{2} y^{\prime \prime \prime }-2 \left (n +1\right ) x y^{\prime \prime }+\left (a \,x^{2}+6 n \right ) y^{\prime }-2 a x y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| 231 |
\begin{align*}
x^{2} y^{\prime \prime \prime }-\left (x^{4}-6 x \right ) y^{\prime \prime }-\left (2 x^{3}-6\right ) y^{\prime }+2 x^{2} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| 232 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+\left (-\nu ^{2}+1\right ) x y^{\prime }+\left (a \,x^{3}+\nu ^{2}-1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| 233 |
\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*} |
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| 234 |
\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*} |
✗ |
✓ |
✓ |
✓ |
0.046 |
|
| 235 |
\begin{align*}
a x^{\prime }&=\left (b -c \right ) y z \\
b y^{\prime }&=\left (c -a \right ) z x \\
c z^{\prime }&=\left (a -b \right ) x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| 236 |
\begin{align*}
y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 237 |
\begin{align*}
x^{\prime }&=-4 x-2 y+\frac {2}{{\mathrm e}^{t}-1} \\
y^{\prime }&=6 x+3 y-\frac {3}{{\mathrm e}^{t}-1} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.046 |
|
| 238 |
\begin{align*}
x^{\prime }&=2 x-7 x y-a x \\
y^{\prime }&=-y+4 x y-a y \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.046 |
|
| 239 |
\begin{align*}
x^{\prime }&=x-4 x y \\
y^{\prime }&=-2 y+x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| 240 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 241 |
\begin{align*}
x^{\prime \prime }+y^{\prime }+6 x&=0 \\
y^{\prime \prime }-x^{\prime }+6 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.046 |
|
| 242 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+\left (1-t \right ) x_{2} \\
x_{2}^{\prime }&=\frac {x_{1}}{t}-x_{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.046 |
|
| 243 |
\begin{align*}
y_{1}^{\prime }&=y_{2} t \\
y_{2}^{\prime }&=-y_{1} t \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.046 |
|
| 244 |
\begin{align*}
y_{1}^{\prime }&=\frac {y_{1}}{t}+1 \\
y_{2}^{\prime }&=\frac {y_{2}}{t}+t \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (1\right ) &= 1 \\
y_{2} \left (1\right ) &= 2 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| 245 |
\begin{align*}
x^{\prime }&=-y+x^{2} y^{3} \\
y^{\prime }&=x-x^{3} y^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.046 |
|
| 246 |
\begin{align*}
2 y^{\prime \prime \prime }+7 y^{\prime \prime }+7 y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 247 |
\begin{align*}
y^{\prime \prime \prime }+27 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 248 |
\begin{align*}
x^{2} y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.047 |
|
| 249 |
\begin{align*}
x^{\prime }&=x-y^{2} \\
y^{\prime }&=x^{2}-y \\
z^{\prime }&={\mathrm e}^{z}-x \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.047 |
|
| 250 |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 251 |
\begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 252 |
\begin{align*}
y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 253 |
\begin{align*}
y^{\prime \prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 254 |
\begin{align*}
\left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 x y^{\prime }-4 y&=8 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.047 |
|
| 255 |
\begin{align*}
x^{6} y^{\prime \prime \prime }+6 x^{5} y^{\prime \prime }+a y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.047 |
|
| 256 |
\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*} |
✗ |
✓ |
✓ |
✓ |
0.047 |
|
| 257 |
\begin{align*}
y^{\prime \prime \prime \prime }-a^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 258 |
\begin{align*}
x^{\prime }-y t&=1 \\
y^{\prime }-x^{\prime } t&=3 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.047 |
|
| 259 |
\begin{align*}
x^{\prime \prime }&=y+4 \,{\mathrm e}^{-2 t} \\
y^{\prime \prime }&=x-{\mathrm e}^{-2 t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.047 |
|
| 260 |
\begin{align*}
3 y^{\prime \prime \prime }+4 y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 261 |
\begin{align*}
y^{\prime \prime \prime \prime }-\ln \left (x +1\right ) y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✓ |
✓ |
✗ |
0.047 |
|
| 262 |
\begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }-17 y^{\prime }+60 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.048 |
|
| 263 |
\begin{align*}
y^{\prime \prime \prime }-9 y^{\prime \prime }+23 y^{\prime }-15 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.048 |
|
| 264 |
\begin{align*}
f \left (x \right ) y+y^{\prime }+f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.048 |
|
| 265 |
\begin{align*}
x^{3} \left (x +1\right ) y^{\prime \prime \prime }-\left (4 x +2\right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-4 \left (1+3 x \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.048 |
|
| 266 |
\begin{align*}
x^{{5}/{2}} y^{\left (5\right )}-a y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.048 |
|
| 267 |
\begin{align*}
{y^{\prime \prime }}^{2}-a y-b&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.048 |
|
| 268 |
\begin{align*}
x^{\prime } t&=2 x-t \\
t^{3} y^{\prime }&=-x+t^{2} y+t \\
t^{4} z^{\prime }&=-x-t^{2} y+t^{3} z+t \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.048 |
|
| 269 |
\begin{align*}
a t x^{\prime }&=b c \left (y-z\right ) \\
b t y^{\prime }&=c a \left (-x+z\right ) \\
c t z^{\prime }&=a b \left (x-y\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.048 |
|
| 270 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.048 |
|
| 271 |
\begin{align*}
-y+x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.048 |
|
| 272 |
\begin{align*}
x^{\prime }+y t&=-1 \\
x^{\prime }+y^{\prime }&=2 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.048 |
|
| 273 |
\begin{align*}
y y^{\prime \prime \prime }+x y^{\prime }+y&=x^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.048 |
|
| 274 |
\begin{align*}
x_{1}^{\prime }&=2 \sin \left (t \right ) x_{1}+\ln \left (t \right ) x_{2} \\
x_{2}^{\prime }&=\frac {x_{1}}{t -2}+\frac {{\mathrm e}^{t} x_{2}}{t +1} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (3\right ) &= 0 \\
x_{2} \left (3\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✗ |
✓ |
0.048 |
|
| 275 |
\begin{align*}
x^{\prime }&=2 x+y^{2} \\
y^{\prime }&=3 y-x^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.048 |
|
| 276 |
\begin{align*}
x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.048 |
|
| 277 |
\begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 278 |
\begin{align*}
x^{\prime }&=x t -{\mathrm e}^{t} y+\cos \left (t \right ) \\
y^{\prime }&={\mathrm e}^{-t} x+t^{2} y-\sin \left (t \right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.049 |
|
| 279 |
\begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+16 y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 280 |
\begin{align*}
y^{\prime \prime \prime \prime }&=16 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 281 |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 282 |
\begin{align*}
t^{2} \left (t +3\right ) y^{\prime \prime \prime }-3 t \left (t +2\right ) y^{\prime \prime }+6 \left (t +1\right ) y^{\prime }-6 y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| 283 |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 284 |
\begin{align*}
2 y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 285 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 286 |
\begin{align*}
2 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 287 |
\begin{align*}
4 y^{\prime \prime \prime }-3 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 288 |
\begin{align*}
x_{1}^{\prime }&=-\tan \left (t \right ) x_{1}+3 \cos \left (t \right )^{2} \\
x_{2}^{\prime }&=x_{1}+\tan \left (t \right ) x_{2}+2 \sin \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 4 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.049 |
|
| 289 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 290 |
\begin{align*}
y^{\prime \prime \prime }+3 y^{\prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 291 |
\begin{align*}
y^{\prime \prime \prime }-\left (6 k^{2} \sin \left (x \right )^{2}+a \right ) y^{\prime }+b y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.049 |
|
| 292 |
\begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime }+10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 293 |
\begin{align*}
a \,x^{2} y-6 y^{\prime }+x^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| 294 |
\begin{align*}
x^{2} y^{\prime \prime \prime }-3 \left (p +q \right ) x y^{\prime \prime }+3 p \left (3 q +1\right ) y^{\prime }-x^{2} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| 295 |
\begin{align*}
x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-4 \left (3 x^{2}+1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| 296 |
\begin{align*}
x^{2} y^{\prime \prime \prime \prime }+2 x y^{\prime \prime \prime }+a y-b \,x^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.049 |
|
| 297 |
\begin{align*}
y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x \\
y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (-1\right ) &= 3 \\
y_{2} \left (-1\right ) &= -3 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.049 |
|
| 298 |
\begin{align*}
y_{1}^{\prime }&=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\
y_{2}^{\prime }&=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (2\right ) &= 1 \\
y_{2} \left (2\right ) &= -1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.049 |
|
| 299 |
\begin{align*}
x^{\prime }&=\frac {x}{y} \\
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.049 |
|
| 300 |
\begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|