| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 301 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 302 |
\begin{align*}
y^{\prime \prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 303 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 304 |
\begin{align*}
x x^{\prime }+y&=2 t \\
y^{\prime }+2 x^{2}&=1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| 305 |
\begin{align*}
x^{\prime }&=x \left (3-y\right ) \\
y^{\prime }&=y \left (x-5\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| 306 |
\begin{align*}
x^{\prime \prime }&=1 \\
x^{\prime }+x+y^{\prime \prime }-9 y+z^{\prime }+z&=0 \\
5 x+z^{\prime \prime }-4 z&=2 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
z^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| 307 |
\begin{align*}
y_{1}^{\prime }&=-\frac {y_{2}}{t}+1 \\
y_{2}^{\prime }&=\frac {y_{1}}{t}+\frac {2 y_{2}}{t}-1 \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (1\right ) &= 2 \\
y_{2} \left (1\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| 308 |
\begin{align*}
y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| 309 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| 310 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| 311 |
\begin{align*}
a \,x^{2} y+6 y^{\prime }+6 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.050 |
|
| 312 |
\begin{align*}
x^{2} y^{\prime \prime \prime \prime }+\left (2 n -2 \nu +4\right ) x y^{\prime \prime \prime }+\left (n -\nu +1\right ) \left (n -\nu +2\right ) y^{\prime \prime }-\frac {b^{4} y}{16}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.050 |
|
| 313 |
\begin{align*}
x^{10} y^{\left (5\right )}-a y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.050 |
|
| 314 |
\begin{align*}
x^{\prime }&=-\frac {1}{y} \\
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.050 |
|
| 315 |
\begin{align*}
x^{\prime }&=\frac {y}{x-y} \\
y^{\prime }&=\frac {x}{x-y} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.050 |
|
| 316 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| 317 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| 318 |
\begin{align*}
w^{\prime \prime }+y+z&=-1 \\
w+y^{\prime \prime }-z&=0 \\
-w-y^{\prime }+z^{\prime \prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
w \left (0\right ) &= 0 \\
w^{\prime }\left (0\right ) &= 1 \\
z \left (0\right ) &= -1 \\
z^{\prime }\left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.050 |
|
| 319 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| 320 |
\begin{align*}
y_{1}^{\prime }&=y_{1} t +y_{2} t \\
y_{2}^{\prime }&=-y_{1} t -y_{2} t \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 4 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.050 |
|
| 321 |
\begin{align*}
y_{1}^{\prime }&=\frac {y_{1}}{t}+y_{2} \\
y_{2}^{\prime }&=-y_{1}+\frac {y_{2}}{t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (\pi \right ) &= 1 \\
y_{2} \left (\pi \right ) &= -1 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.050 |
|
| 322 |
\begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2} \\
y_{2}^{\prime }&=\frac {y_{1}}{t}+\frac {y_{2}}{t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (1\right ) &= -3 \\
y_{2} \left (1\right ) &= 4 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.050 |
|
| 323 |
\begin{align*}
y_{1}^{\prime }&=y_{1} t +y_{2} t +4 t \\
y_{2}^{\prime }&=-y_{1} t -y_{2} t +4 t \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 4 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.050 |
|
| 324 |
\begin{align*}
y^{\prime \prime \prime }-8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| 325 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| 326 |
\begin{align*}
y^{\prime \prime \prime }+5 y^{\prime \prime }+9 y^{\prime }+5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| 327 |
\begin{align*}
5 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.051 |
|
| 328 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.051 |
|
| 329 |
\begin{align*}
y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+\left (a +b -1\right ) x y^{\prime }-a b y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.051 |
|
| 330 |
\begin{align*}
a^{3} x^{3} y+3 a^{2} x^{2} y^{\prime }+3 a x y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.051 |
|
| 331 |
\begin{align*}
x y^{\prime \prime \prime }-\left (x +2 v \right ) y^{\prime \prime }-\left (x -2 v -1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.051 |
|
| 332 |
\begin{align*}
2 x \left (x -1\right ) y^{\prime \prime \prime }+3 \left (2 x -1\right ) y^{\prime \prime }+\left (2 a x +b \right ) y^{\prime }+a y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.051 |
|
| 333 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+\left (4 x^{3}+\left (-4 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (4 \nu ^{2}-1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.051 |
|
| 334 |
\begin{align*}
\left (x +3\right ) x^{2} y^{\prime \prime \prime }-3 x \left (x +2\right ) y^{\prime \prime }+6 \left (x +1\right ) y^{\prime }-6 y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.051 |
|
| 335 |
\begin{align*}
x y^{\left (5\right )}-m n y^{\prime \prime \prime \prime }+a x y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.051 |
|
| 336 |
\begin{align*}
z^{\prime \prime }+y^{\prime }&=\cos \left (t \right ) \\
y^{\prime \prime }-z&=\sin \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
z \left (0\right ) &= -1 \\
z^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.051 |
|
| 337 |
\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*} |
✗ |
✓ |
✓ |
✓ |
0.051 |
|
| 338 |
\begin{align*}
2 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }+y x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.051 |
|
| 339 |
\begin{align*}
x y^{\prime \prime \prime }+4 x y^{\prime \prime }-y x&=1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.051 |
|
| 340 |
\begin{align*}
x^{\prime \prime }&=4 y+{\mathrm e}^{t} \\
y^{\prime \prime }&=4 x-{\mathrm e}^{t} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.051 |
|
| 341 |
\begin{align*}
x^{\prime }&=x+2 y-\sin \left (y\right )^{2} \\
y^{\prime }&=-x-3 y+x \left ({\mathrm e}^{\frac {x^{2}}{2}}-1\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.051 |
|
| 342 |
\begin{align*}
y^{\prime \prime \prime \prime }+\alpha y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.051 |
|
| 343 |
\begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.051 |
|
| 344 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| 345 |
\begin{align*}
y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+24 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| 346 |
\begin{align*}
2 y y^{\prime \prime \prime }+2 \left (y+3 y^{\prime }\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}&=\sin \left (x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.052 |
|
| 347 |
\begin{align*}
36 y^{\prime \prime \prime \prime }-37 y^{\prime \prime }+4 y^{\prime }+5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| 348 |
\begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| 349 |
\begin{align*}
y^{\prime \prime \prime }-6 x y^{\prime \prime }+2 \left (4 x^{2}+2 a -1\right ) y^{\prime }-8 a x y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.052 |
|
| 350 |
\begin{align*}
2 x y^{\prime \prime \prime }-4 \left (x +\nu -1\right ) y^{\prime \prime }+\left (2 x +6 \nu -5\right ) y^{\prime }+\left (1-2 \nu \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.052 |
|
| 351 |
\begin{align*}
-2 \left (x^{2}+4\right ) y+x \left (x^{2}+8\right ) y^{\prime }-4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.052 |
|
| 352 |
\begin{align*}
y^{\prime \prime \prime \prime }+a \left (b x -1\right ) y^{\prime \prime }+a b y^{\prime }+\lambda y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.052 |
|
| 353 |
\begin{align*}
x^{2} y^{\prime \prime \prime \prime }+6 x y^{\prime \prime \prime }+6 y^{\prime \prime }-\lambda ^{2} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.052 |
|
| 354 |
\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 (\cos \left (t \right ) t -\sin \left (t \right )\right ) x+t \left (1-\cos \left (t \right ) t \right ) y \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.052 |
|
| 355 |
\begin{align*}
\left (x-y\right ) \left (x-z\right ) x^{\prime }&=f \left (t \right ) \\
\left (-x+y\right ) \left (y-z\right ) y^{\prime }&=f \left (t \right ) \\
\left (-x+z\right ) \left (-y+z\right ) z^{\prime }&=f \left (t \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.052 |
|
| 356 |
\begin{align*}
y^{\prime \prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| 357 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| 358 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| 359 |
\begin{align*}
a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| 360 |
\begin{align*}
2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| 361 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| 362 |
\begin{align*}
3 y x +y^{\prime } \left (x^{2}+2\right )+4 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=2 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.052 |
|
| 363 |
\begin{align*}
y^{\left (5\right )}-y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| 364 |
\begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+\alpha y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| 365 |
\begin{align*}
2 y y^{\prime \prime \prime }&=y^{\prime } \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.052 |
|
| 366 |
\begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+16 y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| 367 |
\begin{align*}
2 y^{\prime \prime \prime }-y^{\prime \prime }-5 y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| 368 |
\begin{align*}
y^{\prime \prime \prime }+27 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| 369 |
\begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }-8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| 370 |
\begin{align*}
x^{\prime }&=-x-x \,y^{2} \\
y^{\prime }&=-y-y \,x^{2} \\
z^{\prime }&=1-z+x^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.053 |
|
| 371 |
\begin{align*}
y^{\prime \prime \prime }-7 y^{\prime \prime }+16 y^{\prime }-12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| 372 |
\begin{align*}
4 y^{\prime \prime \prime }-8 y^{\prime \prime }+5 y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| 373 |
\begin{align*}
x^{\prime }+4 x+2 y&=\frac {2}{{\mathrm e}^{t}-1} \\
6 x-y^{\prime }+3 y&=\frac {3}{{\mathrm e}^{t}-1} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.053 |
|
| 374 |
\begin{align*}
y^{\prime \prime \prime }+f \left (x \right ) \left (x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.053 |
|
| 375 |
\begin{align*}
y^{\prime \prime \prime \prime }+\lambda y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| 376 |
\begin{align*}
x^{\prime }+y^{\prime }&=x y \\
y^{\prime }+z^{\prime }&=y z \\
x^{\prime }+z^{\prime }&=x z \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.053 |
|
| 377 |
\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 (1\right ) &= 1 \\
y_{2} \left (1\right ) &= -1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.053 |
|
| 378 |
\begin{align*}
y^{\prime \prime \prime }+216 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| 379 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.053 |
|
| 380 |
\begin{align*}
x^{\prime }&=x^{2}+y^{2} \\
y^{\prime }&=2 x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.053 |
|
| 381 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| 382 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| 383 |
\begin{align*}
y^{\prime \prime \prime }-x y^{\prime \prime }-y^{\prime }+y x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.053 |
|
| 384 |
\begin{align*}
y^{\prime \prime \prime }-8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| 385 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+x y^{\prime }-y&=-\ln \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.053 |
|
| 386 |
\begin{align*}
x^{\prime \prime }&=-2 y \\
y^{\prime }&=y-x^{\prime } \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 10 \\
y \left (0\right ) &= 5 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.053 |
|
| 387 |
\begin{align*}
y^{\prime \prime \prime }+x^{2} y&={\mathrm e}^{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.053 |
|
| 388 |
\begin{align*}
y_{1}^{\prime }&=t \sin \left (y_{1}\right )-y_{2} \\
y_{2}^{\prime }&=y_{1}+t \cos \left (y_{2}\right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.053 |
|
| 389 |
\begin{align*}
y_{1}^{\prime }&=\left (2 t +1\right ) y_{1}+2 y_{2} t \\
y_{2}^{\prime }&=-2 y_{1} t +\left (1-2 t \right ) y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.053 |
|
| 390 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| 391 |
\begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| 392 |
\begin{align*}
y^{\prime \prime \prime \prime }+7 y^{\prime \prime \prime }+17 y^{\prime \prime }+17 y^{\prime }+6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| 393 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+12 y^{\prime }-10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| 394 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+16 y^{\prime \prime }+24 y^{\prime }+20 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| 395 |
\begin{align*}
x^{\prime }&=x-x^{2}-2 x y \\
y^{\prime }&=2 y-2 y^{2}-3 x y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.054 |
|
| 396 |
\begin{align*}
y^{\prime \prime \prime \prime }-6 y^{\prime \prime }+8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.054 |
|
| 397 |
\begin{align*}
y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.054 |
|
| 398 |
\begin{align*}
y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.054 |
|
| 399 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+x^{2} \left (x +3\right ) y^{\prime \prime }+5 \left (-6+x \right ) x y^{\prime }+\left (4 x +30\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.054 |
|
| 400 |
\begin{align*}
x^{2} y^{\prime \prime \prime \prime }+8 x y^{\prime \prime \prime }+12 y^{\prime \prime }-\lambda ^{2} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.054 |
|