| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 401 |
\begin{align*}
x^{3} y^{\prime \prime \prime \prime }+2 x^{2} y^{\prime \prime \prime }-x y^{\prime \prime }+y^{\prime }-a^{4} x^{3} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.054 |
|
| 402 |
\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*} |
✗ |
✗ |
✗ |
✗ |
0.054 |
|
| 403 |
\begin{align*}
x^{\prime }&=x y-6 y \\
y^{\prime }&=x-y-5 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.054 |
|
| 404 |
\begin{align*}
x^{\prime }&=-x+y+x^{2} \\
y^{\prime }&=y-2 x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.054 |
|
| 405 |
\begin{align*}
x^{\prime }&=-2 y+x y \\
y^{\prime }&=x+4 x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.054 |
|
| 406 |
\begin{align*}
y^{2}+\left (2 y x -1\right ) y^{\prime }+x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.054 |
|
| 407 |
\begin{align*}
2 y^{\prime \prime \prime }+x y^{\prime \prime }+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 \(x=0\). |
✗ |
✓ |
✓ |
✗ |
0.054 |
|
| 408 |
\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*} |
✗ |
✓ |
✓ |
✗ |
0.054 |
|
| 409 |
\begin{align*}
y^{\prime \prime \prime }&=\frac {24 x +24 y}{x^{3}} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.054 |
|
| 410 |
\begin{align*}
y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.054 |
|
| 411 |
\begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.054 |
|
| 412 |
\begin{align*}
x^{\prime }&=\frac {5 x \,{\mathrm e}^{x}}{2}-3 y+\sin \left (x^{2}\right ) \\
y^{\prime }&=2 x+y \,{\mathrm e}^{-\frac {y^{2}}{2}}-y^{4} \cos \left (x\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.054 |
|
| 413 |
\begin{align*}
y^{\prime \prime \prime \prime }+7 y^{\prime \prime \prime }+19 y^{\prime \prime }+23 y^{\prime }+10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.054 |
|
| 414 |
\begin{align*}
2 y^{\prime \prime \prime \prime }+13 y^{\prime \prime \prime }+28 y^{\prime \prime }+23 y^{\prime }+6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.054 |
|
| 415 |
\begin{align*}
2 y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime }+32 y^{\prime \prime }+54 y^{\prime }+20 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.054 |
|
| 416 |
\begin{align*}
y-x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.054 |
|
| 417 |
\begin{align*}
9 y^{\prime \prime \prime }+12 y^{\prime \prime }+4 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.055 |
|
| 418 |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.055 |
|
| 419 |
\begin{align*}
y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.055 |
|
| 420 |
\begin{align*}
x^{\prime }&=a x-b x y \\
y^{\prime }&=-c y+d x y \\
z^{\prime }&=z+x^{2}+y^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.055 |
|
| 421 |
\begin{align*}
x^{\prime }&=-1-y-{\mathrm e}^{x} \\
y^{\prime }&=x^{2}+y \left ({\mathrm e}^{x}-1\right ) \\
z^{\prime }&=x+\sin \left (z\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.055 |
|
| 422 |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-7 y^{\prime \prime }-y^{\prime }+6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.055 |
|
| 423 |
\begin{align*}
-4 y+3 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.055 |
|
| 424 |
\begin{align*}
y^{\prime \prime \prime }-8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.055 |
|
| 425 |
\begin{align*}
x_{1}^{\prime }&=-4 x_{1}-2 x_{2}+\frac {2}{{\mathrm e}^{t}-1} \\
x_{2}^{\prime }&=6 x_{1}+3 x_{2}-\frac {3}{{\mathrm e}^{t}-1} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.055 |
|
| 426 |
\begin{align*}
y^{\prime \prime \prime }-2 x y^{\prime \prime }+4 x^{2} y^{\prime }+8 x^{3} y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.055 |
|
| 427 |
\begin{align*}
y^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.055 |
|
| 428 |
\begin{align*}
x^{2} y^{\prime \prime \prime }-2 \left (x^{2}-x \right ) y^{\prime \prime }+\left (x^{2}-2 x +\frac {1}{4}-\nu ^{2}\right ) y^{\prime }+\left (\nu ^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.055 |
|
| 429 |
\begin{align*}
\operatorname {a11} x^{\prime \prime }+\operatorname {b11} x^{\prime }+\operatorname {c11} x+\operatorname {a12} y^{\prime \prime }+\operatorname {b12} y^{\prime }+\operatorname {c12} y&=0 \\
\operatorname {a21} x^{\prime \prime }+\operatorname {b21} x^{\prime }+\operatorname {c21} x+\operatorname {a22} y^{\prime \prime }+\operatorname {b22} y^{\prime }+\operatorname {c22} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.055 |
|
| 430 |
\begin{align*}
y^{\prime \prime \prime }-8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.055 |
|
| 431 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime \prime \prime }+\left (5+x \right ) y^{\prime \prime }+y \tan \left (x \right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.055 |
|
| 432 |
\begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.055 |
|
| 433 |
\begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.055 |
|
| 434 |
\begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.055 |
|
| 435 |
\begin{align*}
y_{1}^{\prime }&=3 \sec \left (t \right ) y_{1}+5 \sec \left (t \right ) y_{2} \\
y_{2}^{\prime }&=-\sec \left (t \right ) y_{1}-3 \sec \left (t \right ) y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✗ |
✓ |
✗ |
✓ |
0.055 |
|
| 436 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.055 |
|
| 437 |
\begin{align*}
-4 y+3 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 438 |
\begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 439 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 440 |
\begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 441 |
\begin{align*}
12 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 442 |
\begin{align*}
4 y^{\prime \prime \prime }+2 y^{\prime \prime }-4 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 443 |
\begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-7 y^{\prime \prime }-8 y^{\prime }+12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 444 |
\begin{align*}
4 y^{\prime \prime \prime }+12 y^{\prime \prime }-3 y^{\prime }+14 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 445 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-3 x_{1}+4 x_{2}+\frac {{\mathrm e}^{3 t}}{1+{\mathrm e}^{2 t}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.056 |
|
| 446 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-6 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 447 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 448 |
\begin{align*}
x^{2} y^{\prime \prime \prime }-\left (x^{2}-2 x \right ) y^{\prime \prime }-\left (x^{2}+\nu ^{2}-\frac {1}{4}\right ) y^{\prime }+\left (x^{2}-2 x +\nu ^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.056 |
|
| 449 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}-1\right ) x^{2} y^{\prime \prime }-\left (4 n^{2}-1\right ) x y^{\prime }+\left (-4 x^{4}+4 n^{2}-1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.056 |
|
| 450 |
\begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 451 |
\begin{align*}
x_{1}^{\prime }&=-2 t x_{1}^{2} \\
x_{2}^{\prime }&=\frac {x_{2}+t}{t} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.056 |
|
| 452 |
\begin{align*}
x_{1}^{\prime }&={\mathrm e}^{t -x_{1}} \\
x_{2}^{\prime }&=2 \,{\mathrm e}^{x_{1}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.056 |
|
| 453 |
\begin{align*}
x_{1}^{\prime }&=\frac {x_{1}^{2}}{x_{2}} \\
x_{2}^{\prime }&=-x_{1}+x_{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.056 |
|
| 454 |
\begin{align*}
x^{\prime }&=\frac {t +y}{x+y} \\
y^{\prime }&=\frac {x-t}{x+y} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.056 |
|
| 455 |
\begin{align*}
x^{\prime }&=\frac {t -y}{-x+y} \\
y^{\prime }&=\frac {x-t}{-x+y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.056 |
|
| 456 |
\begin{align*}
x^{\prime }&=\frac {t +y}{x+y} \\
y^{\prime }&=\frac {t +x}{x+y} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.056 |
|
| 457 |
\begin{align*}
x^{\prime \prime }&=3 x+y \\
y^{\prime }&=-2 x \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.056 |
|
| 458 |
\begin{align*}
x^{\prime }&=3 x-x^{2} \\
y^{\prime }&=2 x y-3 y+2 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.056 |
|
| 459 |
\begin{align*}
x^{\prime }&=\left (x+2\right ) \left (-x+y\right ) \\
y^{\prime }&=y-x^{2}-y^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.056 |
|
| 460 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=x-\frac {x^{3}}{5}-\frac {y}{5} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.056 |
|
| 461 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 462 |
\begin{align*}
2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 463 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 464 |
\begin{align*}
y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 465 |
\begin{align*}
\left (2 x -1\right )^{3} y^{\prime \prime \prime }+\left (2 x -1\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.056 |
|
| 466 |
\begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.056 |
|
| 467 |
\begin{align*}
x^{\prime \prime \prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 468 |
\begin{align*}
x^{\prime }&=8 x-y^{2} \\
y^{\prime }&=6 x^{2}-6 y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.056 |
|
| 469 |
\begin{align*}
x^{\prime }&=-x+y^{2} \\
y^{\prime }&=x^{2}-y \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.056 |
|
| 470 |
\begin{align*}
x y^{\prime \prime \prime }+2 x y^{\prime \prime }-x y^{\prime }-2 y x&=1 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.056 |
|
| 471 |
\begin{align*}
x^{\prime \prime }+y^{\prime }+x&=y+\sin \left (t \right ) \\
y^{\prime \prime }+x^{\prime }-y&=2 t^{2}-x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= -1 \\
y \left (0\right ) &= -{\frac {9}{2}} \\
y^{\prime }\left (0\right ) &= -{\frac {7}{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.056 |
|
| 472 |
\begin{align*}
y_{1}^{\prime }&=\frac {4 t y_{1}}{t^{2}+1}+\frac {6 y_{2} t}{t^{2}+1}-3 t \\
y_{2}^{\prime }&=-\frac {2 t y_{1}}{t^{2}+1}-\frac {4 y_{2} t}{t^{2}+1}+t \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (1\right ) &= 1 \\
y_{2} \left (1\right ) &= -1 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.056 |
|
| 473 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 474 |
\begin{align*}
2 y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 475 |
\begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+18 y^{\prime \prime }+34 y^{\prime }+20 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 476 |
\begin{align*}
3 y^{\prime \prime \prime \prime }+13 y^{\prime \prime \prime }+19 y^{\prime \prime }+11 y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 477 |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 478 |
\begin{align*}
2 y^{\prime \prime \prime \prime }+11 y^{\prime \prime \prime }+21 y^{\prime \prime }+16 y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 479 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 480 |
\begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 481 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 482 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| 483 |
\begin{align*}
\left (x^{2}-2 x +3\right ) y^{\prime \prime \prime }-\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.056 |
|
| 484 |
\begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }-8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.057 |
|
| 485 |
\begin{align*}
y^{\prime \prime \prime \prime }-16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.057 |
|
| 486 |
\begin{align*}
4 y^{\left (5\right )}-3 y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.057 |
|
| 487 |
\begin{align*}
2 y^{\prime \prime \prime }-3 y^{\prime \prime }+10 y^{\prime }-15 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.057 |
|
| 488 |
\begin{align*}
y^{\prime \prime \prime \prime }-a^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.057 |
|
| 489 |
\begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.057 |
|
| 490 |
\begin{align*}
2 x y^{\prime \prime \prime }+3 \left (2 a x +k \right ) y^{\prime \prime }+6 \left (a k +b x \right ) y^{\prime }+\left (3 b k +2 c x \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.057 |
|
| 491 |
\begin{align*}
x^{2} y^{\prime \prime \prime \prime }-2 \left (\nu ^{2} x^{2}+6\right ) y^{\prime \prime }+\nu ^{2} \left (\nu ^{2} x^{2}+4\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.057 |
|
| 492 |
\begin{align*}
y^{\prime \prime \prime \prime }-16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.057 |
|
| 493 |
\begin{align*}
y^{\prime \prime \prime }+\sin \left (y\right ) x&=0 \\
y \left (0\right ) &= \frac {\pi }{2} \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✓ |
✗ |
✗ |
0.057 |
|
| 494 |
\begin{align*}
x^{\prime }&=\frac {{\mathrm e}^{-x}}{t} \\
y^{\prime }&=\frac {x \,{\mathrm e}^{-y}}{t} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.057 |
|
| 495 |
\begin{align*}
x^{\prime \prime }&=y \\
y^{\prime \prime }&=x \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.057 |
|
| 496 |
\begin{align*}
x^{\prime }&=y \left (2-x-y\right ) \\
y^{\prime }&=-x-y-2 x y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.057 |
|
| 497 |
\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 }&=x^{4}+12 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.057 |
|
| 498 |
\begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.057 |
|
| 499 |
\begin{align*}
y^{\prime }&=-\sqrt {1-y^{2}} \\
x^{\prime }&=x+2 y \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.057 |
|
| 500 |
\begin{align*}
x^{\prime }&=x+4 y-y^{2} \\
y^{\prime }&=6 x-y+2 x y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.057 |
|