| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 501 |
\begin{align*}
2 y^{\prime \prime \prime }-y^{\prime \prime }-5 y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 502 |
\begin{align*}
t \left (-1+t \right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.046 |
|
| 503 |
\begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 504 |
\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*} |
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| 505 |
\begin{align*}
x^{\prime }&=\tan \left (x+y\right ) \\
y^{\prime }&=x+x^{3} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.046 |
|
| 506 |
\begin{align*}
y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 507 |
\begin{align*}
y^{\prime \prime \prime }+11 y^{\prime \prime }+36 y^{\prime }+26 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 508 |
\begin{align*}
h y^{2}+\operatorname {g1} y y^{\prime }+\operatorname {g0} {y^{\prime }}^{2}+\operatorname {f2} y y^{\prime \prime }+\operatorname {f1} y^{\prime } y^{\prime \prime }+\operatorname {f0} {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.046 |
|
| 509 |
\begin{align*}
-15 y-7 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 510 |
\begin{align*}
-4 y+6 y^{\prime }-4 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 511 |
\begin{align*}
-y-2 y^{\prime }+2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 512 |
\begin{align*}
y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 513 |
\begin{align*}
-3 y^{\prime }+11 y^{\prime \prime }-12 y^{\prime \prime \prime }+4 y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 514 |
\begin{align*}
y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 515 |
\begin{align*}
y_{1}^{\prime }&=3 y_{1}+x y_{3} \\
y_{2}^{\prime }&=y_{2}+x^{3} y_{3} \\
y_{3}^{\prime }&=2 x y_{1}-y_{2}+{\mathrm e}^{x} y_{3} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.046 |
|
| 516 |
\begin{align*}
y^{\prime \prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 517 |
\begin{align*}
x^{2} y^{\prime }&=y \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.046 |
|
| 518 | \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*} | ✗ | ✓ | ✓ | ✗ | 0.046 |
|
| 519 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}+3\right ) x^{2} y^{\prime \prime }+\left (12 n^{2}-3\right ) x y^{\prime }-\left (4 x^{4}+12 n^{2}-3\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| 520 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-2 \mu ^{2}-2 \nu ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-2 \mu ^{2}-2 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (8 x^{2}+\left (\mu ^{2}-\nu ^{2}\right )^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| 521 |
\begin{align*}
a t x^{\prime }&=b c \left (y-z\right ) \\
b t y^{\prime }&=c a \left (z-x\right ) \\
c t z^{\prime }&=a b \left (x-y\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.046 |
|
| 522 |
\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*} |
✗ |
✗ |
✗ |
✗ |
0.046 |
|
| 523 |
\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*} |
✗ |
✓ |
✗ |
✗ |
0.046 |
|
| 524 |
\begin{align*}
x^{\prime \prime \prime }-8 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 525 |
\begin{align*}
t^{3} x^{\prime \prime \prime }-\left (t +3\right ) t^{2} x^{\prime \prime }+2 t \left (t +3\right ) x^{\prime }-2 \left (t +3\right ) x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| 526 |
\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*} |
✗ |
✗ |
✗ |
✗ |
0.046 |
|
| 527 |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 528 |
\begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 529 |
\begin{align*}
x^{\prime }&=\cos \left (x\right )^{2} \cos \left (y\right )^{2}+\sin \left (x\right )^{2} \cos \left (y\right )^{2} \\
y^{\prime }&=-\frac {\sin \left (2 x\right ) \sin \left (2 y\right )}{2} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.046 |
|
| 530 |
\begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }-4 y^{\prime }-16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 531 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 532 |
\begin{align*}
a y^{\prime \prime \prime }&=y^{\prime \prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| 533 |
\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*} |
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| 534 |
\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*} |
✗ |
✓ |
✗ |
✗ |
0.046 |
|
| 535 |
\begin{align*}
y^{\prime \prime \prime }+27 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 536 |
\begin{align*}
x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.047 |
|
| 537 |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 538 | \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*} | ✗ | ✗ | ✗ | ✗ | 0.047 |
|
| 539 |
\begin{align*}
x^{\prime \prime }-3 x-4 y&=0 \\
x+y^{\prime \prime }+y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.047 |
|
| 540 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 541 |
\begin{align*}
-a^{3} y+3 a^{2} y^{\prime }-3 a y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 542 |
\begin{align*}
-4 y+3 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 543 |
\begin{align*}
10 f^{\prime }\left (x \right ) y^{\prime }+3 y \left (3 f \left (x \right )^{2}+f^{\prime \prime }\left (x \right )\right )+10 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.047 |
|
| 544 |
\begin{align*}
-2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 545 |
\begin{align*}
3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 546 |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 547 |
\begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime }+10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 548 |
\begin{align*}
x^{2} y^{\prime \prime \prime }-3 \left (x -m \right ) x y^{\prime \prime }+\left (2 x^{2}+4 \left (n -m \right ) x +m \left (2 m -1\right )\right ) y^{\prime }-2 n \left (2 x -2 m +1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.047 |
|
| 549 |
\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*} |
✗ |
✗ |
✗ |
✗ |
0.047 |
|
| 550 |
\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 |
|
| 551 |
\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*} |
✗ |
✓ |
✓ |
✓ |
0.047 |
|
| 552 |
\begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }-4 y^{\prime }+8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 553 |
\begin{align*}
y^{\prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 554 |
\begin{align*}
2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 555 |
\begin{align*}
y^{\prime \prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 556 |
\begin{align*}
y^{\prime \prime \prime }-8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 557 |
\begin{align*}
y^{\prime \prime \prime \prime }-16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 558 | \begin{align*}
y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.047 |
|
| 559 |
\begin{align*}
-y-2 y^{\prime }+2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 560 |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| 561 |
\begin{align*}
y^{\left (5\right )}+t y^{\prime \prime }-3 y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.047 |
|
| 562 |
\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*} |
✗ |
✓ |
✓ |
✗ |
0.047 |
|
| 563 |
\begin{align*}
x^{\prime \prime }+2 x-2 y^{\prime }&=0 \\
3 x^{\prime }+y^{\prime \prime }-8 y&=240 \,{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.048 |
|
| 564 |
\begin{align*}
a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.048 |
|
| 565 |
\begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.048 |
|
| 566 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-\rho ^{2}-\sigma ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-\rho ^{2}-\sigma ^{2}+1\right ) x \right ) y^{\prime }+\left (\rho ^{2} \sigma ^{2}+8 x^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.048 |
|
| 567 |
\begin{align*}
t x^{\prime }&=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 |
|
| 568 |
\begin{align*}
2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.048 |
|
| 569 |
\begin{align*}
y^{\prime \prime \prime }-7 y^{\prime \prime }+12 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.048 |
|
| 570 |
\begin{align*}
y_{1}^{\prime }&=2 x y_{1}-x^{2} y_{2}+4 x \\
y_{2}^{\prime }&={\mathrm e}^{x} y_{1}+3 \,{\mathrm e}^{-x} y_{2}-\cos \left (3 x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.048 |
|
| 571 |
\begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.048 |
|
| 572 |
\begin{align*}
y^{\prime \prime \prime \prime }-9 y^{\prime \prime }+20 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.048 |
|
| 573 |
\begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }-15 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.048 |
|
| 574 |
\begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }-54 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 575 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 576 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 577 |
\begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 578 | \begin{align*}
27 y-12 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.049 |
|
| 579 |
\begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 580 |
\begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 581 |
\begin{align*}
-k y-\left (-a b c +x \right ) y^{\prime }+\left (a b +a c +b c +a +b +c +1\right ) x y^{\prime \prime }+\left (3+a +b +c \right ) x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| 582 |
\begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 583 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 584 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 585 |
\begin{align*}
y^{\prime \prime \prime \prime }+16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 586 |
\begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 587 |
\begin{align*}
2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 588 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }-2 n \left (n +1\right ) x^{2} y^{\prime \prime }+4 n \left (n +1\right ) x y^{\prime }+\left (a \,x^{4}+n \left (n +1\right ) \left (n +3\right ) \left (-2+n \right )\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| 589 |
\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 (t \cos \left (t \right )-\sin \left (t \right )\right ) x+t \left (1-t \cos \left (t \right )\right ) y \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.049 |
|
| 590 |
\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*} |
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| 591 |
\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*} |
✗ |
✗ |
✗ |
✗ |
0.049 |
|
| 592 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 593 |
\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 |
|
| 594 |
\begin{align*}
y^{\prime \prime \prime \prime }&=-2 y^{\prime \prime \prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 595 |
\begin{align*}
y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 596 |
\begin{align*}
y^{\prime \prime \prime \prime }-10 y^{\prime \prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 597 |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| 598 | \begin{align*}
y^{\prime \prime \prime }+216 y&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.049 |
|
| 599 |
\begin{align*}
y^{\prime \prime \prime }&=3 y^{\prime } y \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= {\frac {3}{2}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.049 |
|
| 600 |
\begin{align*}
x^{\prime }&=x-4 x y \\
y^{\prime }&=-2 y+x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.049 |
|