| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10401 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| 10402 |
\begin{align*}
\left (-1+y\right ) y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| 10403 |
\begin{align*}
y^{\prime \prime }+y&=x \,{\mathrm e}^{x} \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| 10404 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-3\right ) y-{\mathrm e}^{x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.725 |
|
| 10405 |
\begin{align*}
x^{\prime \prime }-x&={\mathrm e}^{t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| 10406 |
\begin{align*}
4 y+y^{\prime \prime }&=\sec \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| 10407 |
\begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }-5 \left (x -1\right ) y^{\prime }+9 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.725 |
|
| 10408 |
\begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| 10409 |
\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 ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| 10410 |
\begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +\left (1+t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.726 |
|
| 10411 |
\begin{align*}
y^{\prime \prime }&=3 \sin \left (x \right )-4 y \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| 10412 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }-2 y&=-6 \,{\mathrm e}^{\pi -t} \\
y \left (\pi \right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 4 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| 10413 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| 10414 |
\begin{align*}
y^{\prime \prime }+{\mathrm e}^{x} y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| 10415 |
\begin{align*}
y^{2} {y^{\prime }}^{2}-a^{2}+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| 10416 |
\begin{align*}
x^{\prime \prime }+100 x&=225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \\
x \left (0\right ) &= 375 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 10417 |
\begin{align*}
3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 10418 |
\begin{align*}
2 y+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 10419 |
\begin{align*}
y^{\prime \prime }+\left (p +\frac {1}{2}-\frac {x^{2}}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 10420 |
\begin{align*}
y^{\prime \prime } x +a \left (-y+y^{\prime } x \right )^{2}-b&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.727 |
|
| 10421 |
\begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=3 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 10422 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 10423 |
\begin{align*}
y^{\prime \prime }+9 y&=\tan \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 10424 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y&=\sin \left (\ln \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 10425 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}-3 x_{2}-2 x_{3} \\
x_{2}^{\prime }&=8 x_{1}-5 x_{2}-4 x_{3} \\
x_{3}^{\prime }&=-4 x_{1}+3 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 10426 |
\begin{align*}
y^{\prime \prime }-4 y&=x \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 10427 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (3-2 x \right ) y^{\prime }+\left (3 x +4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| 10428 |
\begin{align*}
x^{\prime }&=2 x-y+\cos \left (t \right ) \\
y^{\prime }&=5 x-2 y+\sin \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| 10429 |
\begin{align*}
4 y+y^{\prime \prime }&=\sin \left (x \right )+\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| 10430 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| 10431 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| 10432 |
\begin{align*}
v^{\prime }-2 v+2 w^{\prime }&=2-4 \,{\mathrm e}^{2 x} \\
2 v^{\prime }-3 v+3 w^{\prime }-w&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| 10433 |
\begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +t^{2} y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| 10434 |
\begin{align*}
9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| 10435 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| 10436 |
\begin{align*}
s^{\prime \prime }-3 s^{\prime }+2 s&=8 t^{2}+12 \,{\mathrm e}^{-t} \\
s \left (0\right ) &= 0 \\
s^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| 10437 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| 10438 |
\begin{align*}
y^{\prime }+y&=2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| 10439 |
\begin{align*}
8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| 10440 |
\begin{align*}
y \left (1+{y^{\prime }}^{2}\right )&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| 10441 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| 10442 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| 10443 |
\begin{align*}
y^{\prime \prime }+a y^{\prime }+\left (b \,{\mathrm e}^{\lambda x}+c \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.730 |
|
| 10444 |
\begin{align*}
2 x^{2} y^{\prime \prime }+x \left (3+2 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.731 |
|
| 10445 |
\begin{align*}
9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.731 |
|
| 10446 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\frac {1}{{\mathrm e}^{2 x}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.731 |
|
| 10447 |
\begin{align*}
x^{\prime \prime }+x&=\cos \left (\frac {9 t}{10}\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.731 |
|
| 10448 |
\begin{align*}
y^{\prime \prime } x&=y^{\prime }+{y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.731 |
|
| 10449 |
\begin{align*}
y^{2}-2 y y^{\prime } x +{y^{\prime }}^{2} \left (x^{2}-1\right )&=m^{2} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.731 |
|
| 10450 |
\begin{align*}
y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\left (n^{2}+\frac {2}{x^{2}}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.731 |
|
| 10451 |
\begin{align*}
4 y+y^{\prime \prime }&=\sec \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.731 |
|
| 10452 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.731 |
|
| 10453 |
\begin{align*}
y^{\prime \prime }+y&=12 \cos \left (2 x \right )-\sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.731 |
|
| 10454 |
\begin{align*}
2 t y^{\prime \prime }+y^{\prime }+t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.731 |
|
| 10455 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.732 |
|
| 10456 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.732 |
|
| 10457 |
\begin{align*}
y^{\prime \prime }&=\frac {a}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.732 |
|
| 10458 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.732 |
|
| 10459 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.732 |
|
| 10460 |
\begin{align*}
y^{\prime \prime }+y&=2 \cos \left (x \right )-2 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.732 |
|
| 10461 |
\begin{align*}
2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| 10462 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+{\mathrm e}^{-t} y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| 10463 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-4 x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=x_{1}-x_{2}+{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| 10464 |
\begin{align*}
y^{\prime \prime }+y&=\tan \left (\frac {x}{3}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| 10465 |
\begin{align*}
y^{\prime \prime }+9 y&=18 \sec \left (3 x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| 10466 |
\begin{align*}
\left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.733 |
|
| 10467 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| 10468 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| 10469 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}+n^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| 10470 |
\begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.733 |
|
| 10471 |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=6 x_{1}+4 \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| 10472 |
\begin{align*}
y^{\prime \prime }+10 y^{\prime }+25 y&=\frac {{\mathrm e}^{-5 x} \ln \left (x \right )}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| 10473 |
\begin{align*}
y_{1}^{\prime }&=-y_{1}+y_{2} \\
y_{2}^{\prime }&=y_{1}-y_{2}-2 y_{3} \\
y_{3}^{\prime }&=-y_{1}-y_{2}-y_{3} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 6 \\
y_{2} \left (0\right ) &= 5 \\
y_{3} \left (0\right ) &= -7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| 10474 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| 10475 |
\begin{align*}
-12 y-2 \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right )^{2} y^{\prime \prime }&=6 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.734 |
|
| 10476 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x -x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.734 |
|
| 10477 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=2-12 x +6 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| 10478 |
\begin{align*}
y_{1}^{\prime }&=2 y_{1}+y_{2}-2 y_{3} \\
y_{2}^{\prime }&=3 y_{2}-2 y_{3} \\
y_{3}^{\prime }&=3 y_{1}+y_{2}-3 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| 10479 |
\begin{align*}
y^{\prime \prime }&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| 10480 |
\begin{align*}
2 x y y^{\prime \prime }&=-y y^{\prime }+x {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.735 |
|
| 10481 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+\frac {1}{4}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| 10482 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=x \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| 10483 |
\begin{align*}
x^{3} y^{\prime \prime }-\left (-y+y^{\prime } x \right )^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.735 |
|
| 10484 |
\begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+\left (x^{2}+x -6\right ) y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| 10485 |
\begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+y&={\mathrm e}^{-\frac {t}{2}} \\
y \left (0\right ) &= a \\
y^{\prime }\left (0\right ) &= b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| 10486 |
\begin{align*}
y^{\prime \prime }&=\sqrt {-{y^{\prime }}^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.735 |
|
| 10487 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+3 x_{3} \\
x_{2}^{\prime }&=6 x_{1}+4 x_{2}+6 x_{3} \\
x_{3}^{\prime }&=-5 x_{1}-2 x_{2}-4 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= -2 \\
x_{3} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| 10488 |
\begin{align*}
\left (x^{2}+x \right ) y^{\prime }+2 x +1+2 \cos \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| 10489 |
\begin{align*}
y^{\prime \prime }+k y&={\mathrm e}^{i \omega t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| 10490 |
\begin{align*}
y^{\prime \prime }-y&=1+x \,{\mathrm e}^{x}+{\mathrm e}^{x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| 10491 |
\begin{align*}
2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| 10492 |
\begin{align*}
x^{\prime }&=-5 x+3 y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| 10493 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \left (3 x^{2}+2 x +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| 10494 |
\begin{align*}
a x -2 y^{\prime } y^{\prime \prime }+x {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.736 |
|
| 10495 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (-1\right ) &= 5 \\
y^{\prime }\left (-1\right ) &= -5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| 10496 |
\begin{align*}
y^{\prime \prime }+4 y&=2 \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| 10497 |
\begin{align*}
x^{\prime }&=4 x-5 y+4 t -1 \\
y^{\prime }&=x-2 y+t \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| 10498 |
\begin{align*}
x_{1}^{\prime }&=\frac {x_{1}}{2}-x_{2}-\frac {3 x_{3}}{2} \\
x_{2}^{\prime }&=\frac {3 x_{1}}{2}-2 x_{2}-\frac {3 x_{3}}{2} \\
x_{3}^{\prime }&=-2 x_{1}+2 x_{2}+x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| 10499 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-4 x_{2}-2 x_{4} \\
x_{2}^{\prime }&=x_{2} \\
x_{3}^{\prime }&=6 x_{1}-12 x_{2}-x_{3}-6 x_{4} \\
x_{4}^{\prime }&=-4 x_{2}-x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| 10500 |
\begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.737 |
|