| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10501 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}-2 \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| 10502 |
\begin{align*}
6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| 10503 |
\begin{align*}
y^{\prime \prime }-y&=\frac {1}{\sinh \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| 10504 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{a x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| 10505 |
\begin{align*}
2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| 10506 |
\begin{align*}
\sqrt {t}\, x^{\prime }&=\cos \left (\sqrt {t}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| 10507 |
\begin{align*}
3 y+y^{\prime }&=\delta \left (t -2\right ) \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| 10508 |
\begin{align*}
4 x^{2} y^{\prime \prime }+y&=x^{3} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| 10509 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=16 x^{3} {\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| 10510 |
\begin{align*}
x^{\prime }&=3 x+2 y \\
y^{\prime }&=-5 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| 10511 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{2 x}}{\left (1+{\mathrm e}^{x}\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.794 |
|
| 10512 |
\begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y&=2 t \\
y \left (0\right ) &= a \\
y^{\prime }\left (0\right ) &= b \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.794 |
|
| 10513 |
\begin{align*}
x^{\prime }&=-2 x-y \\
y^{\prime }&=3 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| 10514 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=4 x_{1}+2 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -2 \\
x_{2} \left (0\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| 10515 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=5 x \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| 10516 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{8}&=\frac {\sin \left (x \right )}{8}-\frac {\cos \left (x \right )}{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| 10517 |
\begin{align*}
y^{b}+x^{a} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.795 |
|
| 10518 |
\begin{align*}
y^{\prime \prime }-x y^{\prime }-y x -x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.795 |
|
| 10519 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} x&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| 10520 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{2}-1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| 10521 |
\begin{align*}
y_{1}^{\prime }&=y_{2}+y_{4} \\
y_{2}^{\prime }&=y_{1}-y_{3} \\
y_{3}^{\prime }&=y_{4} \\
y_{4}^{\prime }&=y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| 10522 |
\begin{align*}
x^{\prime }+x+y&=t^{2} \\
y^{\prime }+y+z&=2 t \\
z^{\prime }+z&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| 10523 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| 10524 |
\begin{align*}
{\mathrm e}^{x^{\prime }}&=x \\
x \left (t_{0} \right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| 10525 |
\begin{align*}
x^{\prime }&=x+z \\
y^{\prime }&=-y \\
z^{\prime }&=4 z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| 10526 |
\begin{align*}
x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.795 |
|
| 10527 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 10528 |
\begin{align*}
x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3+5 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 10529 |
\begin{align*}
4 x^{2} \left (4 x^{2}+1\right ) y^{\prime \prime }+32 x^{3} y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 10530 |
\begin{align*}
y_{1}^{\prime }&=4 y_{1}-2 y_{2}-2 y_{3} \\
y_{2}^{\prime }&=-2 y_{1}+3 y_{2}-y_{3} \\
y_{3}^{\prime }&=2 y_{1}-y_{2}+3 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 10531 |
\begin{align*}
x_{1}^{\prime }&=9 x_{1}-2 x_{2}+9 t \\
x_{2}^{\prime }&=5 x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 10532 |
\begin{align*}
4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 10533 |
\begin{align*}
x^{\prime }&=x-8 y \\
y^{\prime }&=x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 10534 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{3} \cos \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.796 |
|
| 10535 |
\begin{align*}
2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=x \sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.796 |
|
| 10536 |
\begin{align*}
y^{\prime \prime }+b y^{\prime }+c y&=0 \\
y \left (\pi \right ) &= 0 \\
y \left (2 \pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 10537 |
\begin{align*}
\tan \left (y^{\prime }\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 10538 |
\begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=16 \,{\mathrm e}^{\frac {t}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 10539 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.797 |
|
| 10540 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{-x}}{\sqrt {-x^{2}+4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.797 |
|
| 10541 |
\begin{align*}
\left (c x +b \right ) y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.797 |
|
| 10542 |
\begin{align*}
a {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.797 |
|
| 10543 |
\begin{align*}
\sin \left (x \right ) y^{\prime }-y^{2} \sin \left (x \right )^{2}+\left (\cos \left (x \right )-3 \sin \left (x \right )\right ) y+4&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.797 |
|
| 10544 |
\begin{align*}
a y \left (-1+y\right ) y^{\prime \prime }-\left (a -1\right ) \left (-1+2 y\right ) {y^{\prime }}^{2}+f y \left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.797 |
|
| 10545 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=2 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.797 |
|
| 10546 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x}-{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.797 |
|
| 10547 |
\begin{align*}
x^{2} y^{\prime \prime }+a x y^{\prime }+\left (b \,x^{n}+c \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.798 |
|
| 10548 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.798 |
|
| 10549 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\frac {2 x}{\left (x +1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.798 |
|
| 10550 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+\sqrt {2}\, x_{2}+{\mathrm e}^{-t} \\
x_{2}^{\prime }&=\sqrt {2}\, x_{1}-2 x_{2}-{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| 10551 |
\begin{align*}
y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }-4 y&=-{\mathrm e}^{-x} \left (\cos \left (x \right )-\sin \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| 10552 |
\begin{align*}
y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| 10553 |
\begin{align*}
\left (3 y-1\right )^{2} {y^{\prime }}^{2}&=4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.799 |
|
| 10554 |
\begin{align*}
x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| 10555 |
\begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.799 |
|
| 10556 |
\begin{align*}
x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.799 |
|
| 10557 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| 10558 |
\begin{align*}
\left (y+1\right ) y^{\prime \prime }&={y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.799 |
|
| 10559 |
\begin{align*}
{y^{\prime }}^{2} \left (x^{2}-1\right )&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| 10560 |
\begin{align*}
y^{\prime \prime }+y&=2 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| 10561 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=7+75 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| 10562 |
\begin{align*}
y \left (x y^{\prime }-y\right )^{2}&=y-2 x y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.799 |
|
| 10563 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2}+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 10564 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 10565 |
\begin{align*}
9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 10566 |
\begin{align*}
2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 10567 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }-7 x^{3} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 10568 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 10569 |
\begin{align*}
x^{\prime }&=-3 y \\
y^{\prime }&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 10570 |
\begin{align*}
y^{\prime \prime }+8 y^{\prime }+16 y&=4 \\
y \left (0\right ) &= {\frac {5}{4}} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 10571 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=x \,{\mathrm e}^{x} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.800 |
|
| 10572 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.800 |
|
| 10573 |
\begin{align*}
x^{\prime \prime }+9 x&=10 \cos \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| 10574 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}+7 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| 10575 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {4 \,{\mathrm e}^{-2 x}}{x^{2}+1}+2 x^{2}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.801 |
|
| 10576 |
\begin{align*}
x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }&=0 \\
y \left (2\right ) &= 5 \\
y^{\prime }\left (2\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| 10577 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| 10578 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 10579 |
\begin{align*}
y^{\prime }&=1-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 10580 |
\begin{align*}
x^{2} y y^{\prime \prime }&=-y^{2}+{y^{\prime }}^{2} x^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.802 |
|
| 10581 |
\begin{align*}
x^{\prime }&=3 x-y-z \\
y^{\prime }&=x+y-z \\
z^{\prime }&=x-y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 10582 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x \sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.802 |
|
| 10583 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 10584 |
\begin{align*}
x^{\prime }&=a x+y \\
y^{\prime }&=-x+a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 10585 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 10586 |
\begin{align*}
4 y+y^{\prime \prime }&={\mathrm e}^{x}+\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 10587 |
\begin{align*}
y^{\prime \prime }&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 10588 |
\begin{align*}
y^{\prime \prime }+4 y&=F \cos \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 10589 |
\begin{align*}
y^{\prime \prime }+9 y&=\sin \left (x \right )^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 10590 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }&=1 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 10591 |
\begin{align*}
\left (x^{2}-3 x -4\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+\left (x^{2}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 10592 |
\begin{align*}
x_{1}^{\prime }&=a x_{1}+5 x_{3} \\
x_{2}^{\prime }&=-x_{2}-2 x_{3} \\
x_{3}^{\prime }&=-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 10593 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=2 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 10594 |
\begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right ) \csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 10595 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 \left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| 10596 |
\begin{align*}
2 y y^{\prime \prime }&=y^{2} \left (a x +b y\right )+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.804 |
|
| 10597 |
\begin{align*}
2 y {y^{\prime }}^{2}-\left (4 x -5\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.804 |
|
| 10598 |
\begin{align*}
-\left (5+4 x \right ) y+32 x y^{\prime }+16 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| 10599 |
\(\left [\begin {array}{ccc} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.804 |
|
| 10600 |
\begin{align*}
4 y^{\prime \prime }+\frac {\left (4 x -3\right ) y}{\left (x -1\right )^{2}}&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.804 |
|