| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10601 |
\begin{align*}
\left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.557 |
|
| 10602 |
\begin{align*}
\sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 y \sin \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.557 |
|
| 10603 |
\begin{align*}
2 x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| 10604 |
\begin{align*}
2 x^{\prime }-x-y^{\prime }+y&=4 t \,{\mathrm e}^{-t}-3 \,{\mathrm e}^{-t} \\
x^{\prime }+4 x-2 y^{\prime }-4 y&=2 t \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| 10605 |
\begin{align*}
2 {y^{\prime }}^{2}+y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.557 |
|
| 10606 |
\begin{align*}
y^{\prime }&=y-1 \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| 10607 |
\begin{align*}
\left (x^{2}-2 x -3\right ) y^{\prime \prime }+y^{\prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=-4\). |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 10608 |
\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 \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 10609 |
\begin{align*}
-\left (-x^{2}+2\right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 10610 |
\begin{align*}
4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 10611 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+2 x&=t \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 10612 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 10613 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y&=3 \cos \left (6 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 10614 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 10615 |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }+2 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 10616 |
\begin{align*}
p^{\prime }&=15-20 p \\
p \left (0\right ) &= {\frac {7}{10}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 10617 |
\begin{align*}
y^{\prime \prime }+4 y&=F \cos \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 10618 | \begin{align*}
2 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (2 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.559 |
|
| 10619 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-x_{1}-x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 10620 |
\begin{align*}
2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 10621 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 10622 |
\begin{align*}
x^{\prime }&=-5 x+3 y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 10623 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 10624 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=2 \cos \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 10625 |
\begin{align*}
y^{\prime \prime }+9 y&=\cos \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 10626 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+5 \left (x +1\right ) y^{\prime }+\left (x^{2}-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 10627 |
\begin{align*}
y^{\prime }&=k y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 10628 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }-7 x^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 10629 |
\begin{align*}
y^{\prime \prime }&=\frac {y^{\prime }}{x \ln \left (x \right )}+\ln \left (x \right )^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.559 |
|
| 10630 |
\begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }&=\sin \left (2 x \right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 10631 |
\begin{align*}
4 y+y^{\prime \prime }&=\cos \left (x \right ) \delta \left (x -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 10632 |
\begin{align*}
y^{2} y^{\prime \prime }+y^{\prime \prime }+2 y {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.559 |
|
| 10633 |
\begin{align*}
x^{\prime }&=5 x-6 y+1 \\
y^{\prime }&=6 x-7 y+1 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 10634 |
\begin{align*}
t y^{\prime \prime }-2 y^{\prime }+t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 10635 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+5 x&=10 \cos \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| 10636 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
x_{2}^{\prime }&=3 x_{1}+x_{2} \\
x_{3}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -4 \\
x_{2} \left (0\right ) &= 4 \\
x_{3} \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| 10637 | \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\cosh \left (x \right ) \sin \left (x \right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 0.560 |
|
| 10638 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| 10639 |
\begin{align*}
x^{\prime }&=z \\
y^{\prime }&=-z \\
z^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| 10640 |
\begin{align*}
y^{\prime \prime }-a \left (-y+y^{\prime } x \right )^{v}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.560 |
|
| 10641 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| 10642 |
\begin{align*}
x^{\prime }&=2 x-6 y \\
y^{\prime }&=2 x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| 10643 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| 10644 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| 10645 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=4 x \,{\mathrm e}^{2 x} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| 10646 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| 10647 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime } x -4 y&={\mathrm e}^{x} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.561 |
|
| 10648 |
\begin{align*}
y^{\prime \prime }+12 y^{\prime }+37 y&={\mathrm e}^{-6 t} \csc \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| 10649 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=2 x +{\mathrm e}^{-x}-2 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| 10650 |
\begin{align*}
y^{\prime \prime }+\frac {5 y^{\prime }}{x -1}+\frac {4 y}{\left (x -1\right )^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| 10651 |
\begin{align*}
{y^{\prime }}^{2}+y^{\prime } x +1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| 10652 |
\begin{align*}
-2 y+a \,x^{2} y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.562 |
|
| 10653 |
\begin{align*}
f \left (x \right )+a y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.562 |
|
| 10654 |
\begin{align*}
u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| 10655 |
\begin{align*}
9 x^{2} y^{\prime \prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| 10656 | \begin{align*}
x^{\prime }&=9 x+4 y \\
y^{\prime }&=-6 x-y \\
z^{\prime }&=6 x+4 y+3 z \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.562 |
|
| 10657 |
\begin{align*}
y^{\prime \prime }&=-\frac {y^{\prime }}{x^{4}}+\frac {y}{x^{5}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.562 |
|
| 10658 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }-12 y&=\delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| 10659 |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=\sec \left (t \right )^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✗ |
✓ |
✓ |
0.562 |
|
| 10660 |
\begin{align*}
x^{\prime \prime }-4 x^{\prime }+3 x&=2 \,{\mathrm e}^{t}-5 \,{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| 10661 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| 10662 |
\begin{align*}
x^{2} y^{\prime \prime }&=x^{2}+1 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| 10663 |
\begin{align*}
x^{2} y^{\prime \prime }+\frac {7 y^{\prime } x}{2}-\frac {3 y}{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| 10664 |
\begin{align*}
\left (x -2\right )^{2} y^{\prime \prime }-\left (x -2\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| 10665 |
\begin{align*}
28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 10666 |
\begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 10667 |
\begin{align*}
-a \,x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.563 |
|
| 10668 |
\begin{align*}
-y x -\left (2 x^{2}+1\right ) y^{\prime }+2 y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.563 |
|
| 10669 |
\begin{align*}
\frac {y-y^{\prime } x}{y^{\prime }+y^{2}}&=\frac {y-y^{\prime } x}{1+x^{2} y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 10670 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x&={\mathrm e}^{x} x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 10671 |
\begin{align*}
y^{\prime }&=y^{2}-y^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 10672 |
\begin{align*}
y^{\prime \prime }+y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 10673 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x -x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.563 |
|
| 10674 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right ) \\
y^{\prime }\left (1\right ) &= 0 \\
y \left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 10675 | \begin{align*}
\frac {x y^{\prime \prime }}{1-x}+y x&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.563 |
|
| 10676 |
\begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+y \ln \left (x \right )&=x \,{\mathrm e}^{x} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.563 |
|
| 10677 |
\begin{align*}
y&=y^{\prime } x +\frac {a}{y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.563 |
|
| 10678 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 y+z \\
z^{\prime }&=x+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 10679 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 10680 |
\begin{align*}
x^{\prime }&=-3 x+2 y \\
y^{\prime }&=-2 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 10681 |
\begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=x+2 y-{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 10682 |
\begin{align*}
\left (1-x \right ) x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (2 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 10683 |
\begin{align*}
y^{\prime \prime }+\frac {\left (1-x \right ) y^{\prime }}{2 x}-\frac {y}{4 x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 10684 |
\begin{align*}
-\left (n \left (n -1\right )-a^{2} x^{2}\right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 10685 |
\begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 10686 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0<t <\pi \\ \pi & \pi <t \end {array}\right . \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 10687 |
\begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=-2 x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 10688 |
\begin{align*}
y^{\prime \prime }&=2 y^{\prime } y \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.564 |
|
| 10689 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -30 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 10690 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 t}}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 10691 |
\begin{align*}
x^{\prime }&=y+z-x \\
y^{\prime }&=x-y+z \\
z^{\prime }&=x+y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 10692 |
\begin{align*}
t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y&={\mathrm e}^{2 t} t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.564 |
|
| 10693 |
\begin{align*}
x^{\prime }-x-2 y&=0 \\
y^{\prime }-2 y-3 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 10694 |
\begin{align*}
y^{\prime \prime }+4 y&=2 t -8 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 10695 | \begin{align*}
y^{\prime \prime }-2 y^{\prime }-y&=2 \cos \left (3 x \right )-3 \sin \left (2 x \right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.564 |
|
| 10696 |
\begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=18 x_{1}+7 x_{2}+4 x_{3} \\
x_{3}^{\prime }&=-27 x_{1}-9 x_{2}-5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.565 |
|
| 10697 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.565 |
|
| 10698 |
\begin{align*}
a k \,x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.565 |
|
| 10699 |
\begin{align*}
y^{\prime \prime }+y&=x \,{\mathrm e}^{x} \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.565 |
|
| 10700 |
\begin{align*}
x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.565 |
|