| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 7601 |
\begin{align*}
y^{\prime }&=y^{2}-\tan \left (x \right ) y+a \left (1-a \right ) \cot \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.678 |
|
| 7602 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=\frac {y y^{\prime }}{\sqrt {x^{2}+1}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.678 |
|
| 7603 |
\begin{align*}
y^{\prime \prime }+3 y&=5 \delta \left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 7604 |
\begin{align*}
y&=-y^{\prime } t +\frac {{y^{\prime }}^{5}}{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.678 |
|
| 7605 |
\begin{align*}
s y^{\prime \prime }+\lambda y&=0 \\
y \left (0\right ) &= 0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.678 |
|
| 7606 |
\begin{align*}
\left (2 x^{2}+3 x +1\right ) y^{\prime \prime }+\left (6+8 x \right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| 7607 |
\begin{align*}
y_{1}^{\prime }&=y_{1}+10 y_{2}-12 y_{3} \\
y_{2}^{\prime }&=2 y_{1}+2 y_{2}+3 y_{3} \\
y_{3}^{\prime }&=2 y_{1}-y_{2}+6 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| 7608 |
\begin{align*}
\left (x +4\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.679 |
|
| 7609 |
\begin{align*}
a x {y^{\prime }}^{2}-\left (a y+b x -a -b \right ) y^{\prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.679 |
|
| 7610 |
\begin{align*}
x^{\prime }&=x-8 y \\
y^{\prime }&=x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| 7611 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| 7612 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x \left (2+x \right ) y^{\prime }+2 \left (x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.680 |
|
| 7613 |
\begin{align*}
{\mathrm e}^{y^{\prime }}&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| 7614 |
\begin{align*}
y^{\prime \prime }&=2 y y^{\prime } \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.680 |
|
| 7615 |
\begin{align*}
y^{\prime }+3 y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 7616 |
\begin{align*}
2 t^{2} y^{\prime \prime }+3 y^{\prime } t -\left (1+t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 7617 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}+\frac {9}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.681 |
|
| 7618 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 7619 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +y&=0 \\
y \left (1\right ) &= -6 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 7620 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.681 |
|
| 7621 |
\begin{align*}
x^{\prime }-y^{\prime }&=x+y-t \\
2 x^{\prime }+3 y^{\prime }&=2 x+6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 7622 |
\begin{align*}
\cos \left (x \right ) y^{\prime }-\sin \left (x \right )&=0 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 7623 |
\begin{align*}
x^{\prime }&=3-2 y \\
y^{\prime }&=2 x-2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 7624 |
\begin{align*}
x {y^{\prime }}^{2}-y y^{\prime }+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.681 |
|
| 7625 |
\begin{align*}
t^{2} x^{\prime \prime }-3 t x^{\prime }+\left (4-t \right ) x&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.681 |
|
| 7626 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 7627 |
\begin{align*}
y_{1}^{\prime }&=2 y_{1}-y_{2}+{\mathrm e}^{t} \\
y_{2}^{\prime }&=3 y_{1}-2 y_{2}+{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.681 |
|
| 7628 |
\begin{align*}
5 y^{\prime \prime }+5 y^{\prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.682 |
|
| 7629 |
\begin{align*}
{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.682 |
|
| 7630 |
\begin{align*}
y^{\prime \prime }+y&=\frac {1}{x} \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.682 |
|
| 7631 |
\begin{align*}
\left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.682 |
|
| 7632 |
\begin{align*}
{y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.683 |
|
| 7633 |
\begin{align*}
\left (x -y\right ) y^{\prime }+x {y^{\prime }}^{2}+x \left (x +y\right ) y^{\prime \prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.683 |
|
| 7634 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.683 |
|
| 7635 |
\begin{align*}
y^{\prime }&=y+\sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.683 |
|
| 7636 |
\begin{align*}
y^{\prime }&=x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 7637 |
\begin{align*}
x^{2} \left (4 x +1\right ) y^{\prime \prime }-x \left (1-4 x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 7638 |
\begin{align*}
t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 7639 |
\begin{align*}
t^{2} y^{\prime \prime }+t \left (1+t \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 7640 |
\begin{align*}
{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.684 |
|
| 7641 |
\begin{align*}
y^{\prime }&=\frac {1}{-3+y} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 7642 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.684 |
|
| 7643 |
\begin{align*}
y^{\prime }&=-\lambda \,{\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\mu x} y-a \,{\mathrm e}^{\left (\mu -\lambda \right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.684 |
|
| 7644 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 7645 |
\begin{align*}
x^{\prime }+2 y^{\prime }-2 x+2 y&=3 \,{\mathrm e}^{t} \\
3 x^{\prime }+y^{\prime }+2 x+y&=4 \,{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 7646 |
\begin{align*}
{y^{\prime }}^{3}+y {y^{\prime }}^{2}-x^{2} y^{\prime }-x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 7647 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=8 x-2 y+{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 7648 |
\begin{align*}
x^{\prime }&=7 x+4 y-4 z \\
y^{\prime }&=4 x-8 y-z \\
z^{\prime }&=-4 x-y-8 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 7649 |
\begin{align*}
x^{\prime }&=3 x+2 y+2 z \\
y^{\prime }&=x+4 y+z \\
z^{\prime }&=-2 x-4 y-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*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 7650 |
\begin{align*}
x^{\prime }&=3 x-4 y+{\mathrm e}^{t} \\
y^{\prime }&=x-y+{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| 7651 |
\begin{align*}
y x -y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| 7652 |
\begin{align*}
f \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| 7653 |
\begin{align*}
y^{\prime } x +2 y x&=\sqrt {x} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.685 |
|
| 7654 |
\begin{align*}
x^{2} {y^{\prime }}^{2}-4 x \left (y+2\right ) y^{\prime }+4 \left (y+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| 7655 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}-f \left (x \right ) y y^{\prime }-g \left (x \right ) y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.685 |
|
| 7656 |
\begin{align*}
x^{\prime }&=x+3 y+2 t \\
y^{\prime }&=x-y+t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| 7657 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| 7658 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| 7659 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}+2 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{2}-4 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-4 x_{2}+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 ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| 7660 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\
y \left (0\right ) &= 7 \\
y^{\prime }\left (0\right ) &= 11 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.686 |
|
| 7661 |
\begin{align*}
y_{1}^{\prime }&=3 y_{1}+2 y_{2}-2 y_{3} \\
y_{2}^{\prime }&=-2 y_{1}+7 y_{2}-2 y_{3} \\
y_{3}^{\prime }&=-10 y_{1}+10 y_{2}-5 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.686 |
|
| 7662 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime } x +7 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.686 |
|
| 7663 |
\begin{align*}
\left (1-t \right ) y^{\prime \prime }+y^{\prime } t -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.686 |
|
| 7664 |
\begin{align*}
y^{\prime \prime }-a \,x^{n} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.686 |
|
| 7665 |
\begin{align*}
\left (3 x +2\right ) y^{\prime \prime }+3 y^{\prime } x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.686 |
|
| 7666 |
\begin{align*}
x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.686 |
|
| 7667 |
\begin{align*}
y {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.686 |
|
| 7668 |
\begin{align*}
x^{\prime }&=-12 x-7 y \\
y^{\prime }&=19 x+11 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.686 |
|
| 7669 |
\begin{align*}
\left (3 x^{2}+8 x +4\right ) y^{\prime \prime }+\left (16+12 x \right ) y^{\prime }+6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| 7670 |
\begin{align*}
y y^{\prime \prime }&=-f \left (x \right ) y^{3}+y^{4}-f \left (x \right ) y^{\prime }+{y^{\prime }}^{2}+y f^{\prime \prime }\left (x \right ) \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
0.687 |
|
| 7671 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| 7672 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| 7673 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| 7674 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| 7675 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| 7676 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x -9 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| 7677 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2} \\
x_{2}^{\prime }&=-14 x_{1}-5 x_{2}+x_{3} \\
x_{3}^{\prime }&=15 x_{1}+5 x_{2}-2 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 5 \\
x_{2} \left (0\right ) &= 5 \\
x_{3} \left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| 7678 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| 7679 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1} \\
x_{2}^{\prime }&=x_{1}-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=-x_{1}+x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.689 |
|
| 7680 |
\begin{align*}
y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.689 |
|
| 7681 |
\begin{align*}
x^{\prime }&=3 y \\
y^{\prime }&=3 \pi y-\frac {x}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.689 |
|
| 7682 |
\begin{align*}
y-y^{\prime } t&=-2 {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.689 |
|
| 7683 |
\begin{align*}
x^{\prime }&=5 x+3 y+1 \\
y^{\prime }&=-6 x-4 y+{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.689 |
|
| 7684 |
\begin{align*}
t^{2} y^{\prime \prime }+t^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.689 |
|
| 7685 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{2}-x_{3} \\
x_{2}^{\prime }&=x_{1}+3 x_{2}-x_{3} \\
x_{3}^{\prime }&=3 x_{1}+3 x_{2}-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 ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.690 |
|
| 7686 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.690 |
|
| 7687 |
\begin{align*}
x^{\prime \prime }-x&=\delta \left (t -5\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.690 |
|
| 7688 |
\begin{align*}
x^{\prime }+y&=t^{2} \\
-x+y^{\prime }&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.690 |
|
| 7689 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=-x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| 7690 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2}-{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| 7691 |
\begin{align*}
x^{\prime }-x+y&=2 \sin \left (t \right ) \\
x^{\prime }+y^{\prime }&=3 y-3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| 7692 |
\begin{align*}
4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.691 |
|
| 7693 |
\begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.691 |
|
| 7694 |
\begin{align*}
a x {y^{\prime }}^{2}+\left (b x -a y+c \right ) y^{\prime }-b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.691 |
|
| 7695 |
\begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=\cos \left (x \right ) x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| 7696 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| 7697 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| 7698 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x \left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| 7699 |
\begin{align*}
y^{\prime \prime }+y&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| 7700 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}-x_{2}-2 x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{3} \\
x_{3}^{\prime }&=x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.692 |
|