| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 11601 |
\begin{align*}
y^{\prime \prime }+2 n^{2} y^{\prime }+n^{4} y&=\sin \left (k x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.637 |
|
| 11602 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&=\delta \left (t -\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.637 |
|
| 11603 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+a^{3} x^{2} y&=2 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.637 |
|
| 11604 |
\begin{align*}
2 \left (1-x \right ) x y^{\prime \prime }+y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.637 |
|
| 11605 |
\begin{align*}
x^{\prime }&=7 x+y-1-6 \,{\mathrm e}^{t} \\
y^{\prime }&=-4 x+3 y+4 \,{\mathrm e}^{t}-3 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.637 |
|
| 11606 |
\begin{align*}
x^{\prime }&=\cos \left (t \right ) \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.637 |
|
| 11607 |
\begin{align*}
x^{\prime }&=5 x-6 y+1 \\
y^{\prime }&=6 x-7 y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.637 |
|
| 11608 |
\begin{align*}
y^{\prime \prime }+9 y&=2 \sec \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 11609 |
\begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=-4 x_{1}+x_{2} \\
x_{3}^{\prime }&=3 x_{1}+6 x_{2}+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 ) &= -30 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 11610 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-2 x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}-4 x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{1}+2 x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 11611 |
\begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 11612 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{x} \left (x +1\right )+2 \,{\mathrm e}^{2 x}+3 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 11613 |
\begin{align*}
-4 y x +x^{2} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.638 |
|
| 11614 |
\begin{align*}
2 y y^{\prime \prime }&=y^{2} \left (a +b y\right )+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.638 |
|
| 11615 |
\begin{align*}
\left (-y^{\prime }+y^{\prime \prime } x \right )^{2}&=1+{y^{\prime \prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.638 |
|
| 11616 |
\begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (16 x^{4}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 11617 |
\begin{align*}
y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 11618 | \begin{align*}
{y^{\prime }}^{2}+\left (b x +a y\right ) y^{\prime }+a b x y&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.638 |
|
| 11619 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 11620 |
\begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (3\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
0.638 |
|
| 11621 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 t} \arctan \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 11622 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 11623 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=\delta \left (-1+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 11624 |
\begin{align*}
x_{1}^{\prime }&=-k_{1} x_{1} \\
x_{2}^{\prime }&=k_{1} x_{1}-k_{2} x_{2} \\
x_{3}^{\prime }&=k_{2} x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= m_{0} \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 11625 |
\begin{align*}
x^{\prime }+4 x+3 y&=t \\
y^{\prime }+2 x+5 y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 11626 |
\begin{align*}
y^{\prime \prime }+y&=x \,{\mathrm e}^{-x}+3 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 11627 |
\begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=-3 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 11628 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+\frac {y}{16}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.638 |
|
| 11629 |
\begin{align*}
4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| 11630 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| 11631 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{6}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| 11632 |
\begin{align*}
4 x^{\prime }+9 y^{\prime }+11 x+31 y&={\mathrm e}^{t} \\
3 x^{\prime }+7 y^{\prime }+8 x+24 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| 11633 |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (a x +b -c \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.639 |
|
| 11634 |
\begin{align*}
x^{\prime \prime }+4 x&=\sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| 11635 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| 11636 |
\begin{align*}
y^{\prime \prime }&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| 11637 | \begin{align*}
y^{\prime \prime }&=x^{n} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.640 |
|
| 11638 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}-x_{3} \\
x_{2}^{\prime }&=3 x_{1}-4 x_{2}-3 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| 11639 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.640 |
|
| 11640 |
\begin{align*}
y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2}+a x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.640 |
|
| 11641 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| 11642 |
\begin{align*}
4 y+y^{\prime \prime }&={\mathrm e}^{x}+\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| 11643 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| 11644 |
\begin{align*}
t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| 11645 |
\begin{align*}
y+y^{\prime }&=\operatorname {Heaviside}\left (t -2\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| 11646 |
\begin{align*}
x^{\prime }&=4 x+y+2 t \\
y^{\prime }&=-2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| 11647 |
\begin{align*}
4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| 11648 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| 11649 |
\begin{align*}
y^{\prime \prime } x&=y^{\prime }+{y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| 11650 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-6\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.641 |
|
| 11651 |
\begin{align*}
4 {y^{\prime }}^{2}-9 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| 11652 |
\begin{align*}
x^{2} y^{2} y^{\prime \prime }-3 y^{2} y^{\prime } x +4 y^{3}+x^{6}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.641 |
|
| 11653 |
\begin{align*}
4 y+y^{\prime \prime }&=3 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| 11654 |
\begin{align*}
3 y^{\prime } y+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.641 |
|
| 11655 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| 11656 | \begin{align*}
5 y+{y^{\prime }}^{2}&=x \left (x +y^{\prime }\right ) \\
\end{align*} | ✓ | ✓ | ✗ | ✓ | 0.642 |
|
| 11657 |
\begin{align*}
x^{2} y^{2} y^{\prime \prime }&=\left (y^{2}+x^{2}\right ) \left (-y+y^{\prime } x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.642 |
|
| 11658 |
\begin{align*}
x \left (2+x \right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| 11659 |
\begin{align*}
y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.642 |
|
| 11660 |
\begin{align*}
x^{2} \left (x -a \right )^{2} y^{\prime \prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.642 |
|
| 11661 |
\begin{align*}
y&=x \left (1+y^{\prime }\right )+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| 11662 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+20 y&=-3 \sin \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| 11663 |
\begin{align*}
x^{\prime }&=5 x+4 y+2 z \\
y^{\prime }&=4 x+5 y+2 z \\
z^{\prime }&=2 x+2 y+2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| 11664 |
\begin{align*}
a^{2}-x y^{\prime } \sqrt {-a^{2}+x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| 11665 |
\begin{align*}
y^{\prime \prime }+4 y&=3 \csc \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.643 |
|
| 11666 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.643 |
|
| 11667 |
\begin{align*}
-\left (p^{2}-x^{2}\right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.643 |
|
| 11668 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=3 y-3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.643 |
|
| 11669 |
\begin{align*}
y^{\prime \prime }+b y^{\prime }+c y&=0 \\
y \left (\pi \right ) &= 0 \\
y \left (2 \pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.643 |
|
| 11670 |
\begin{align*}
x^{\prime }&=5 x+2 y \\
y^{\prime }&=-17 x-5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.643 |
|
| 11671 |
\begin{align*}
x^{\prime }&=x-6 y \\
y^{\prime }&=-2 x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.643 |
|
| 11672 |
\begin{align*}
i^{\prime }+5 i&=10 \\
i \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.643 |
|
| 11673 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.643 |
|
| 11674 |
\begin{align*}
2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| 11675 |
\begin{align*}
y_{1}^{\prime }-y_{2}&=0 \\
4 y_{1}+y_{2}^{\prime }-4 y_{2}-2 y_{3}&=0 \\
-2 y_{1}+y_{2}+y_{3}^{\prime }+y_{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| 11676 | \begin{align*}
-2 y^{\prime }+\left (a -x \right ) y^{\prime \prime }&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.644 |
|
| 11677 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+y^{\prime } x \right )&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| 11678 |
\begin{align*}
x^{6} {y^{\prime }}^{2}&=8 y^{\prime } x +16 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| 11679 |
\begin{align*}
\left (x +3\right ) x^{2} y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| 11680 |
\begin{align*}
x^{2} \left (x -y\right ) y^{\prime \prime }+a \left (-y+y^{\prime } x \right )^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.644 |
|
| 11681 |
\begin{align*}
y^{\prime \prime }+y&=\frac {1}{1+\sin \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| 11682 |
\begin{align*}
x^{\prime }&=5 x-4 y+{\mathrm e}^{3 t} \\
y^{\prime }&=x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| 11683 |
\begin{align*}
x^{\prime }&=y-x+{\mathrm e}^{t} \\
y^{\prime }&=x-y+{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| 11684 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\
x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| 11685 |
\begin{align*}
a y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| 11686 |
\begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| 11687 |
\begin{align*}
y^{\prime }+2 y&=-6 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| 11688 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.645 |
|
| 11689 |
\begin{align*}
4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x^{2} y^{\prime }+\left (1-5 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.645 |
|
| 11690 |
\begin{align*}
x^{3} {y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.645 |
|
| 11691 |
\begin{align*}
2 \left (b x +3 a \right ) y-2 x \left (b x +2 a \right ) y^{\prime }+x^{2} \left (b x +a \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.645 |
|
| 11692 |
\begin{align*}
\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.645 |
|
| 11693 |
\begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.645 |
|
| 11694 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-1\right ) y&=-3 \,{\mathrm e}^{x^{2}} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.645 |
|
| 11695 | \begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=3 x-2 y \\
z^{\prime }&=2 y+3 z \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.645 |
|
| 11696 |
\begin{align*}
x^{\prime }&=4 x \\
y^{\prime }&=x-2 y \\
z^{\prime }&=x-4 y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.645 |
|
| 11697 |
\begin{align*}
\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime \prime }-a \,\lambda ^{2} {\mathrm e}^{\lambda x} y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.645 |
|
| 11698 |
\begin{align*}
x^{\prime }&=-5 x+3 y+{\mathrm e}^{-t} \\
y^{\prime }&=2 x-10 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.645 |
|
| 11699 |
\begin{align*}
y^{\prime }&={\mathrm e}^{-y}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.645 |
|
| 11700 |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=6 x_{1}+4 \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (1\right ) &= 0 \\
x_{2} \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.645 |
|