| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 9701 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=10 \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| 9702 |
\begin{align*}
4 y+y^{\prime \prime }&=\frac {1}{\cos \left (2 x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| 9703 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| 9704 |
\begin{align*}
y_{1}^{\prime }&=-3 y_{1}-3 y_{2}+4 y_{3} \\
y_{2}^{\prime }&=4 y_{1}+5 y_{2}-8 y_{3} \\
y_{3}^{\prime }&=2 y_{1}+3 y_{2}-5 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| 9705 |
\begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=3 y_{2}-2 y_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| 9706 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| 9707 |
\begin{align*}
y^{\prime \prime }&=\frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (a \left (a +1\right )-a \,x^{2} \left (a +3\right )\right ) y}{x^{2} \left (x^{2}-1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.721 |
|
| 9708 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| 9709 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }-18 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| 9710 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| 9711 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| 9712 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=x \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| 9713 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| 9714 |
\begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=-x+2 y-z \\
z^{\prime }&=-y+3 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| 9715 |
\begin{align*}
x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| 9716 |
\begin{align*}
x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-9 x^{2}+5\right ) y^{\prime }+\left (-3 x^{2}+4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.722 |
|
| 9717 |
\begin{align*}
2 y^{\prime \prime }-y^{\prime }+3 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.722 |
|
| 9718 |
\begin{align*}
\left (x^{2}+2 y^{\prime }\right ) y^{\prime \prime }+2 x y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.722 |
|
| 9719 |
\begin{align*}
y^{\prime \prime }+8 y^{\prime }+20 y&=\sin \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.722 |
|
| 9720 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=1-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.722 |
|
| 9721 |
\begin{align*}
9 x \left (1-x \right ) y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.722 |
|
| 9722 |
\begin{align*}
\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y&=\left (2 x +1\right )^{2} {\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.723 |
|
| 9723 |
\begin{align*}
-y+y^{\prime }&=t \,{\mathrm e}^{t} \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| 9724 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| 9725 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| 9726 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=-12 x +8 \\
y \left (1\right ) &= -2 \\
y^{\prime }\left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| 9727 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=3 x +25 \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| 9728 |
\begin{align*}
4 x y^{\prime \prime }+8 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| 9729 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| 9730 |
\begin{align*}
\operatorname {a3} y+\operatorname {a2} y^{\prime }+\operatorname {a1} y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| 9731 |
\begin{align*}
-y+x y^{\prime }+x^{3} y^{\prime \prime \prime }&=x \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| 9732 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| 9733 |
\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*} |
✓ |
✓ |
✓ |
✗ |
0.724 |
|
| 9734 |
\begin{align*}
y^{\prime \prime }&=-\frac {b^{2} y}{\left (-a^{2}+x^{2}\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| 9735 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| 9736 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| 9737 |
\begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=1-2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| 9738 |
\begin{align*}
y^{\prime }&=\frac {\cos \left (\frac {1}{x}\right )}{x^{2}} \\
y \left (\frac {2}{\pi }\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| 9739 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| 9740 |
\begin{align*}
y^{\prime \prime }&=x^{2} y-y^{\prime } \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| 9741 |
\begin{align*}
y^{\prime \prime }+\left (x -1\right ) y&={\mathrm e}^{x} \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✗ |
0.724 |
|
| 9742 |
\begin{align*}
y^{\prime \prime }+y&=x \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| 9743 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| 9744 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2}+3 \,{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}+2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| 9745 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 t}}{t^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.724 |
|
| 9746 |
\begin{align*}
4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| 9747 |
\begin{align*}
y_{1}^{\prime }&=3 y_{1}+y_{2}-y_{3} \\
y_{2}^{\prime }&=3 y_{1}+5 y_{2}+y_{3} \\
y_{3}^{\prime }&=-6 y_{1}+2 y_{2}+4 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| 9748 |
\begin{align*}
y^{\prime }&=\ln \left (x \right ) \\
y \left ({\mathrm e}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| 9749 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.725 |
|
| 9750 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=t \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| 9751 |
\begin{align*}
y+3 x y^{\prime }+9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=\left (1+\ln \left (x \right )\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| 9752 |
\begin{align*}
{y^{\prime }}^{2}-4 y^{\prime }+2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| 9753 |
\begin{align*}
4 y+y^{\prime \prime }&=8 \cos \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| 9754 |
\begin{align*}
y^{\prime \prime }-y&=\frac {2 \,{\mathrm e}^{-x}}{\left (1+{\mathrm e}^{-2 x}\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| 9755 |
\begin{align*}
y^{\prime }+y-v^{\prime }-v&=0 \\
y^{\prime }+v^{\prime }-v&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| 9756 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| 9757 |
\begin{align*}
{y^{\prime }}^{3}-{\mathrm e}^{2 x} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| 9758 |
\begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+9 y^{\prime }-10 y&=10 \,{\mathrm e}^{2 x}+20 \,{\mathrm e}^{x} \sin \left (2 x \right )-10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| 9759 |
\begin{align*}
y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.726 |
|
| 9760 |
\begin{align*}
x^{\prime }&=4 x-3 y \\
y^{\prime }&=8 x-6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| 9761 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| 9762 |
\begin{align*}
x^{\prime }+5 x+y&={\mathrm e}^{t} \\
y^{\prime }-x+3 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| 9763 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x +2 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| 9764 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 9765 |
\begin{align*}
3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 9766 |
\begin{align*}
y_{1}^{\prime }&=-y_{1}+y_{2}-y_{3} \\
y_{2}^{\prime }&=-2 y_{1}+2 y_{3} \\
y_{3}^{\prime }&=-y_{1}+3 y_{2}-y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 9767 |
\begin{align*}
y&=x y^{\prime }+k {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 9768 |
\begin{align*}
y^{\prime \prime }+16 y&=4 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 9769 |
\begin{align*}
y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (a -1\right ) b +a \,x^{2}+\left (1-a \right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.727 |
|
| 9770 |
\begin{align*}
x^{\prime }&=x+7 y \\
y^{\prime }&=3 x+5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 9771 |
\begin{align*}
x^{\prime \prime }-4 x&=t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 9772 |
\begin{align*}
x^{\prime }&=-3 x+2 \pi y \\
y^{\prime }&=4 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 9773 |
\begin{align*}
x^{\prime }&=\beta y \\
y^{\prime }&=\gamma x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 9774 |
\begin{align*}
x^{\prime }&=8 x+2 y-17 \\
y^{\prime }&=4 x+y-13 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 9775 |
\begin{align*}
y^{\prime \prime }-16 y&=16 t \,{\mathrm e}^{-4 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 9776 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 9777 |
\begin{align*}
y^{\prime }&=3 \sin \left (x \right ) \\
y \left (\pi \right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 9778 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }+\left (2-x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 9779 |
\begin{align*}
y^{\prime }&=\frac {1}{t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 9780 |
\begin{align*}
\sin \left (x \right ) y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 9781 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (-4 x^{3}+x \right ) y^{\prime }-x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| 9782 |
\begin{align*}
2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (-2 x^{2}+3\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| 9783 |
\begin{align*}
6 x^{2} y^{\prime \prime }+7 x y^{\prime }-\left (x^{2}+2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| 9784 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| 9785 |
\begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=2 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| 9786 |
\begin{align*}
y^{\prime \prime }-2 y x&=0 \\
y \left (2\right ) &= 1 \\
y^{\prime }\left (2\right ) &= 6 \\
\end{align*}
Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| 9787 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| 9788 |
\begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2}+y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.728 |
|
| 9789 |
\begin{align*}
y_{1}^{\prime }&=-y_{1}-12 y_{2}+8 y_{3} \\
y_{2}^{\prime }&=y_{1}-9 y_{2}+4 y_{3} \\
y_{3}^{\prime }&=y_{1}-6 y_{2}+y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| 9790 |
\begin{align*}
\left (2 x y^{3}+y\right ) y^{\prime }+2 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| 9791 |
\begin{align*}
x^{\prime }&=x-5 y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| 9792 |
\begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| 9793 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+3 x y^{\prime }+y x&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| 9794 |
\begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| 9795 |
\begin{align*}
2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (2 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| 9796 |
\begin{align*}
x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (-x^{2}+14\right ) y^{\prime }+2 \left (x^{2}+9\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| 9797 |
\begin{align*}
y^{\prime \prime }-y&=10 \,{\mathrm e}^{2 x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| 9798 |
\begin{align*}
y^{\prime \prime }-2 m y^{\prime }+m^{2} y&=\frac {{\mathrm e}^{m x}}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.730 |
|
| 9799 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2}+5 \,{\mathrm e}^{4 t} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| 9800 |
\begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.730 |
|