| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10701 |
\begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=4 x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| 10702 |
\begin{align*}
4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10703 |
\begin{align*}
y^{\prime \prime }+3 y&=t^{3}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10704 |
\begin{align*}
x \left (-1+{y^{\prime }}^{2}\right )&=2 y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10705 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10706 |
\begin{align*}
z^{\prime \prime }+3 z^{\prime }+2 z&=24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10707 |
\begin{align*}
x^{\prime \prime }-3 x^{\prime }+2 x&=5 \cos \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10708 |
\begin{align*}
16 x^{2} y^{\prime \prime }+16 y^{\prime } x +\left (16 x^{2}-1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10709 |
\begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-x-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10710 |
\begin{align*}
y^{\prime \prime }+9 y&=\sec \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10711 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=4 \,{\mathrm e}^{x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10712 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10713 |
\begin{align*}
x \left (-1+{y^{\prime }}^{2}\right )&=2 y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| 10714 |
\begin{align*}
9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y&=x^{4}+x^{2} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.762 |
|
| 10715 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+\left (4 x -1\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| 10716 |
\begin{align*}
y^{\prime \prime }+9 y&=8 \cos \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= -1 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| 10717 |
\begin{align*}
y^{\prime \prime \prime }-8 y&={\mathrm e}^{i x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| 10718 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (\left (\alpha +\beta +1\right ) \left (x -a \right )^{2} \left (-b +x \right )+\left (1-\alpha -\beta \right ) \left (-b +x \right )^{2} \left (x -a \right )\right ) y^{\prime }}{\left (x -a \right )^{2} \left (-b +x \right )^{2}}-\frac {\alpha \beta \left (a -b \right )^{2} y}{\left (x -a \right )^{2} \left (-b +x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.762 |
|
| 10719 |
\begin{align*}
y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.762 |
|
| 10720 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=3 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{-t} \cos \left (t \right )+4 \,{\mathrm e}^{-t} t^{2} \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| 10721 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{3} \\
x_{2}^{\prime }&=9 x_{1}-x_{2}+2 x_{3} \\
x_{3}^{\prime }&=-9 x_{1}+4 x_{2}-x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 17 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10722 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10723 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10724 |
\begin{align*}
x_{1}^{\prime }&=-x_{2} \\
x_{2}^{\prime }&=x_{1} \\
x_{3}^{\prime }&=x_{1}-x_{4} \\
x_{4}^{\prime }&=x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10725 |
\begin{align*}
y x +3 x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10726 |
\begin{align*}
4 y+y^{\prime \prime }&=\sin \left (2 x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10727 |
\begin{align*}
x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.763 |
|
| 10728 |
\begin{align*}
\left (2 x^{2}+1\right ) y^{\prime \prime }+11 y^{\prime } x +9 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10729 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10730 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10731 |
\begin{align*}
y^{\prime \prime }&=9 x^{2}+2 x -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10732 |
\begin{align*}
y^{\prime \prime }-y x&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10733 |
\begin{align*}
t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.764 |
|
| 10734 |
\begin{align*}
x_{1}^{\prime }&=-x_{2}+x_{3} \\
x_{2}^{\prime }&=2 x_{1}-3 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}-x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.764 |
|
| 10735 |
\begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| 10736 |
\begin{align*}
y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| 10737 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+8 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| 10738 |
\begin{align*}
a^{4} y+2 a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=8 \cos \left (a x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| 10739 |
\begin{align*}
y^{\prime \prime }-x y^{\prime \prime \prime }+{y^{\prime \prime \prime }}^{3}&=0 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
0.765 |
|
| 10740 |
\begin{align*}
x^{\prime }&=5 x-6 y+1 \\
y^{\prime }&=6 x-7 y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| 10741 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}+5 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-6 x_{1}-6 x_{2}-5 x_{3} \\
x_{3}^{\prime }&=6 x_{1}+6 x_{2}+5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10742 |
\begin{align*}
z y^{\prime \prime }+\left (1-z \right ) y^{\prime }+\lambda y&=0 \\
\end{align*} Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10743 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10744 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+2 x_{3} \\
x_{2}^{\prime }&=2 x_{2}+2 x_{3} \\
x_{3}^{\prime }&=-x_{1}+x_{2}+3 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 11 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10745 |
\begin{align*}
y^{\prime }+y^{\prime \prime \prime }&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10746 |
\begin{align*}
\left (x +1\right ) y^{\prime \prime }+2 y^{\prime }&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10747 |
\begin{align*}
y^{\prime }&=z \\
z^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10748 |
\begin{align*}
y^{\prime }&=-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10749 |
\begin{align*}
y^{\prime \prime }+\sin \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10750 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (2 x \right )^{2}+\sin \left (\frac {x}{2}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10751 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.767 |
|
| 10752 |
\begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right ) \csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10753 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=8 \sin \left (4 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10754 |
\begin{align*}
2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| 10755 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| 10756 |
\begin{align*}
\left (x +1\right ) \left (x^{2}+1\right ) y^{\prime }&=2 x^{2}+x \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| 10757 |
\begin{align*}
y^{\prime }&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| 10758 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| 10759 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| 10760 |
\begin{align*}
-x^{\prime }+2 y^{\prime }&=x+3 y+{\mathrm e}^{t} \\
3 x^{\prime }-4 y^{\prime }&=x-15 y+{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10761 |
\begin{align*}
y^{2} {y^{\prime }}^{2}+2 y y^{\prime } x +a -y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.769 |
|
| 10762 |
\begin{align*}
x^{2} y^{\prime \prime }+4 \left (a +x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.769 |
|
| 10763 |
\begin{align*}
y^{\prime }&=\frac {1}{y-3} \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10764 |
\begin{align*}
\left (x +1\right ) \left (x^{2}+1\right ) y^{\prime }&=2 x^{2}+x \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10765 |
\begin{align*}
{y^{\prime }}^{2} \left (x^{2}-1\right )&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10766 |
\begin{align*}
x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y&=x^{4}+2 x -5 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.769 |
|
| 10767 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}+5\right ) y&=x \,{\mathrm e}^{-\frac {x^{2}}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.769 |
|
| 10768 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-x^{2}-6 x +1\right ) y^{\prime }+\left (x^{2}+6 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 10769 |
\begin{align*}
2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=x^{3}+1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.770 |
|
| 10770 |
\begin{align*}
2 y-a y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.770 |
|
| 10771 |
\begin{align*}
\left (\operatorname {a2} x +\operatorname {c2} \right ) {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {a0} x +\operatorname {b0} y+\operatorname {c0}&=0 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
0.770 |
|
| 10772 |
\begin{align*}
y^{\prime \prime }+p_{1} y^{\prime }+p_{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 10773 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=-2 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 ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10774 |
\begin{align*}
2 y^{\prime \prime } x -y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10775 |
\begin{align*}
x +3 y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10776 |
\begin{align*}
y^{\prime \prime }+y&=-\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10777 |
\begin{align*}
y^{\prime \prime }&=-\frac {2 y^{\prime }}{x}-\frac {c y}{x^{2} \left (a x +b \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.771 |
|
| 10778 |
\begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}+b x y+c \,x^{n}+s \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.771 |
|
| 10779 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{4 x^{2}}\right ) y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.771 |
|
| 10780 |
\begin{align*}
4 x^{\prime }-y^{\prime }+3 x&=\sin \left (t \right ) \\
x^{\prime }+y&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10781 |
\begin{align*}
u^{\prime }&=2 v-1 \\
v^{\prime }&=1+2 u \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10782 |
\begin{align*}
y^{\prime \prime }&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10783 |
\begin{align*}
t^{2} y^{\prime \prime }+3 y^{\prime } t -3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| 10784 |
\begin{align*}
y^{\prime \prime }&=\cos \left (y x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} Series expansion around \(x=\frac {\pi }{2}\). |
✓ |
✓ |
✓ |
✗ |
0.772 |
|
| 10785 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| 10786 |
\begin{align*}
4 x^{2} y^{\prime \prime }+8 y^{\prime } x -\left (4 x^{2}+12 x +3\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.772 |
|
| 10787 |
\begin{align*}
y^{\prime } x +2&=\sqrt {x} \\
y \left (1\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| 10788 |
\begin{align*}
y^{\prime }-{\mathrm e}^{x} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| 10789 |
\begin{align*}
y^{\prime }&=x \sin \left (x^{2}\right ) \\
y \left (\frac {\sqrt {2}\, \sqrt {\pi }}{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10790 |
\begin{align*}
t^{2} y^{\prime \prime }-t \left (1+t \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10791 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y&=0 \\
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*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10792 |
\begin{align*}
3 y^{\prime }+12 y&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10793 |
\begin{align*}
x^{\prime }&=-x+4 y+2 z \\
y^{\prime }&=4 x-y-2 z \\
z^{\prime }&=6 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10794 |
\begin{align*}
y^{\prime \prime }&=-\frac {y^{\prime }}{x +1}-\frac {y}{x \left (x +1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.773 |
|
| 10795 |
\begin{align*}
x^{\prime \prime }-x&=\frac {{\mathrm e}^{t}}{1+{\mathrm e}^{t}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10796 |
\begin{align*}
4 x^{\prime }-y^{\prime }+3 x&=\sin \left (t \right ) \\
x^{\prime }+y&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10797 |
\begin{align*}
4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10798 |
\begin{align*}
y^{\prime \prime }+y&=x +2 \,{\mathrm e}^{-x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10799 |
\begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (-2+t \right )+\operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10800 |
\begin{align*}
x_{1}^{\prime }&=-\frac {5 x_{1}}{4}+\frac {3 x_{2}}{4}+2 t \\
x_{2}^{\prime }&=\frac {3 x_{1}}{4}-\frac {5 x_{2}}{4}+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|