| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 6701 |
\begin{align*}
\left (x +y^{2}\right ) y^{\prime \prime }&=2 \left (x -y^{2}\right ) {y^{\prime }}^{3}-y^{\prime } \left (1+4 y y^{\prime }\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.569 |
|
| 6702 |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (0\right ) &= -4 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.569 |
|
| 6703 |
\begin{align*}
y^{\prime \prime \prime }&={y^{\prime \prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| 6704 |
\begin{align*}
\left (y^{2}-4\right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| 6705 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| 6706 |
\begin{align*}
y_{1}^{\prime }&=5 y_{1}+2 y_{2}+t \\
y_{2}^{\prime }&=-8 y_{1}-3 y_{2}-2 t \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| 6707 |
\begin{align*}
\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| 6708 |
\begin{align*}
y^{\prime \prime }&=\operatorname {f4} \left (x \right )+\operatorname {f3} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\left (\operatorname {f1} \left (x \right )-2 y\right ) y^{\prime } \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.570 |
|
| 6709 |
\begin{align*}
\left ({y^{\prime }}^{2}+a \left (-y+y^{\prime } x \right )\right ) y^{\prime \prime }&=b \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.570 |
|
| 6710 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| 6711 |
\begin{align*}
\left (x^{2}+2 y^{\prime }\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| 6712 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 x+2 y-z \\
z^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| 6713 |
\begin{align*}
y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.570 |
|
| 6714 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| 6715 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\
y \left (\frac {1}{2}\right ) &= 10 \\
\end{align*} Series expansion around \(x={\frac {1}{2}}\). |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| 6716 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +p^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| 6717 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| 6718 |
\begin{align*}
y y^{\prime \prime }&=g \left (x \right ) y^{2}+f \left (x \right ) y y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.571 |
|
| 6719 |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime \prime }&=\left (1+y^{2}\right ) \left (-y+y^{\prime } x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.571 |
|
| 6720 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| 6721 |
\begin{align*}
3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.571 |
|
| 6722 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| 6723 |
\begin{align*}
x^{\prime }+2 y^{\prime }&=t \\
x^{\prime }-y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| 6724 |
\begin{align*}
x^{\prime }&=-4 x-10 y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| 6725 |
\begin{align*}
2 n y-2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| 6726 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+3 x_{2} \\
x_{2}^{\prime }&=-2 x_{1}+5 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -2 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| 6727 |
\begin{align*}
\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.572 |
|
| 6728 |
\begin{align*}
y^{\prime \prime } x +a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.572 |
|
| 6729 |
\begin{align*}
x^{3} y^{\prime \prime }-a \left (-y+y^{\prime } x \right )^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.572 |
|
| 6730 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=2 x^{2}+4 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| 6731 |
\begin{align*}
x y^{\prime \prime \prime }+y^{\prime } x&=4 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
y^{\prime \prime }\left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| 6732 |
\begin{align*}
y^{\prime }&=x \,{\mathrm e}^{x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| 6733 |
\begin{align*}
y^{\prime }+3 y&=5 \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| 6734 |
\begin{align*}
\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.573 |
|
| 6735 |
\begin{align*}
16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.573 |
|
| 6736 |
\begin{align*}
y&=y^{\prime } x +\frac {1}{y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.573 |
|
| 6737 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
z^{\prime }&=2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.573 |
|
| 6738 |
\begin{align*}
x^{\prime }&=x+y+{\mathrm e}^{t} \\
y^{\prime }&=x+y-{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.573 |
|
| 6739 |
\begin{align*}
2 x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.573 |
|
| 6740 |
\begin{align*}
y y^{\prime }&=1+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.573 |
|
| 6741 |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.574 |
|
| 6742 |
\begin{align*}
x_{1}^{\prime }&=-\frac {5 x_{1}}{2}+x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}-\frac {5 x_{2}}{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2}-\frac {5 x_{3}}{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 3 \\
x_{3} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.574 |
|
| 6743 |
\begin{align*}
2 t^{2} y^{\prime \prime }-y^{\prime } t +\left (1+t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.574 |
|
| 6744 |
\begin{align*}
y^{\prime }&=x^{2} \ln \left (x \right ) \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.574 |
|
| 6745 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.574 |
|
| 6746 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.574 |
|
| 6747 |
\begin{align*}
\sqrt {y}\, y^{\prime \prime }-a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.574 |
|
| 6748 |
\begin{align*}
4 x^{\prime }+9 y^{\prime }+44 x+49 y&=t \\
3 x^{\prime }+7 y^{\prime }+34 x+38 y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.574 |
|
| 6749 |
\begin{align*}
x^{\prime }&=5 x+2 y+5 t \\
y^{\prime }&=3 x+4 y+17 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.574 |
|
| 6750 |
\begin{align*}
y&=2 y^{\prime } x +\sin \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.574 |
|
| 6751 |
\begin{align*}
t^{2} \left (1-t \right ) y^{\prime \prime }+\left (t^{2}+t \right ) y^{\prime }+\left (1-2 t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.574 |
|
| 6752 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}-6 x_{3} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}-2 x_{3} \\
x_{3}^{\prime }&=4 x_{1}-2 x_{2}-4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| 6753 |
\begin{align*}
\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y&=0 \\
y \left (-1\right ) &= 3 \\
y^{\prime }\left (-1\right ) &= -3 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| 6754 |
\begin{align*}
\left (2+x \right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+y&=0 \\
y \left (-1\right ) &= -2 \\
y^{\prime }\left (-1\right ) &= 3 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| 6755 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| 6756 |
\begin{align*}
y^{\prime }&=4 y+8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| 6757 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +56 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| 6758 |
\begin{align*}
\left (x^{3}+8\right ) y^{\prime \prime }+3 x^{2} y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| 6759 |
\begin{align*}
\left (x^{2}-2 x +2\right ) y^{\prime \prime }-4 \left (x -1\right ) y^{\prime }+6 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| 6760 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.576 |
|
| 6761 |
\begin{align*}
x^{\prime }&=a y \\
y^{\prime }&=-a x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| 6762 |
\begin{align*}
y^{\prime \prime } x -2 \left (x +1\right ) y^{\prime }+2 y&=0 \\
y \left (3\right ) &= 2 \\
y^{\prime }\left (3\right ) &= 0 \\
\end{align*} Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| 6763 |
\begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| 6764 |
\begin{align*}
y^{\prime }&=x \sqrt {x^{2}+9} \\
y \left (-4\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.577 |
|
| 6765 |
\begin{align*}
2 t^{2} y^{\prime \prime }+3 y^{\prime } t -\left (1+t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.577 |
|
| 6766 |
\begin{align*}
{y^{\prime }}^{2}+a x y^{\prime }&=b c \,x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.577 |
|
| 6767 |
\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 \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.578 |
|
| 6768 |
\begin{align*}
-4 y+3 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=4 \,{\mathrm e}^{x}+3 \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.578 |
|
| 6769 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.578 |
|
| 6770 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+a^{3} x^{2} y&=2 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.578 |
|
| 6771 |
\begin{align*}
x^{\prime }&=4 x-3 y \\
y^{\prime }&=6 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.578 |
|
| 6772 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| 6773 |
\begin{align*}
\left (3 x^{2}-6 x +5\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+12 y&=0 \\
y \left (1\right ) &= -1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| 6774 |
\begin{align*}
y y^{\prime \prime }&=y^{2} \left (f \left (x \right ) y+g^{\prime }\left (x \right )\right )+y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.579 |
|
| 6775 |
\begin{align*}
{y^{\prime }}^{2}&=4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| 6776 |
\begin{align*}
y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| 6777 |
\begin{align*}
\left (3 x^{2}+6 x +5\right ) y^{\prime \prime }+9 \left (x +1\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
0.580 |
|
| 6778 |
\begin{align*}
\left (2 x +1\right ) y^{\prime \prime }-\left (1-2 x \right ) y^{\prime }-\left (3-2 x \right ) y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -2 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.580 |
|
| 6779 |
\begin{align*}
\left (x^{2}+x -6\right ) y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.580 |
|
| 6780 |
\begin{align*}
y^{\prime }-y^{2}+\sin \left (x \right ) y-\cos \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.580 |
|
| 6781 |
\begin{align*}
y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.580 |
|
| 6782 |
\begin{align*}
y^{2}-2 \sin \left (2 t \right )+\left (1+2 t y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.580 |
|
| 6783 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.581 |
|
| 6784 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +8 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.581 |
|
| 6785 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.581 |
|
| 6786 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x \left (2+x \right ) y^{\prime }+2 \left (x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.581 |
|
| 6787 |
\begin{align*}
x^{\prime }&=x+3 z \\
y^{\prime }&=-y \\
z^{\prime }&=-3 x+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.581 |
|
| 6788 |
\begin{align*}
\left (8 {y^{\prime }}^{3}-27\right ) x&=12 y {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.581 |
|
| 6789 |
\begin{align*}
x^{\prime }&=2 x+4 y \\
y^{\prime }&=-2 x+6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.581 |
|
| 6790 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.581 |
|
| 6791 |
\begin{align*}
y_{1}^{\prime }&=y_{2}-y_{1} \\
y_{2}^{\prime }&=3 y_{1}-4 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| 6792 |
\begin{align*}
y y^{\prime \prime }&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.582 |
|
| 6793 |
\begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=24 x \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| 6794 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| 6795 |
\begin{align*}
y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y^{2} {y^{\prime }}^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.582 |
|
| 6796 |
\begin{align*}
x^{\prime }&=1+y \\
y^{\prime }&=1+x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| 6797 |
\begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=2 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| 6798 |
\begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
0.582 |
|
| 6799 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=4 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| 6800 |
\begin{align*}
y^{\prime }&=-t +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.582 |
|