| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12701 |
\begin{align*}
y {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| 12702 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+x&=5 \sin \left (2 t \right )+{\mathrm e}^{t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| 12703 |
\begin{align*}
y_{1}^{\prime }&=4 y_{1}+6 y_{2}+6 y_{3} \\
y_{2}^{\prime }&=y_{1}+3 y_{2}+2 y_{3} \\
y_{3}^{\prime }&=-y_{1}-4 y_{2}-3 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| 12704 |
\begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| 12705 |
\begin{align*}
9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| 12706 |
\begin{align*}
y^{\prime \prime }-\left (\frac {1}{x}+2\right ) y^{\prime }+\left (x +\frac {1}{x^{2}}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| 12707 |
\begin{align*}
y^{\prime }&=-y+3 t \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| 12708 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (x^{2} \sin \left (x \right )-2 \cos \left (x \right ) x \right ) y^{\prime }}{x^{2} \cos \left (x \right )}-\frac {\left (2 \cos \left (x \right )-x \sin \left (x \right )\right ) y}{x^{2} \cos \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.748 |
|
| 12709 |
\begin{align*}
y^{\prime \prime }+4 y&=3 \sec \left (2 t \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.748 |
|
| 12710 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+2 x_{2}-x_{4} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+2 x_{4} \\
x_{3}^{\prime }&=3 x_{3} \\
x_{4}^{\prime }&=-x_{1}+2 x_{2}+2 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.748 |
|
| 12711 |
\begin{align*}
x^{\prime }&=4 x \left (7-x\right ) \\
x \left (0\right ) &= 11 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.749 |
|
| 12712 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.749 |
|
| 12713 |
\begin{align*}
y_{1}^{\prime }&=-2 y_{1}+2 y_{2}-6 y_{3} \\
y_{2}^{\prime }&=2 y_{1}+6 y_{2}+2 y_{3} \\
y_{3}^{\prime }&=-2 y_{1}-2 y_{2}+2 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.749 |
|
| 12714 |
\begin{align*}
y^{\prime }-i y&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.749 |
|
| 12715 |
\begin{align*}
y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.749 |
|
| 12716 |
\begin{align*}
4 y+y^{\prime \prime }&=\tan \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.749 |
|
| 12717 |
\begin{align*}
4 y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= \beta \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.750 |
|
| 12718 | \begin{align*}
y^{\prime }-3 y&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 1 & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. | ✓ | ✓ | ✓ | ✗ | 0.750 |
|
| 12719 |
\begin{align*}
-y+y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.750 |
|
| 12720 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=\frac {2}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| 12721 |
\begin{align*}
4 x^{2} y^{\prime \prime }+\left (1-2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| 12722 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x +3\right ) y^{\prime }+\left (2 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| 12723 |
\begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -5\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.750 |
|
| 12724 |
\begin{align*}
{y^{\prime }}^{2}&=\frac {1}{x^{2} y^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.750 |
|
| 12725 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+3 y^{\prime } x +a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.750 |
|
| 12726 |
\begin{align*}
y^{\prime \prime }+2 a \,x^{n} y^{\prime }+a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.750 |
|
| 12727 |
\begin{align*}
y^{\prime \prime }+a^{2} y&=\delta \left (x -\pi \right ) f \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| 12728 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| 12729 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| 12730 |
\begin{align*}
y^{\prime \prime }&=1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| 12731 |
\begin{align*}
\ln \left (x^{2}+1\right ) y^{\prime \prime }+\frac {4 x y^{\prime }}{x^{2}+1}+\frac {\left (-x^{2}+1\right ) y}{\left (x^{2}+1\right )^{2}}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.751 |
|
| 12732 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| 12733 |
\begin{align*}
\left (x^{3} y^{3}+y^{2} x^{2}+y x +1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-y x +1\right ) x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| 12734 |
\begin{align*}
3 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| 12735 |
\begin{align*}
9 y+6 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| 12736 |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.752 |
|
| 12737 |
\begin{align*}
{y^{\prime }}^{2}&=a^{2} y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.752 |
|
| 12738 | \begin{align*}
2 y y^{\prime \prime }&=-y^{2} \left (1+a y^{3}\right )+6 {y^{\prime }}^{2} \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 0.752 |
|
| 12739 |
\begin{align*}
y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.752 |
|
| 12740 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.752 |
|
| 12741 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=2 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.752 |
|
| 12742 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.752 |
|
| 12743 |
\begin{align*}
9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| 12744 |
\begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y&={\mathrm e}^{x} \left (12 x -2 \cos \left (x \right )+2 \sin \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| 12745 |
\begin{align*}
9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| 12746 |
\begin{align*}
y^{\prime \prime } x +\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| 12747 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{t}+\lambda y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| 12748 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| 12749 |
\begin{align*}
n \,x^{3} y^{\prime \prime }&=\left (y-y^{\prime } x \right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.753 |
|
| 12750 |
\begin{align*}
x \left (x^{2}-4\right ) y^{\prime }&=1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| 12751 |
\begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.753 |
|
| 12752 |
\begin{align*}
y_{1}^{\prime }&=4 y_{2} \\
y_{2}^{\prime }&=-y_{1} \\
y_{3}^{\prime }&=y_{1}+4 y_{2}-y_{3} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= 1 \\
y_{3} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| 12753 |
\begin{align*}
-6 y x +6 x^{2} y^{\prime }+\left (-2 x^{3}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| 12754 |
\begin{align*}
\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| 12755 |
\begin{align*}
y^{2} {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.754 |
|
| 12756 |
\begin{align*}
2 y+y^{\prime }&=3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| 12757 | \begin{align*}
2 y^{\prime \prime } x -\left (2 x +3\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.754 |
|
| 12758 |
\begin{align*}
2 y^{\prime \prime }+t y^{\prime }-2 y&=10 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.754 |
|
| 12759 |
\begin{align*}
t x^{\prime \prime }&=t x+1 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(t=0\). |
✗ |
✗ |
✗ |
✗ |
0.754 |
|
| 12760 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| 12761 |
\begin{align*}
x_{1}^{\prime }&=-20 x_{1}+11 x_{2}+13 x_{3} \\
x_{2}^{\prime }&=12 x_{1}-x_{2}-7 x_{3} \\
x_{3}^{\prime }&=-48 x_{1}+21 x_{2}+31 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.755 |
|
| 12762 |
\begin{align*}
u^{\prime }&=-a \left (u-100 t \right ) \\
u \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.755 |
|
| 12763 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= {\frac {5}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.755 |
|
| 12764 |
\begin{align*}
2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.755 |
|
| 12765 |
\begin{align*}
2 \left (x +3\right )^{2} y^{\prime \prime }-\left (x^{2}+5 x +6\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=-3\). |
✓ |
✓ |
✓ |
✓ |
0.755 |
|
| 12766 |
\begin{align*}
\left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y&=3 x^{2} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.756 |
|
| 12767 |
\begin{align*}
3 x^{4} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| 12768 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| 12769 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+\cos \left (t w \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| 12770 |
\begin{align*}
y^{\prime \prime }+y&=\frac {1}{\cos \left (2 x \right )^{{3}/{2}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.756 |
|
| 12771 |
\begin{align*}
y^{\prime }&=4 y+1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| 12772 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| 12773 |
\begin{align*}
x^{\prime }&=3 x \left (5-x\right ) \\
x \left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 12774 |
\begin{align*}
x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 12775 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{3} \\
x_{2}^{\prime }&=-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=2 x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 12776 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-5 x_{2}+x_{3} \\
x_{2}^{\prime }&=4 x_{1}-9 x_{2}-x_{3} \\
x_{3}^{\prime }&=3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 12777 | \begin{align*}
4 x -2 y^{\prime } y+x {y^{\prime }}^{2}&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.757 |
|
| 12778 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 12779 |
\begin{align*}
2 \left (1-x \right ) y-\left (-x^{2}+2\right ) y^{\prime }+\left (-x +2\right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.757 |
|
| 12780 |
\begin{align*}
\left (y^{2}+x^{2}\right ) y^{\prime }+2 x \left (2 x +y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.757 |
|
| 12781 |
\begin{align*}
\left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 12782 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.757 |
|
| 12783 |
\begin{align*}
4 y+y^{\prime \prime }&=12 x^{2}-16 x \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 12784 |
\begin{align*}
y^{\prime }&=12+4 y-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 12785 |
\begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 12786 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=t +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 12787 |
\begin{align*}
t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.758 |
|
| 12788 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{2 x}-\frac {\left (x +1\right ) y}{2 x^{2}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| 12789 |
\begin{align*}
t^{2} x^{\prime \prime }-3 t x^{\prime }+\left (-t +4\right ) x&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.758 |
|
| 12790 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| 12791 |
\begin{align*}
y_{1}^{\prime }&=4 y_{1}-y_{2}-4 y_{3} \\
y_{2}^{\prime }&=4 y_{1}-3 y_{2}-2 y_{3} \\
y_{3}^{\prime }&=y_{1}-y_{2}-y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| 12792 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=x_{1}+2 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+10 x_{2}+2 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -1 \\
x_{2} \left (0\right ) &= -4 \\
x_{3} \left (0\right ) &= 13 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| 12793 |
\begin{align*}
a \sqrt {1+{y^{\prime }}^{2}}+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.759 |
|
| 12794 |
\begin{align*}
x \left (x +1\right )^{2} y y^{\prime \prime }&=a \left (2+x \right ) y^{2}-2 \left (x^{2}+1\right ) y y^{\prime }+x \left (x +1\right )^{2} {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.759 |
|
| 12795 |
\begin{align*}
3 z^{\prime }+11 z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| 12796 | \begin{align*}
y&=-y^{\prime } x +x^{4} {y^{\prime }}^{2} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.759 |
|
| 12797 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-n^{2}+x^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.759 |
|
| 12798 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| 12799 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2}+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| 12800 |
\begin{align*}
x^{2} y^{\prime \prime }+y&=3 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|