| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12001 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 12002 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 x^{2} y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.674 |
|
| 12003 |
\begin{align*}
2 y^{\prime \prime } x +5 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 12004 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 12005 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 12006 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{2}+\cos \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.674 |
|
| 12007 |
\begin{align*}
y y^{\prime \prime }-a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.674 |
|
| 12008 |
\begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
0.674 |
|
| 12009 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 12010 |
\begin{align*}
\left (2+3 y\right ) y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.674 |
|
| 12011 |
\begin{align*}
\sin \left (t \right ) y^{\prime \prime \prime }-\cos \left (t \right ) y^{\prime }&=2 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.674 |
|
| 12012 |
\begin{align*}
x_{1}^{\prime }&=-40 x_{1}-12 x_{2}+54 x_{3} \\
x_{2}^{\prime }&=35 x_{1}+13 x_{2}-46 x_{3} \\
x_{3}^{\prime }&=-25 x_{1}-7 x_{2}+34 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 12013 |
\begin{align*}
t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y&={\mathrm e}^{2 t} t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.675 |
|
| 12014 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=4 \,{\mathrm e}^{-x} \left (1-6 x \right )-2 \cos \left (x \right ) x +2 \left (x +1\right ) \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 12015 |
\begin{align*}
{y^{\prime }}^{2}+y^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 12016 |
\begin{align*}
-\left (x^{2}+4 x +2\right ) y-\left (-x^{3}-3 x^{2}+2 x +2\right ) y^{\prime }+x \left (-x^{2}+2\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.675 |
|
| 12017 |
\begin{align*}
\cos \left (y\right ) \sin \left (x \right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\
y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 12018 | \begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&={\mathrm e}^{-2 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.675 |
|
| 12019 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }-y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.675 |
|
| 12020 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 12021 |
\begin{align*}
y^{\prime }-7 y&=14 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 12022 |
\begin{align*}
y^{\prime }&=y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 12023 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\
y \left (1\right ) &= {\mathrm e} \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 12024 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 12025 |
\begin{align*}
y_{1}^{\prime }&=-y_{1}-4 y_{2}+4 \\
y_{2}^{\prime }&=y_{1}-y_{2}+1 \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 12026 |
\begin{align*}
y^{\prime }&=y-x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| 12027 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 \left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| 12028 |
\begin{align*}
-3 y+\left (-x +2\right ) y^{\prime }+\left (-x +2\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| 12029 |
\begin{align*}
y^{\prime \prime }&=-\frac {27 x y}{16 \left (x^{3}-1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| 12030 |
\begin{align*}
x^{\prime \prime }+4 x&=289 t \,{\mathrm e}^{t} \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| 12031 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+10 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| 12032 |
\begin{align*}
x_{1}^{\prime }&=-\frac {x_{1}}{4}+x_{2} \\
x_{2}^{\prime }&=-x_{1}-\frac {x_{2}}{4} \\
x_{3}^{\prime }&=\frac {x_{3}}{10} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 12033 |
\begin{align*}
4 t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 12034 |
\begin{align*}
9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.677 |
|
| 12035 |
\begin{align*}
x -y^{2}+2 x y^{\prime } y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 12036 |
\begin{align*}
3 y^{3}-y x -\left (x^{2}+6 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 12037 | \begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.677 |
|
| 12038 |
\begin{align*}
y^{\prime \prime } x -4 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 12039 |
\begin{align*}
x^{\prime }&=-x-y \\
y^{\prime }&=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\
z^{\prime }&=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 12040 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x -x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.677 |
|
| 12041 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x -\left (4 x^{2}+1\right ) y-4 \sqrt {x^{3}}\, {\mathrm e}^{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.677 |
|
| 12042 |
\begin{align*}
x^{\prime }&=-12 x-7 y \\
y^{\prime }&=19 x+11 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 12043 |
\begin{align*}
y^{\prime \prime } x -\left (x -1\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 12044 |
\begin{align*}
y^{\prime \prime }&=x {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 12045 |
\begin{align*}
y^{\prime \prime }+{\mathrm e}^{-2 y}&=0 \\
y \left (3\right ) &= 0 \\
y^{\prime }\left (3\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.677 |
|
| 12046 |
\begin{align*}
y^{\prime \prime }&=2 t +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 12047 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+5 x&=10 \cos \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 12048 |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }+26 x&=600 \cos \left (10 t \right ) \\
x \left (0\right ) &= 10 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 12049 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 12050 |
\begin{align*}
y_{1}^{\prime }&=-y_{1}-4 y_{2}-y_{3} \\
y_{2}^{\prime }&=3 y_{1}+6 y_{2}+y_{3} \\
y_{3}^{\prime }&=-3 y_{1}-2 y_{2}+3 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 ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 12051 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{3 x}}{2}-\frac {{\mathrm e}^{-3 x}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 12052 |
\begin{align*}
3 x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 12053 |
\begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x -2 x^{2}}{x^{2}-y x +y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.678 |
|
| 12054 |
\begin{align*}
-y+\left (x +1\right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.678 |
|
| 12055 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+4 y x&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.678 |
|
| 12056 | \begin{align*}
x^{\prime }&=x+y+4 z \\
y^{\prime }&=2 y \\
z^{\prime }&=x+y+z \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 3 \\
z \left (0\right ) &= 0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.678 |
|
| 12057 |
\begin{align*}
4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.678 |
|
| 12058 |
\begin{align*}
x^{\prime }+p x&=q \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 12059 |
\begin{align*}
9 y+6 y^{\prime }+y^{\prime \prime }&=169 \sin \left (2 x \right ) \\
y \left (0\right ) &= -10 \\
y^{\prime }\left (0\right ) &= 9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 12060 |
\begin{align*}
y^{\prime \prime } x&=3 y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 12061 |
\begin{align*}
y^{\prime \prime }+16 y&=\sin \left (4 x +\alpha \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 12062 |
\begin{align*}
9 y+6 y^{\prime }+y^{\prime \prime }&=10 \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 12063 |
\begin{align*}
x_{1}^{\prime }&=-7 x_{1}+9 x_{2}-6 x_{3} \\
x_{2}^{\prime }&=-8 x_{1}+11 x_{2}-7 x_{3} \\
x_{3}^{\prime }&=-2 x_{1}+3 x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 12064 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 12065 |
\begin{align*}
y^{\prime }+a y&=b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 12066 |
\begin{align*}
y_{1}^{\prime }&=3 y_{1}-2 y_{2} \\
y_{2}^{\prime }&=y_{2}-y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| 12067 |
\begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
0.679 |
|
| 12068 |
\begin{align*}
x^{\prime }&=a x+10 y \\
y^{\prime }&=-x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| 12069 |
\begin{align*}
y^{\prime \prime }+p \left (t \right ) y^{\prime }+q \left (t \right ) y&=t +1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.680 |
|
| 12070 |
\begin{align*}
2 y^{\prime \prime } x +5 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| 12071 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +p^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| 12072 |
\begin{align*}
y^{\prime \prime }&=-a \,x^{2 a -1} x^{-2 a} y^{\prime }-b^{2} x^{-2 a} y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.680 |
|
| 12073 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| 12074 |
\begin{align*}
4 x \left (x -1\right ) \left (x -2\right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| 12075 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| 12076 | \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=4 x-y \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.680 |
|
| 12077 |
\begin{align*}
y^{\prime }&=x -y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 12078 |
\begin{align*}
m x^{\prime \prime }+k x&=F_{0} \cos \left (\omega t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 12079 |
\begin{align*}
y_{1}^{\prime }&=-6 y_{1}-4 y_{2}-8 y_{3} \\
y_{2}^{\prime }&=-4 y_{1}-4 y_{3} \\
y_{3}^{\prime }&=-8 y_{1}-4 y_{2}-6 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 12080 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x^{2}-1\right ) y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 12081 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=3 x_{1}-x_{2}+5 \,{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 12082 |
\begin{align*}
2 f \left (x \right )^{2} y^{\prime \prime }&=2 f \left (x \right )^{2} y^{3}+f \left (x \right ) y^{2} f^{\prime }\left (x \right )+f \left (x \right ) \left (-2 f \left (x \right ) y+3 f^{\prime }\left (x \right )\right ) y^{\prime }+y \left (-2 f \left (x \right )^{3}-2 {f^{\prime }\left (x \right )}^{2}+f \left (x \right ) f^{\prime \prime }\left (x \right )\right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.681 |
|
| 12083 |
\begin{align*}
s^{\prime }&=k s \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 12084 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 12085 |
\begin{align*}
y^{\prime }&=y+x \,{\mathrm e}^{y} \\
y \left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✗ |
✓ |
0.681 |
|
| 12086 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 12087 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 12088 |
\begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=-x+2 y+4 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 12089 |
\begin{align*}
x^{2} \left (2+x \right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.681 |
|
| 12090 |
\begin{align*}
y^{\prime }+y&=\left \{\begin {array}{cc} 1 & 0\le x <2 \\ 0 & 0<x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.681 |
|
| 12091 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 12092 |
\begin{align*}
4 x^{\prime }+2 x^{\prime \prime }&=-5 x \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 12093 |
\begin{align*}
x^{\prime }&=x+z \\
y^{\prime }&=z-y \\
z^{\prime }&=y-z \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 12094 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }+\left (-x +2\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 12095 | \begin{align*}
4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.682 |
|
| 12096 |
\begin{align*}
x {y^{\prime }}^{2}+x y y^{\prime \prime }&=3 y^{\prime } y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.682 |
|
| 12097 |
\begin{align*}
8 y {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.682 |
|
| 12098 |
\begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=5 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.682 |
|
| 12099 |
\begin{align*}
y {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.683 |
|
| 12100 |
\begin{align*}
x {y^{\prime }}^{2}&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.683 |
|