| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12001 |
\begin{align*}
y+3 y^{\prime } x +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*} |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| 12002 |
\begin{align*}
y^{\prime }&=6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| 12003 |
\begin{align*}
2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| 12004 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| 12005 |
\begin{align*}
y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| 12006 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| 12007 |
\begin{align*}
y_{1}^{\prime }-y_{2}&=0 \\
4 y_{1}+y_{2}^{\prime }-4 y_{2}-2 y_{3}&=0 \\
-2 y_{1}+y_{2}+y_{3}^{\prime }+y_{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.942 |
|
| 12008 |
\begin{align*}
2 y y^{\prime \prime }&=-1+2 x f \left (x \right ) y^{2}-y^{4}-4 y^{2} y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.942 |
|
| 12009 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }&=12 x -10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.942 |
|
| 12010 |
\begin{align*}
x^{\prime }&=2 x-7 y \\
y^{\prime }&=5 x+10 y+4 z \\
z^{\prime }&=5 y+2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.942 |
|
| 12011 |
\begin{align*}
y^{\prime }-\frac {1}{\sqrt {\operatorname {a4} \,x^{4}+\operatorname {a3} \,x^{3}+\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.942 |
|
| 12012 |
\begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.942 |
|
| 12013 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| 12014 |
\begin{align*}
\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-y^{\prime } x +\left (1-x \right ) y&=x^{2} \left (x +1\right )^{2} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.943 |
|
| 12015 |
\begin{align*}
x^{\prime }-4 x+3 y&=\sin \left (t \right ) \\
-2 x+y^{\prime }+y&=-2 \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| 12016 |
\begin{align*}
y^{\prime \prime }-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| 12017 |
\begin{align*}
\sqrt {x}\, y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| 12018 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| 12019 |
\begin{align*}
y^{\prime }&=\tan \left (x -\frac {y^{\prime }}{1+{y^{\prime }}^{2}}\right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.943 |
|
| 12020 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=x +{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| 12021 |
\begin{align*}
x y \left (x^{2}+y^{2}\right ) \left (-1+{y^{\prime }}^{2}\right )&=y^{\prime } \left (x^{4}+y^{2} x^{2}+y^{4}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| 12022 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=t^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| 12023 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| 12024 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3}+7 x_{4} \\
x_{2}^{\prime }&=x_{1}+4 x_{2}+10 x_{3}+x_{4} \\
x_{3}^{\prime }&=x_{1}+10 x_{2}+4 x_{3}+x_{4} \\
x_{4}^{\prime }&=7 x_{1}+x_{2}+x_{3}+4 x_{4} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 3 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
x_{4} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| 12025 |
\begin{align*}
y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| 12026 |
\begin{align*}
y^{\prime \prime }&=f \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| 12027 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| 12028 |
\begin{align*}
x^{\prime }&=\left (x-1\right )^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.944 |
|
| 12029 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x +{\mathrm e}^{-x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| 12030 |
\begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=8 x^{{5}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.945 |
|
| 12031 |
\begin{align*}
x^{\prime }-y&=0 \\
-x+y^{\prime }&={\mathrm e}^{t}+{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| 12032 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=\cos \left (x \right ) {\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| 12033 |
\begin{align*}
x^{\prime }&=2 x+2 y-z \\
y^{\prime }&=y+z \\
z^{\prime }&=z-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| 12034 |
\begin{align*}
y_{1}^{\prime }&=2 y_{1}+y_{2}-y_{3} \\
y_{2}^{\prime }&=y_{2}+y_{3} \\
y_{3}^{\prime }&=y_{1}+y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| 12035 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| 12036 |
\begin{align*}
x^{2} y^{2} y^{\prime \prime }&=\left (x^{2}+y^{2}\right ) \left (-y+y^{\prime } x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.946 |
|
| 12037 |
\begin{align*}
\sin \left (y^{\prime }\right )&=x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| 12038 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+50 y&={\mathrm e}^{-t} \csc \left (7 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| 12039 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=x \,{\mathrm e}^{x} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.946 |
|
| 12040 |
\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*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| 12041 |
\begin{align*}
\frac {2 y x +1}{y}+\frac {\left (-x +y\right ) y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.947 |
|
| 12042 |
\begin{align*}
y^{\prime \prime } x -4 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| 12043 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} \frac {t}{2} & 0\le t <6 \\ 3 & 6\le t \end {array}\right . \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| 12044 |
\begin{align*}
x^{2} \left (-y^{\prime } x +y\right )&=y {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.947 |
|
| 12045 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=3 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| 12046 |
\begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.948 |
|
| 12047 |
\begin{align*}
y^{\prime \prime }+9 y&=15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.948 |
|
| 12048 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.948 |
|
| 12049 |
\begin{align*}
y+y^{\prime }&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.948 |
|
| 12050 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.948 |
|
| 12051 |
\begin{align*}
y^{\prime } x +2 y x&=\sqrt {x} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.948 |
|
| 12052 |
\begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=x^{2} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.948 |
|
| 12053 |
\begin{align*}
5 {y^{\prime }}^{2}+6 y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.948 |
|
| 12054 |
\begin{align*}
y^{\prime }-4 y&=-8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.948 |
|
| 12055 |
\begin{align*}
y^{\prime \prime }+9 y&=\tan \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.949 |
|
| 12056 |
\begin{align*}
\left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+2 y&=x^{2} \left (2+x \right )^{2} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.949 |
|
| 12057 |
\begin{align*}
x \left (x -2\right )^{2} y^{\prime \prime }-2 \left (x -2\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.949 |
|
| 12058 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.949 |
|
| 12059 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3}+7 x_{4} \\
x_{2}^{\prime }&=x_{1}+4 x_{2}+10 x_{3}+x_{4} \\
x_{3}^{\prime }&=x_{1}+10 x_{2}+4 x_{3}+x_{4} \\
x_{4}^{\prime }&=7 x_{1}+x_{2}+x_{3}+4 x_{4} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 3 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
x_{4} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| 12060 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}+f^{\prime }\left (x \right ) y^{\prime }-y f^{\prime \prime }\left (x \right )+f \left (x \right ) y^{3}-y^{4}&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
0.950 |
|
| 12061 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -30 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| 12062 |
\begin{align*}
y^{\prime \prime }+\frac {y}{4}&=\sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| 12063 |
\begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}+\left (1-\frac {m^{2}}{x^{2}}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| 12064 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| 12065 |
\begin{align*}
-\left (-4 x^{2}+3\right ) y-4 y^{\prime } x +y^{\prime \prime }&={\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.951 |
|
| 12066 |
\begin{align*}
2 y+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.951 |
|
| 12067 |
\begin{align*}
x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.951 |
|
| 12068 |
\begin{align*}
y^{\prime }&=4 y+8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.951 |
|
| 12069 |
\begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }&=\left (2 x^{2}+x \right ) {\mathrm e}^{-2 x}+5 \cos \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.952 |
|
| 12070 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-2 x_{2}+2 x_{3}-{\mathrm e}^{3 t} \\
x_{2}^{\prime }&=2 x_{1}+4 x_{2}-x_{3}+4 \,{\mathrm e}^{3 t} \\
x_{3}^{\prime }&=3 x_{3}+3 \,{\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.952 |
|
| 12071 |
\begin{align*}
{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.952 |
|
| 12072 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.952 |
|
| 12073 |
\begin{align*}
\left (x^{2}+1\right )^{2} y^{\prime \prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.952 |
|
| 12074 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-3 x_{2} \\
x_{3}^{\prime }&=x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.953 |
|
| 12075 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.953 |
|
| 12076 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 \left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.953 |
|
| 12077 |
\begin{align*}
y^{\prime \prime }-\frac {1}{\left (a y^{2}+b x y+c \,x^{2}+\alpha y+\beta x +\gamma \right )^{{3}/{2}}}&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.953 |
|
| 12078 |
\begin{align*}
9 y+6 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{-3 x}}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.953 |
|
| 12079 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}-2 x_{3}+3 x_{4} \\
x_{2}^{\prime }&=2 x_{1}-\frac {3 x_{2}}{2}-x_{3}+\frac {7 x_{4}}{2} \\
x_{3}^{\prime }&=-x_{1}+\frac {x_{2}}{2}-\frac {3 x_{4}}{2} \\
x_{4}^{\prime }&=-2 x_{1}+\frac {3 x_{2}}{2}+3 x_{3}-\frac {7 x_{4}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.953 |
|
| 12080 |
\begin{align*}
y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y&={\mathrm e}^{x} \left (\left (7+8 x \right ) \cos \left (2 x \right )+\left (8-4 x \right ) \sin \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.954 |
|
| 12081 |
\begin{align*}
{y^{\prime }}^{2}-2 \left (x -y\right ) y^{\prime }-4 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.954 |
|
| 12082 |
\begin{align*}
-y+y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.954 |
|
| 12083 |
\begin{align*}
y^{\prime \prime }-a \left (-y+y^{\prime } x \right )^{v}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.954 |
|
| 12084 |
\begin{align*}
x&=t x^{\prime }+\frac {1}{x^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.954 |
|
| 12085 |
\begin{align*}
-a^{2} y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.955 |
|
| 12086 |
\begin{align*}
x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.955 |
|
| 12087 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.955 |
|
| 12088 |
\begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.955 |
|
| 12089 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x -6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.955 |
|
| 12090 |
\begin{align*}
a y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.955 |
|
| 12091 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.956 |
|
| 12092 |
\begin{align*}
y^{\prime \prime }-4 y&=-3 \,{\mathrm e}^{t} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.956 |
|
| 12093 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{-3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.956 |
|
| 12094 |
\begin{align*}
\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.957 |
|
| 12095 |
\begin{align*}
2 y y^{\prime \prime }&=y^{3}+2 {y^{\prime }}^{2} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.957 |
|
| 12096 |
\begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.957 |
|
| 12097 |
\begin{align*}
\operatorname {a0} \operatorname {a1} \left (-k +x \right ) y+\left (1-\operatorname {a0} +\operatorname {a1} +\operatorname {a0} \operatorname {a2} -\operatorname {a3} +\left (\operatorname {a2} +\operatorname {a3} \right ) x +\left (1+\operatorname {a0} +\operatorname {a1} \right ) x^{2}\right ) y^{\prime }+\left (1-x \right ) \left (a -x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.957 |
|
| 12098 |
\begin{align*}
b y+a {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.957 |
|
| 12099 |
\begin{align*}
a y y^{\prime }+2 x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.957 |
|
| 12100 |
\begin{align*}
2 y^{\prime }+4 {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.957 |
|