| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12001 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{4 x^{2}}\right ) y&=\sqrt {x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.986 |
|
| 12002 |
\begin{align*}
\left (2 x +1\right ) y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.986 |
|
| 12003 |
\begin{align*}
x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.987 |
|
| 12004 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.987 |
|
| 12005 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-x_{2}-2 x_{3}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}+3 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 ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.987 |
|
| 12006 |
\begin{align*}
2 y_{1}^{\prime }+y_{2}^{\prime }-4 y_{1}-y_{2}&={\mathrm e}^{x} \\
y_{1}^{\prime }+3 y_{1}+y_{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.987 |
|
| 12007 |
\begin{align*}
\left (2 x^{2}+1\right ) y^{\prime \prime }+11 x y^{\prime }+9 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.987 |
|
| 12008 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+25 y&=\sin \left (\alpha t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.987 |
|
| 12009 |
\begin{align*}
x_{1}^{\prime }&=-7 x_{1}+6 x_{2}-6 x_{3} \\
x_{2}^{\prime }&=-9 x_{1}+5 x_{2}-9 x_{3} \\
x_{3}^{\prime }&=-x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.987 |
|
| 12010 |
\begin{align*}
\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-b^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.987 |
|
| 12011 |
\begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }&=\left (2 x +3\right ) \left (2 x +4\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.987 |
|
| 12012 |
\begin{align*}
y^{\prime \prime }+y x&=\sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.987 |
|
| 12013 |
\begin{align*}
3 v^{\prime }+2 v+w^{\prime }-6 w&=5 \,{\mathrm e}^{x} \\
4 v^{\prime }+2 v+w^{\prime }-8 w&=5 \,{\mathrm e}^{x}+2 x -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.987 |
|
| 12014 |
\begin{align*}
\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.988 |
|
| 12015 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.988 |
|
| 12016 |
\begin{align*}
{y^{\prime }}^{2} x +\left (x -y\right ) y^{\prime }+1-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.989 |
|
| 12017 |
\begin{align*}
x^{2} \left (8+x \right ) y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.990 |
|
| 12018 |
\begin{align*}
x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.990 |
|
| 12019 |
\begin{align*}
x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.990 |
|
| 12020 |
\begin{align*}
y^{\prime }&=y+x \,{\mathrm e}^{y} \\
y \left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✗ |
✓ |
0.990 |
|
| 12021 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }&=12 x -10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.990 |
|
| 12022 |
\begin{align*}
4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.991 |
|
| 12023 |
\begin{align*}
x^{\prime }+2 x-y&=-{\mathrm e}^{2 t} \\
y^{\prime }+3 x-2 y&=6 \,{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.991 |
|
| 12024 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.992 |
|
| 12025 |
\begin{align*}
2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.992 |
|
| 12026 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.992 |
|
| 12027 |
\begin{align*}
y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+5\right ) y&=x \,{\mathrm e}^{-\frac {x^{2}}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.992 |
|
| 12028 |
\begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2}-{y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.992 |
|
| 12029 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| 12030 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }&=10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| 12031 |
\begin{align*}
x^{\prime }&=-x+4 y+2 z \\
y^{\prime }&=4 x-y-2 z \\
z^{\prime }&=6 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| 12032 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{2}-1} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| 12033 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| 12034 |
\begin{align*}
y^{\prime }+\sqrt {2 x^{2}+1}\, y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| 12035 |
\begin{align*}
x y^{\prime }&=-\frac {1}{\ln \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| 12036 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{3} \\
x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| 12037 |
\begin{align*}
x^{\prime \prime }-2 a x^{\prime }+b x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| 12038 |
\begin{align*}
u^{\prime }&=2 v-1 \\
v^{\prime }&=1+2 u \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| 12039 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| 12040 |
\begin{align*}
2 y^{\prime }+2 y {y^{\prime }}^{2}+\left (x +y^{2}\right ) y^{\prime \prime }&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.994 |
|
| 12041 |
\begin{align*}
\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.994 |
|
| 12042 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.994 |
|
| 12043 |
\begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=4 x+5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.994 |
|
| 12044 |
\begin{align*}
y^{\prime \prime }+2 n \cot \left (n x \right ) y^{\prime }+\left (m^{2}-n^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.994 |
|
| 12045 |
\begin{align*}
x {y^{\prime }}^{3}&=a +b y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.994 |
|
| 12046 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.995 |
|
| 12047 |
\begin{align*}
y^{\prime \prime }+\frac {y}{4}&=\sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.995 |
|
| 12048 |
\begin{align*}
x y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.995 |
|
| 12049 |
\begin{align*}
y^{\prime }&=\tan \left (x \right ) \\
y \left (\frac {\pi }{4}\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.996 |
|
| 12050 |
\begin{align*}
y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+32 y^{\prime \prime }+64 y^{\prime }+39 y&={\mathrm e}^{-2 x} \left (\left (4-15 x \right ) \cos \left (3 x \right )-\left (4+15 x \right ) \sin \left (3 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.996 |
|
| 12051 |
\begin{align*}
x^{\prime \prime }+\omega _{0}^{2} x&=a \cos \left (\omega t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.996 |
|
| 12052 |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=-b x_{1}-a x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.996 |
|
| 12053 |
\begin{align*}
y^{\prime }+y^{2}&=x^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.996 |
|
| 12054 |
\begin{align*}
a \,x^{r} y^{s}+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.996 |
|
| 12055 |
\begin{align*}
2 x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✓ |
0.996 |
|
| 12056 |
\begin{align*}
x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.996 |
|
| 12057 |
\begin{align*}
x^{\prime }+y^{\prime }-2 x-4 y&={\mathrm e}^{t} \\
x^{\prime }+y^{\prime }-y&={\mathrm e}^{4 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.996 |
|
| 12058 |
\begin{align*}
{y^{\prime }}^{2} x^{2}-3 x y y^{\prime }+x^{3}+2 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.996 |
|
| 12059 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.996 |
|
| 12060 |
\begin{align*}
y^{\prime \prime }&=x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| 12061 |
\begin{align*}
y^{5} x +2 y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.997 |
|
| 12062 |
\begin{align*}
y^{\prime \prime }+y&=\cot \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| 12063 |
\begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.997 |
|
| 12064 |
\begin{align*}
y^{\prime \prime }+\left (y+3 f \left (x \right )\right ) y^{\prime }-y^{3}+f \left (x \right ) y^{2}+y \left (2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.997 |
|
| 12065 |
\begin{align*}
x^{\prime }&=5 x-4 y+{\mathrm e}^{3 t} \\
y^{\prime }&=x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| 12066 |
\begin{align*}
4 y+y^{\prime \prime }&=\sec \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| 12067 |
\begin{align*}
x^{\prime }&=x+y+{\mathrm e}^{t} \\
y^{\prime }&=x-y-{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.998 |
|
| 12068 |
\begin{align*}
y^{\prime }+4 y&=3 \delta \left (t -1\right ) \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.998 |
|
| 12069 |
\begin{align*}
y y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.998 |
|
| 12070 |
\begin{align*}
4 y+y^{\prime \prime }&=\sec \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.998 |
|
| 12071 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+4 y&=16 x +20 \,{\mathrm e}^{x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.998 |
|
| 12072 |
\begin{align*}
\left (x -2\right ) y^{\prime \prime }+3 \left (x^{2}-3 x +2\right ) y^{\prime }+\left (x -2\right )^{2} x y&=0 \\
\end{align*}
Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.998 |
|
| 12073 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.998 |
|
| 12074 |
\begin{align*}
\left (5 x^{3}+2 x^{2}\right ) y^{\prime \prime }+\left (-x^{2}+3 x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.999 |
|
| 12075 |
\begin{align*}
x_{1}^{\prime }&=-\frac {x_{1}}{2}-\frac {x_{2}}{8}+\frac {{\mathrm e}^{-\frac {t}{2}}}{2} \\
x_{2}^{\prime }&=2 x_{1}-\frac {x_{2}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.999 |
|
| 12076 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-2 x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}-4 x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{1}+2 x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.999 |
|
| 12077 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.999 |
|
| 12078 |
\begin{align*}
t^{2} \left (t +1\right ) y^{\prime \prime }-t \left (2 t +1\right ) y^{\prime }+\left (2 t +1\right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.999 |
|
| 12079 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+8 x&=f \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| 12080 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| 12081 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| 12082 |
\begin{align*}
x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.000 |
|
| 12083 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.000 |
|
| 12084 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (t \right ) \cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| 12085 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x^{2}+3\right ) y^{\prime }+y&=-2 x^{2}+x \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.000 |
|
| 12086 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-\left (x^{2}+2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| 12087 |
\begin{align*}
\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| 12088 |
\begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=2 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| 12089 |
\begin{align*}
\frac {\left (a +b \right ) y}{x^{2}}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.001 |
|
| 12090 |
\begin{align*}
{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.001 |
|
| 12091 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+{\mathrm e}^{2 t} \cos \left (3 t \right ) \\
x_{2}^{\prime }&=6 x_{2}-4 x_{3}-2 \\
x_{3}^{\prime }&=4 x_{2}-2 x_{3}-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.001 |
|
| 12092 |
\begin{align*}
{y^{\prime }}^{2}&=9-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.002 |
|
| 12093 |
\begin{align*}
x^{\prime }&=-2 x+3 y \\
y^{\prime }&=-6 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.002 |
|
| 12094 |
\begin{align*}
t^{2} y^{\prime \prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.002 |
|
| 12095 |
\begin{align*}
x^{\prime \prime }&=x^{3}-x \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.002 |
|
| 12096 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 12097 |
\begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{x} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 12098 |
\begin{align*}
-\left (2 x +3\right ) y+\left (x^{2}+x +1\right ) y^{\prime }+\left (x^{2}+3 x +4\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.003 |
|
| 12099 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 12100 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=10 \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|