| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 13001 |
\begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.253 |
|
| 13002 |
\begin{align*}
4 x^{2} y^{\prime \prime }+\left (1-2 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.255 |
|
| 13003 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=-12 x +8 \\
y \left (1\right ) &= -2 \\
y^{\prime }\left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.255 |
|
| 13004 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=a +4 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.256 |
|
| 13005 |
\begin{align*}
x^{2} {y^{\prime }}^{2}+\left (a +b \,x^{2} y^{3}\right ) y^{\prime }+a b y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.256 |
|
| 13006 |
\begin{align*}
y x -y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.256 |
|
| 13007 |
\begin{align*}
y^{\prime \prime }-9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.257 |
|
| 13008 |
\begin{align*}
\ln \left (x \right ) y^{\prime }+\frac {x +y}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.257 |
|
| 13009 |
\begin{align*}
y^{\prime } x&=a \,x^{2}+y+b y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.257 |
|
| 13010 |
\begin{align*}
y y^{\prime \prime }+2 y^{\prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.257 |
|
| 13011 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.257 |
|
| 13012 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y&=\frac {1}{x -2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.259 |
|
| 13013 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.259 |
|
| 13014 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.259 |
|
| 13015 |
\begin{align*}
y^{\prime \prime }+y&=x \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.260 |
|
| 13016 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.260 |
|
| 13017 |
\begin{align*}
4 x^{\prime }-2 y&=\cos \left (2 t \right ) \\
x-2 y^{\prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.261 |
|
| 13018 |
\begin{align*}
{y^{\prime }}^{3}+y^{2}&=y y^{\prime } \left (1+y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.261 |
|
| 13019 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime } x +3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.263 |
|
| 13020 |
\begin{align*}
\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} {\mathrm e}^{\lambda x}+b \,\mu ^{2} {\mathrm e}^{\mu x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.263 |
|
| 13021 |
\begin{align*}
2 y-3 y^{\prime \prime } x +4 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.263 |
|
| 13022 |
\begin{align*}
y^{\prime \prime }-x {y^{\prime }}^{2}&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.263 |
|
| 13023 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+a -y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.264 |
|
| 13024 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +y&=0 \\
y \left (1\right ) &= -6 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
2.264 |
|
| 13025 |
\begin{align*}
y^{\prime }&=\frac {1}{2 y+1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.264 |
|
| 13026 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&={\mathrm e}^{x} \cos \left (2 x \right )+\cos \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.264 |
|
| 13027 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+6 y&=10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.264 |
|
| 13028 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
2.265 |
|
| 13029 |
\begin{align*}
y^{\prime \prime }+k^{2} y&=k \sin \left (k x +\alpha \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.266 |
|
| 13030 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=8 \,{\mathrm e}^{t}+5 t \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.266 |
|
| 13031 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.266 |
|
| 13032 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&={\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.266 |
|
| 13033 |
\begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.267 |
|
| 13034 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.267 |
|
| 13035 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (-1\right ) &= 5 \\
y^{\prime }\left (-1\right ) &= -5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.267 |
|
| 13036 |
\begin{align*}
y^{\prime \prime }&=-\frac {b y}{x^{2} \left (x -a \right )^{2}}+c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.267 |
|
| 13037 |
\begin{align*}
x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.267 |
|
| 13038 |
\begin{align*}
\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (2+x \right ) y&=x \left (x +1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.267 |
|
| 13039 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }&=3 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.268 |
|
| 13040 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=n \left (1-2 y x +y^{2}\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.269 |
|
| 13041 |
\begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
2.269 |
|
| 13042 |
\begin{align*}
x^{\prime \prime }+16 x&=0 \\
x \left (0\right ) &= -2 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.269 |
|
| 13043 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=x^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.269 |
|
| 13044 |
\begin{align*}
y^{\prime }&=x \sec \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.270 |
|
| 13045 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime } x +5 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.270 |
|
| 13046 |
\begin{align*}
y^{\prime } t +y&=t \\
y \left (1\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.270 |
|
| 13047 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (c -1\right ) \left (a \,x^{n -1}+b \,x^{m -1}\right ) y&=0 \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
2.270 |
|
| 13048 |
\begin{align*}
x^{\prime }+y^{\prime }-y&=0 \\
y^{\prime }+2 y+z^{\prime }+2 z&=2 \\
x+z^{\prime }-z&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.270 |
|
| 13049 |
\begin{align*}
x^{\prime }&=-10 x+y+7 z \\
y^{\prime }&=-9 x+4 y+5 z \\
z^{\prime }&=-17 x+y+12 z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 6 \\
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.270 |
|
| 13050 |
\begin{align*}
y_{1}^{\prime }&=2 y_{1}-y_{2} \\
y_{2}^{\prime }&=3 y_{1}-2 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.270 |
|
| 13051 |
\begin{align*}
x^{k} y^{\prime }&=a \,x^{m}+b y^{n} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.271 |
|
| 13052 |
\begin{align*}
\left (2 y^{\prime } x -y\right )^{2}&=8 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.271 |
|
| 13053 |
\begin{align*}
{y^{\prime \prime }}^{2}-y^{\prime \prime \prime } y^{\prime }&=\frac {{y^{\prime }}^{2}}{x^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.271 |
|
| 13054 |
\begin{align*}
y^{\prime \prime }-y&=2 t^{2}+2 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.273 |
|
| 13055 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&={\mathrm e}^{-3 x} \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.273 |
|
| 13056 |
\begin{align*}
y^{\prime \prime }+y&=6 \cos \left (x \right )^{2} \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.274 |
|
| 13057 |
\begin{align*}
2 y+y^{\prime }&={\mathrm e}^{-x^{2}-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.276 |
|
| 13058 |
\begin{align*}
2 y^{\prime \prime }+9 y^{\prime } x -36 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.276 |
|
| 13059 |
\begin{align*}
{y^{\prime }}^{2}-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.276 |
|
| 13060 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.277 |
|
| 13061 |
\begin{align*}
y^{\prime \prime }+9 y&=\ln \left (2 \sin \left (\frac {x}{2}\right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.277 |
|
| 13062 |
\begin{align*}
x^{\prime \prime }-3 x^{\prime }+2 x&=5 \cos \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.277 |
|
| 13063 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.277 |
|
| 13064 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.278 |
|
| 13065 |
\begin{align*}
10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.278 |
|
| 13066 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=\cos \left (x \right )^{2}+{\mathrm e}^{x}+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.279 |
|
| 13067 |
\begin{align*}
y x +x +2 y+1+\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.280 |
|
| 13068 |
\begin{align*}
y^{\prime \prime }-a^{2} y&=\frac {6 y}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.280 |
|
| 13069 |
\begin{align*}
y^{\prime }&=F \left (y \,{\mathrm e}^{-b x}\right ) {\mathrm e}^{b x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.280 |
|
| 13070 |
\begin{align*}
y^{\prime }&=\frac {x \left ({\mathrm e}^{-2 x^{2}} x^{4}-4 x^{2} {\mathrm e}^{-x^{2}} y-4 x^{2} {\mathrm e}^{-x^{2}}+4 y^{2}+4 \,{\mathrm e}^{-x^{2}}\right )}{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.280 |
|
| 13071 |
\begin{align*}
\left (2+x \right )^{2} y^{\prime \prime }-\left (2+x \right ) y^{\prime }-3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.280 |
|
| 13072 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=\frac {{\mathrm e}^{x}}{x^{3}} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
y^{\prime \prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.280 |
|
| 13073 |
\begin{align*}
{y^{\prime }}^{2}-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.280 |
|
| 13074 |
\begin{align*}
\left (x^{2}+y^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.281 |
|
| 13075 |
\begin{align*}
6 y-2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.282 |
|
| 13076 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (4 x +4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.283 |
|
| 13077 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }&=16 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.283 |
|
| 13078 |
\begin{align*}
y^{\prime }-\left (-1+y\right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.283 |
|
| 13079 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.284 |
|
| 13080 |
\begin{align*}
y y^{\prime }&=\sqrt {y^{2}-a^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.286 |
|
| 13081 |
\begin{align*}
2 y^{\prime }+y&=y^{3} \left (-1+x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.286 |
|
| 13082 |
\begin{align*}
y^{\prime \prime }+\left (5+2 x \right ) y^{\prime }+\left (4 x +8\right ) y&={\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.286 |
|
| 13083 |
\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 }&=4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.286 |
|
| 13084 |
\begin{align*}
\frac {x+y \,{\mathrm e}^{y}}{x^{\prime }}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.287 |
|
| 13085 |
\begin{align*}
y_{1}^{\prime }&=3 y_{1}+2 y_{2} \\
y_{2}^{\prime }&=3 y_{2}-2 y_{1} \\
y_{3}^{\prime }&=y_{3} \\
y_{4}^{\prime }&=2 y_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.287 |
|
| 13086 |
\begin{align*}
t^{2} y^{\prime \prime }+4 y^{\prime } t +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.288 |
|
| 13087 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.288 |
|
| 13088 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.289 |
|
| 13089 |
\begin{align*}
5 y^{\prime \prime }+2 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.289 |
|
| 13090 |
\begin{align*}
y^{\prime }+\cos \left (x \right ) y-{\mathrm e}^{2 x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.289 |
|
| 13091 |
\begin{align*}
y^{\prime }-3 y&=13 \cos \left (2 t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.289 |
|
| 13092 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+8 y&={\mathrm e}^{2 x} \left (\cos \left (2 x \right )+\sin \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.289 |
|
| 13093 |
\begin{align*}
y^{\prime }&=t \left (1+y\right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.290 |
|
| 13094 |
\begin{align*}
y^{\prime \prime \prime }-y&=x \,{\mathrm e}^{x}+\cos \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.290 |
|
| 13095 |
\begin{align*}
x^{\prime \prime }-x^{\prime }&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.290 |
|
| 13096 |
\begin{align*}
x^{\prime }+2 x-y&=100 \sin \left (t \right ) \\
y^{\prime }-4 x-y&=36 t \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -8 \\
y \left (0\right ) &= -21 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.290 |
|
| 13097 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.291 |
|
| 13098 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.291 |
|
| 13099 |
\begin{align*}
x \left (2+x \right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.292 |
|
| 13100 |
\begin{align*}
y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.292 |
|