| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 8201 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x +3\right ) y^{\prime }+\left (x^{2}+x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 8202 |
\begin{align*}
y {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 8203 |
\begin{align*}
y^{\prime }-y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 8204 |
\begin{align*}
y^{\prime \prime }+y&=\delta \left (t -2 \pi \right ) \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 8205 |
\begin{align*}
5 y^{\prime \prime }+5 y^{\prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 8206 |
\begin{align*}
x {y^{\prime }}^{2}-y y^{\prime }+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.770 |
|
| 8207 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (-3 x^{2}+x \right ) y^{\prime }+{\mathrm e}^{x} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.770 |
|
| 8208 |
\begin{align*}
\left (y^{2}-a^{2}\right ) {y^{\prime }}^{2}+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 8209 |
\begin{align*}
\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.770 |
|
| 8210 |
\begin{align*}
y^{\prime } t -{y^{\prime }}^{3}&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.770 |
|
| 8211 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 8212 |
\begin{align*}
A y+\left (a +2 b x +c \,x^{2}+y^{2}\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.771 |
|
| 8213 |
\begin{align*}
x^{\prime }&=3 x+2 y+4 z \\
y^{\prime }&=2 x+2 z \\
z^{\prime }&=4 x+2 y+3 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 8214 |
\begin{align*}
x^{4} \left (x^{2}-4\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+\left (x^{2}-3 x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 8215 |
\begin{align*}
x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| 8216 |
\begin{align*}
x_{1}^{\prime }&=\frac {x_{1}}{2}-x_{2}-\frac {3 x_{3}}{2} \\
x_{2}^{\prime }&=\frac {3 x_{1}}{2}-2 x_{2}-\frac {3 x_{3}}{2} \\
x_{3}^{\prime }&=-2 x_{1}+2 x_{2}+x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| 8217 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\
x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| 8218 |
\begin{align*}
x^{\prime }&=a x+y \\
y^{\prime }&=-2 x+b y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| 8219 |
\begin{align*}
y^{\prime \prime } x -\left (2 x -1\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| 8220 |
\begin{align*}
y^{\prime \prime }+4 y&=2 \delta \left (t -\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 8221 |
\begin{align*}
y^{\prime }&=y \left (-3+y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 8222 |
\begin{align*}
2 y^{\prime \prime } x -\left (2 x +3\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 8223 |
\begin{align*}
24+12 y x +x^{3} \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right )&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
0.773 |
|
| 8224 |
\begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=1-2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 8225 |
\begin{align*}
y^{\prime \prime }+y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 8226 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\
x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 8227 |
\begin{align*}
y^{\prime \prime }-{y^{\prime }}^{2}-y {y^{\prime }}^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.773 |
|
| 8228 |
\begin{align*}
28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 8229 |
\begin{align*}
2 y^{\prime }+x&=4 \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.774 |
|
| 8230 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 8231 |
\begin{align*}
y^{\prime \prime } x -\left (x +4\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.775 |
|
| 8232 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| 8233 |
\begin{align*}
y^{\prime }&=y^{2} \left (4-y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| 8234 |
\begin{align*}
y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| 8235 |
\begin{align*}
y^{\prime \prime }&=-2 x {y^{\prime }}^{2} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.775 |
|
| 8236 |
\begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| 8237 |
\begin{align*}
y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| 8238 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2}+2 \,{\mathrm e}^{-t} \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+3 t \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= \alpha _{1} \\
x_{2} \left (0\right ) &= \alpha _{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 8239 |
\begin{align*}
3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 8240 |
\begin{align*}
2 \sin \left (t \right ) y^{\prime \prime }+\left (1-t \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.776 |
|
| 8241 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}+1-\operatorname {Heaviside}\left (t -\pi \right ) \\
x_{2}^{\prime }&=2 x_{1}-2 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 8242 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -{\frac {17}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 8243 |
\begin{align*}
y^{\prime }&=y^{2}+a^{2} x^{2}+b x +c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.776 |
|
| 8244 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\
x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 8245 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 8246 |
\begin{align*}
8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| 8247 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 1 \\
y \left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| 8248 |
\begin{align*}
x_{1}^{\prime }&=-\frac {5 x_{1}}{4}+\frac {3 x_{2}}{4}+2 t \\
x_{2}^{\prime }&=\frac {3 x_{1}}{4}-\frac {5 x_{2}}{4}+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 8249 |
\begin{align*}
x^{2} y^{\prime }+2 y&=2 \,{\mathrm e}^{\frac {1}{x}} \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 8250 |
\begin{align*}
2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 8251 |
\begin{align*}
2 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+\left (3 x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 8252 |
\begin{align*}
\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 8253 |
\begin{align*}
y^{\prime \prime }-f \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.778 |
|
| 8254 |
\begin{align*}
x^{\prime }&=8 x+2 y-17 \\
y^{\prime }&=4 x+y-13 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 8255 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 8256 |
\begin{align*}
y^{\prime }&=a f \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 8257 |
\begin{align*}
2 y^{3} y^{\prime }+x y^{2}-x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.779 |
|
| 8258 |
\begin{align*}
x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 8259 |
\begin{align*}
x^{\prime \prime }+x&=3 \delta \left (t -2 \pi \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 8260 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=1-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 8261 |
\begin{align*}
{y^{\prime }}^{3}&=y {y^{\prime }}^{2}-x^{2} y^{\prime }+x^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 8262 |
\begin{align*}
\frac {y^{\prime \prime }}{x}+\frac {3 \left (x -4\right ) y^{\prime }}{6+x}+\frac {x^{2} \left (x -2\right ) y}{x -1}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 8263 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 8264 |
\begin{align*}
y^{\prime }-7 y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 8265 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.780 |
|
| 8266 |
\begin{align*}
4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| 8267 |
\begin{align*}
x \left (x +1\right ) y^{\prime \prime }-4 y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.780 |
|
| 8268 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| 8269 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| 8270 |
\begin{align*}
2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.781 |
|
| 8271 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=0 \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= -9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.781 |
|
| 8272 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }+y^{\prime } x +\frac {y}{x}&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.781 |
|
| 8273 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+\left (x +4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.781 |
|
| 8274 |
\begin{align*}
x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| 8275 |
\begin{align*}
y_{1}^{\prime }&=y_{1}-y_{2}-2 y_{3} \\
y_{2}^{\prime }&=y_{1}-2 y_{2}-3 y_{3} \\
y_{3}^{\prime }&=-4 y_{1}+y_{2}-y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| 8276 |
\begin{align*}
y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| 8277 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| 8278 |
\begin{align*}
9 x^{2} y^{\prime \prime }+10 y^{\prime } x +y&=x -1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.783 |
|
| 8279 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2}+t \\
x_{2}^{\prime }&=-2 x_{1}+x_{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 8280 |
\begin{align*}
2 x +3 y+4+\left (3 x +4 y+5\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 8281 |
\begin{align*}
y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 8282 |
\begin{align*}
x^{\prime }&=-x+4 y+2 z \\
y^{\prime }&=4 x-y-2 z \\
z^{\prime }&=6 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 8283 |
\begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 8284 |
\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*} |
✓ |
✓ |
✓ |
✗ |
0.783 |
|
| 8285 |
\begin{align*}
6 y^{\prime \prime } x +6 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 8286 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 8287 |
\begin{align*}
y_{1}^{\prime }&=3 y_{1}+5 y_{2}+8 y_{3} \\
y_{2}^{\prime }&=y_{1}-y_{2}-2 y_{3} \\
y_{3}^{\prime }&=-y_{1}-y_{2}-y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.784 |
|
| 8288 |
\begin{align*}
y_{1}^{\prime }&=y_{1}-y_{2}+2 y_{3} \\
y_{2}^{\prime }&=12 y_{1}-4 y_{2}+10 y_{3} \\
y_{3}^{\prime }&=-6 y_{1}+y_{2}-7 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.784 |
|
| 8289 |
\begin{align*}
x_{1}^{\prime }&=-8 x_{1}+6 x_{2}-3 x_{3} \\
x_{2}^{\prime }&=-12 x_{1}+10 x_{2}-3 x_{3} \\
x_{3}^{\prime }&=-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.784 |
|
| 8290 |
\begin{align*}
4 x^{2} {y^{\prime }}^{2}-4 y y^{\prime } x&=8 x^{3}-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.784 |
|
| 8291 |
\begin{align*}
2 y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.784 |
|
| 8292 |
\begin{align*}
3 {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.784 |
|
| 8293 |
\begin{align*}
9 x^{2} y^{\prime \prime }+9 y^{\prime } x -\left (1+3 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 8294 |
\begin{align*}
x_{1}^{\prime }&=-7 x_{1}-6 x_{2}-7 x_{3} \\
x_{2}^{\prime }&=-3 x_{1}-3 x_{2}-3 x_{3} \\
x_{3}^{\prime }&=7 x_{1}+6 x_{2}+7 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 8295 |
\begin{align*}
x_{1}^{\prime }&=-4 x_{1}+x_{2} \\
x_{2}^{\prime }&=x_{1}-5 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{2}-4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 8296 |
\begin{align*}
2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 8297 |
\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*} |
✓ |
✓ |
✓ |
✗ |
0.785 |
|
| 8298 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 8299 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{2}-2 x_{3} \\
x_{2}^{\prime }&=-x_{1}+2 x_{2}+x_{3} \\
x_{3}^{\prime }&=4 x_{1}+x_{2}-3 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 ) &= -7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 8300 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{2}+x_{3} \\
x_{2}^{\prime }&=-2 x_{1}-x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|