| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 8301 |
\begin{align*}
x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| 8302 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| 8303 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| 8304 |
\begin{align*}
x^{4} y^{\prime \prime }&=-4 y^{2}+x^{2} y^{\prime } \left (x +y^{\prime }\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.063 |
|
| 8305 |
\begin{align*}
3 y^{\prime \prime }+4 y^{\prime }-4 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| 8306 |
\begin{align*}
2 y^{\prime \prime }-3 y^{\prime }+17 y&=17 t -1 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| 8307 |
\begin{align*}
y^{\prime \prime }+9 y&=6 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| 8308 |
\begin{align*}
x^{2} y^{\prime \prime }-2 \left (x^{2}+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.063 |
|
| 8309 |
\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 ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| 8310 |
\begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u&=3 \cos \left (2 t \right ) \\
u \left (0\right ) &= 2 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.064 |
|
| 8311 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=4 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| 8312 |
\begin{align*}
y^{\prime }&=2 x^{2}+3 y \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| 8313 |
\begin{align*}
y^{\prime }-y^{2}-3 y+4&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| 8314 |
\begin{align*}
\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{3}+b x \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+y^{\prime }+b x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| 8315 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.065 |
|
| 8316 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| 8317 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| 8318 |
\begin{align*}
9 x^{2} y^{\prime \prime }+10 y^{\prime } x +y&=-1+x \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.066 |
|
| 8319 |
\begin{align*}
-2 y+y^{\prime } x +x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.066 |
|
| 8320 |
\begin{align*}
y^{\prime \prime }-\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.066 |
|
| 8321 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.066 |
|
| 8322 |
\begin{align*}
4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.067 |
|
| 8323 |
\begin{align*}
y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.067 |
|
| 8324 |
\begin{align*}
y^{2} {y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.067 |
|
| 8325 |
\begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.067 |
|
| 8326 |
\begin{align*}
x^{2} y^{\prime \prime }&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.067 |
|
| 8327 |
\begin{align*}
{y^{\prime }}^{2} \left (x^{2}-1\right )-2 y y^{\prime } x +y^{2}-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.067 |
|
| 8328 |
\begin{align*}
\left (-2+t \right )^{2} y^{\prime \prime }+5 \left (-2+t \right ) y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.068 |
|
| 8329 |
\begin{align*}
y^{\prime }&={\mathrm e}^{y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.068 |
|
| 8330 |
\begin{align*}
3 x^{2} y^{\prime \prime }+\left (-x^{2}+5 x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.068 |
|
| 8331 |
\begin{align*}
x^{\prime }&=-3 x+4 y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.068 |
|
| 8332 |
\begin{align*}
\left (3 x y^{3}-4 y x +y\right ) y^{\prime }+y^{2} \left (y^{2}-2\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.068 |
|
| 8333 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.068 |
|
| 8334 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=g \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.068 |
|
| 8335 |
\begin{align*}
x^{2} y^{\prime \prime }+x \cos \left (x \right ) y^{\prime }-2 \,{\mathrm e}^{x} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| 8336 |
\begin{align*}
-\left (x +1\right ) y+y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.069 |
|
| 8337 |
\begin{align*}
\left (b +c \,x^{2 k}\right ) y+a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.069 |
|
| 8338 |
\begin{align*}
\frac {x^{\prime \prime }}{2}+\frac {5 x^{\prime }}{6}+\frac {2 x}{9}&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| 8339 |
\begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.069 |
|
| 8340 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x} \cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| 8341 |
\begin{align*}
z^{\prime \prime }+6 z^{\prime }+9 z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| 8342 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| 8343 |
\begin{align*}
\left (8-x \right ) x^{2} y^{\prime \prime }+6 y^{\prime } x -y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.070 |
|
| 8344 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.070 |
|
| 8345 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.070 |
|
| 8346 |
\begin{align*}
2 x +y \cos \left (y x \right )+\left (x \cos \left (y x \right )-2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.070 |
|
| 8347 |
\begin{align*}
w^{\prime }+w x&={\mathrm e}^{x} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.070 |
|
| 8348 |
\begin{align*}
y^{\prime }+y&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
1.070 |
|
| 8349 |
\begin{align*}
y^{\prime \prime }+y&=x^{2} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.070 |
|
| 8350 |
\begin{align*}
3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.071 |
|
| 8351 |
\begin{align*}
y^{\prime \prime }+25 y&=\cos \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.071 |
|
| 8352 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=0 \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.071 |
|
| 8353 |
\begin{align*}
y^{\prime \prime } x +\left (2 x -1\right ) y^{\prime }&=-4 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.071 |
|
| 8354 |
\begin{align*}
x^{\prime }&=-x-4 y-4 \\
y^{\prime }&=x-y-6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.071 |
|
| 8355 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.072 |
|
| 8356 |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t}+\ln \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.072 |
|
| 8357 |
\begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=3 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| 8358 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-3\right ) y-{\mathrm e}^{x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.072 |
|
| 8359 |
\begin{align*}
4 \left (x^{2}+1\right )^{2} y^{\prime \prime }+\left (a \,x^{2}+a -3\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| 8360 |
\begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&=0 \\
y \left (0\right ) &= -4 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| 8361 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| 8362 |
\begin{align*}
y^{\prime \prime }+9 y&=\sec \left (3 t \right ) \tan \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| 8363 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=2 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= {\frac {3}{2}} \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| 8364 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| 8365 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.073 |
|
| 8366 |
\begin{align*}
g \left (x \right ) y^{2}+f \left (x \right ) y y^{\prime }+a {y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.073 |
|
| 8367 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| 8368 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| 8369 |
\begin{align*}
x^{\prime }&=-3 x-y \\
y^{\prime }&=4 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| 8370 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&={\mathrm e}^{4 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| 8371 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| 8372 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| 8373 |
\begin{align*}
9 x^{2} y^{\prime \prime }+9 \left (-x^{2}+x \right ) y^{\prime }+\left (-1+x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.074 |
|
| 8374 |
\begin{align*}
4 \left (1-x \right ) x^{2} y^{\prime \prime }+3 x \left (2 x +1\right ) y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.075 |
|
| 8375 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=4 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.075 |
|
| 8376 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 x+2 y-z \\
z^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.075 |
|
| 8377 |
\begin{align*}
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.075 |
|
| 8378 |
\begin{align*}
\cos \left (x \right )^{2} y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.075 |
|
| 8379 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.075 |
|
| 8380 |
\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. |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| 8381 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-8 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| 8382 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| 8383 |
\begin{align*}
\left (1+y^{2}\right ) y^{\prime \prime }-3 y {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.076 |
|
| 8384 |
\begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=2 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| 8385 |
\begin{align*}
2 y+y^{\prime }&=4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| 8386 |
\begin{align*}
y^{\prime }+k y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| 8387 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=\left (12 x -7\right ) {\mathrm e}^{-x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| 8388 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=\cos \left (x \right ) {\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.078 |
|
| 8389 |
\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*} |
✗ |
✓ |
✗ |
✗ |
1.078 |
|
| 8390 |
\begin{align*}
x^{\prime \prime }+4 x&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.078 |
|
| 8391 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.078 |
|
| 8392 |
\begin{align*}
2 x^{2} y^{\prime \prime }+x \left (x +5\right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.079 |
|
| 8393 |
\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*} |
✓ |
✓ |
✓ |
✓ |
1.079 |
|
| 8394 |
\begin{align*}
{y^{\prime }}^{3} x -2 y {y^{\prime }}^{2}+4 x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.079 |
|
| 8395 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.079 |
|
| 8396 |
\begin{align*}
y^{\prime \prime } x -\left (x +1\right ) y^{\prime }-2 \left (-1+x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.079 |
|
| 8397 |
\begin{align*}
x^{\prime }&=2 x+3 y+2 \sin \left (2 t \right ) \\
y^{\prime }&=-3 x+2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.079 |
|
| 8398 |
\begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y&=-{\mathrm e}^{x} \left (\left (4 x^{2}+5 x +9\right ) \cos \left (2 x \right )-\left (-3 x^{2}-5 x +6\right ) \sin \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| 8399 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=\cos \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
1.080 |
|
| 8400 |
\begin{align*}
x^{\prime }&=5 x+3 y \\
y^{\prime }&=-6 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.080 |
|