| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 8401 |
\begin{align*}
18 x^{2} y^{\prime \prime }+3 x \left (x +5\right ) y^{\prime }-\left (10 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| 8402 |
\begin{align*}
y^{\prime \prime }+y&=x +2 \,{\mathrm e}^{-x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| 8403 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+\cos \left (w t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 8404 |
\begin{align*}
\sinh \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime }&=y x \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.805 |
|
| 8405 |
\begin{align*}
y^{\prime \prime }&=2 y y^{\prime } \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.805 |
|
| 8406 |
\begin{align*}
\left (1+3 x \right ) y^{\prime \prime }-3 y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 8407 |
\begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 8408 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 8409 |
\begin{align*}
x^{\prime }&=-x+y-z \\
y^{\prime }&=2 x-y+2 z \\
z^{\prime }&=2 x+2 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 8410 |
\begin{align*}
8 y^{\prime \prime }-10 y^{\prime }+3 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 8411 |
\begin{align*}
9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 8412 |
\begin{align*}
y^{\prime }+a y&={\mathrm e}^{-a t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 8413 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 8414 |
\begin{align*}
y^{\prime }&=y^{2}-4 y-12 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.807 |
|
| 8415 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 8416 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 8417 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 8418 |
\begin{align*}
x^{\prime }+y^{\prime }-x-6 y&={\mathrm e}^{3 t} \\
x^{\prime }+2 y^{\prime }-2 x-6 y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 8419 |
\begin{align*}
8 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| 8420 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}-10 x_{2} \\
x_{2}^{\prime }&=5 x_{1}+11 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| 8421 |
\begin{align*}
x^{2} {y^{\prime }}^{2}-\left (2 y x +1\right ) y^{\prime }+1+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.810 |
|
| 8422 |
\begin{align*}
3 x y^{2}-12 x^{2} y y^{\prime }+4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}+8 \left (-x^{3}+1\right ) y y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.810 |
|
| 8423 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{2}^{\prime }&=-4 x_{1}-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=4 x_{1}+4 x_{2}+2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.811 |
|
| 8424 |
\begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.811 |
|
| 8425 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+2 x_{3} \\
x_{2}^{\prime }&=2 x_{2}+2 x_{3} \\
x_{3}^{\prime }&=-x_{1}+x_{2}+3 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 11 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.811 |
|
| 8426 |
\begin{align*}
y^{\prime }&=y^{2}-y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.811 |
|
| 8427 |
\begin{align*}
x^{\prime }-y&=0 \\
-x+y^{\prime }&={\mathrm e}^{t}+{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| 8428 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| 8429 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| 8430 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y-6 x^{3} \left (x -1\right ) \ln \left (x \right )+x^{3} \left (8+x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| 8431 |
\(\left [\begin {array}{ccc} 1 & 0 & 1 \\ 0 & 1 & -1 \\ -2 & 0 & -1 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.813 |
|
| 8432 |
\begin{align*}
x^{\prime }&=4 x+2 y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| 8433 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-x_{2}-1 \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| 8434 |
\begin{align*}
y^{2} {y^{\prime }}^{2}+y y^{\prime } x -2 x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| 8435 |
\begin{align*}
x y^{\prime } \left (y^{\prime }+2\right )&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| 8436 |
\begin{align*}
x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (\left (1-n \right ) x -\left (6-4 n \right ) x^{2}\right ) y^{\prime }+n \left (1-n \right ) x y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| 8437 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=3 y-3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| 8438 |
\begin{align*}
4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| 8439 |
\begin{align*}
x^{\prime \prime }-x+3 x^{2}&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.814 |
|
| 8440 |
\begin{align*}
6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| 8441 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| 8442 |
\begin{align*}
x {y^{\prime }}^{2}&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| 8443 |
\(\left [\begin {array}{cccc} 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.815 |
|
| 8444 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\frac {2}{y}} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
0.815 |
|
| 8445 |
\begin{align*}
x^{\prime }&=4 x-5 y+4 t -1 \\
y^{\prime }&=x-2 y+t \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| 8446 |
\begin{align*}
y^{\prime }&=\frac {\sin \left (x \right )+\cos \left (x \right ) x}{y \left (2 \ln \left (y\right )+1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| 8447 |
\begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| 8448 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{2 x}+\frac {y}{4 x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| 8449 |
\begin{align*}
2 y^{\prime \prime }-15 y^{\prime }+27 y&=0 \\
y \left (0\right ) &= 7 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| 8450 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }+\left (-x +2\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| 8451 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-\left (x +5\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.816 |
|
| 8452 |
\begin{align*}
u^{\prime \prime }-\frac {a^{2} u}{x^{{2}/{3}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.816 |
|
| 8453 |
\begin{align*}
y^{\prime \prime }+\sin \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.816 |
|
| 8454 |
\begin{align*}
3 \left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✗ |
0.816 |
|
| 8455 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.816 |
|
| 8456 |
\begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2} \left (1+{y^{\prime }}^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.816 |
|
| 8457 |
\begin{align*}
y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.816 |
|
| 8458 |
\begin{align*}
x^{\prime }&=8 x+2 y+7 \,{\mathrm e}^{2 t} \\
y^{\prime }&=4 x+y-7 \,{\mathrm e}^{2 t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.816 |
|
| 8459 |
\begin{align*}
y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y&=96 \sin \left (2 x \right ) \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.816 |
|
| 8460 |
\begin{align*}
{y^{\prime }}^{3}&=y^{4} \left (y^{\prime } x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.816 |
|
| 8461 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.817 |
|
| 8462 |
\begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
0.817 |
|
| 8463 |
\begin{align*}
y^{\prime }+y \sqrt {x^{2}+1}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.817 |
|
| 8464 |
\begin{align*}
3 {y^{\prime }}^{2}+4 y^{\prime } x +x^{2}-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.818 |
|
| 8465 |
\begin{align*}
y^{\prime \prime }+4 y&=\sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.818 |
|
| 8466 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| 8467 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.819 |
|
| 8468 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.819 |
|
| 8469 |
\begin{align*}
y^{\prime \prime }+y \ln \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| 8470 |
\begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&=x \,{\mathrm e}^{x}+\frac {\cos \left (x \right )}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| 8471 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=3 \delta \left (t -1\right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| 8472 |
\begin{align*}
x^{\prime }+2 x&=3 t \\
x^{\prime }+2 y^{\prime }+y&=\cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.820 |
|
| 8473 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{2}+x +1 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.820 |
|
| 8474 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.820 |
|
| 8475 |
\begin{align*}
y^{\prime \prime }+y&=10 \,{\mathrm e}^{2 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.820 |
|
| 8476 |
\begin{align*}
t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.821 |
|
| 8477 |
\begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=\sin \left (x \right ) \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.821 |
|
| 8478 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.821 |
|
| 8479 |
\begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=4 x+24 t \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.821 |
|
| 8480 |
\begin{align*}
y^{\prime }&=x -y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| 8481 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2} \\
x_{2}^{\prime }&=-x_{1}+2 x_{2}+4 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| 8482 |
\begin{align*}
y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| 8483 |
\begin{align*}
{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| 8484 |
\begin{align*}
x_{1}^{\prime }&=-7 x_{1}+9 x_{2}-6 x_{3} \\
x_{2}^{\prime }&=-8 x_{1}+11 x_{2}-7 x_{3} \\
x_{3}^{\prime }&=-2 x_{1}+3 x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| 8485 |
\begin{align*}
2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.823 |
|
| 8486 |
\begin{align*}
2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.823 |
|
| 8487 |
\begin{align*}
4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (4 x +1\right ) y^{\prime }-\left (49+27 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.823 |
|
| 8488 |
\begin{align*}
4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
0.823 |
|
| 8489 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1} \\
x_{2}^{\prime }&=5 x_{2}-7 x_{3} \\
x_{3}^{\prime }&=2 x_{2}-4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.823 |
|
| 8490 |
\begin{align*}
y^{\prime \prime }-2 a y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.823 |
|
| 8491 |
\begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=3 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.823 |
|
| 8492 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (3 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.824 |
|
| 8493 |
\begin{align*}
x^{2} \left (x +y\right ) y^{\prime \prime }-\left (-y+y^{\prime } x \right )^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.824 |
|
| 8494 |
\begin{align*}
x^{\prime }&=z-y \\
y^{\prime }&=z \\
z^{\prime }&=z-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.824 |
|
| 8495 |
\begin{align*}
x^{\prime }&=x+y+4 z \\
y^{\prime }&=2 y \\
z^{\prime }&=x+y+z \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 3 \\
z \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.825 |
|
| 8496 |
\begin{align*}
x^{\prime }&=2 x+3 y-7 \\
y^{\prime }&=-x-2 y+5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.825 |
|
| 8497 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=-x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.825 |
|
| 8498 |
\begin{align*}
y^{\prime }+2 y&=6 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.825 |
|
| 8499 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.826 |
|
| 8500 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.826 |
|