| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10401 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| 10402 |
\begin{align*}
x^{\prime \prime }+x&=\cos \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| 10403 |
\begin{align*}
x^{\prime \prime }+x&=\cos \left (\frac {9 t}{10}\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| 10404 |
\begin{align*}
-\left (a^{2}+1\right ) y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.799 |
|
| 10405 |
\begin{align*}
y^{\prime \prime }-y&=\frac {2 \,{\mathrm e}^{-x}}{\left (1+{\mathrm e}^{-2 x}\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| 10406 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| 10407 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 10408 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.800 |
|
| 10409 |
\begin{align*}
2 x^{\prime }+4 y^{\prime }+x-y&=3 \,{\mathrm e}^{t} \\
x^{\prime }+y^{\prime }+2 x+2 y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 10410 |
\begin{align*}
x V^{\prime }&=x^{2}+1 \\
V \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 10411 |
\begin{align*}
x^{\prime }&=4 y \\
y^{\prime }&=-x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 10412 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&={\mathrm e}^{-3 t} \ln \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 10413 |
\begin{align*}
y^{\prime }&=-x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 10414 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 10415 |
\begin{align*}
u^{\prime \prime }+\left (\tan \left (x \right )-2 \cos \left (x \right )\right ) u^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 10416 |
\begin{align*}
t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&={\mathrm e}^{-t} t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.800 |
|
| 10417 |
\begin{align*}
y^{\prime }+y&=2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| 10418 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\sin \left (2 x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| 10419 |
\begin{align*}
{y^{\prime }}^{2}-2 y^{\prime }+a \left (x -y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| 10420 |
\begin{align*}
x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.801 |
|
| 10421 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| 10422 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| 10423 |
\begin{align*}
y^{\prime \prime }&=\frac {2 y}{x \left (x -1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.801 |
|
| 10424 |
\begin{align*}
\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 y y^{\prime } x +y^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.801 |
|
| 10425 |
\begin{align*}
y^{\prime }&=x^{2}+6 y+4 z \\
z^{\prime }&=y+3 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| 10426 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 10427 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-x_{2}-1 \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 10428 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 10429 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }-2 y&=-6 \,{\mathrm e}^{\pi -t} \\
y \left (\pi \right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 4 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 10430 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=\left (2 x^{2}+4 x +8\right ) \cos \left (x \right )+\left (6 x^{2}+8 x +12\right ) \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 10431 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{\sqrt {x^{2}-1}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 10432 |
\begin{align*}
\frac {31 y^{\prime \prime \prime }}{100}+\frac {56 y^{\prime \prime }}{5}-\frac {49 y^{\prime }}{5}+\frac {53 y}{10}&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= -1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.802 |
|
| 10433 |
\begin{align*}
2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=10 x +\frac {10}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 10434 |
\begin{align*}
x^{\prime }&=5 x+4 y+2 z \\
y^{\prime }&=4 x+5 y+2 z \\
z^{\prime }&=2 x+2 y+2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 10435 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x}+{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 10436 |
\begin{align*}
y^{\prime \prime }+9 y&=f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 10437 |
\begin{align*}
16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 10438 |
\begin{align*}
y^{\prime \prime }+\sin \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 10439 |
\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*} |
✓ |
✓ |
✓ |
✗ |
0.803 |
|
| 10440 |
\begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2}+2 y_{3} \\
y_{2}^{\prime }&=y_{1}+y_{2}+2 y_{3} \\
y_{3}^{\prime }&=2 y_{1}+2 y_{2}+4 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 10441 |
\begin{align*}
2 y^{\prime \prime }&=\frac {y^{\prime }}{x}+\frac {x^{2}}{y^{\prime }} \\
y \left (1\right ) &= \frac {\sqrt {2}}{5} \\
y^{\prime }\left (1\right ) &= \frac {\sqrt {2}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 10442 |
\begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 10443 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=2 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 10444 |
\begin{align*}
x^{\prime }&=4 x-13 y \\
y^{\prime }&=2 x-6 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 10445 |
\begin{align*}
\left (x +3\right ) x^{2} y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| 10446 |
\begin{align*}
x_{1}^{\prime }&=-4 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=10 x_{1}+9 x_{2}+x_{3} \\
x_{3}^{\prime }&=-4 x_{1}-3 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*} |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| 10447 |
\begin{align*}
x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| 10448 |
\begin{align*}
c y^{2}+b x y y^{\prime }+a \,x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.804 |
|
| 10449 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| 10450 |
\begin{align*}
{\mathrm e}^{y^{\prime }}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| 10451 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| 10452 |
\begin{align*}
x^{\prime }+3 x-y&=0 \\
y^{\prime }+y-3 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| 10453 |
\begin{align*}
-\left (-4 x^{2}+3\right ) y-4 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.805 |
|
| 10454 |
\begin{align*}
x {y^{\prime }}^{2}+y^{\prime \prime } x&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 10455 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 x} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 10456 |
\begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (16 x^{4}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 10457 |
\begin{align*}
y^{\prime }&=\ln \left (x \right ) \\
y \left ({\mathrm e}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 10458 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 10459 |
\begin{align*}
x^{\prime \prime }+x&=\cos \left (\frac {7 t}{10}\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 10460 |
\begin{align*}
x^{\prime }&=2 x-\frac {5 y}{2} \\
y^{\prime }&=\frac {9 x}{5}-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 10461 |
\begin{align*}
y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.805 |
|
| 10462 |
\begin{align*}
3 {y^{\prime }}^{5}-y y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.805 |
|
| 10463 |
\begin{align*}
{y^{\prime }}^{2} \left (x^{2}-1\right )-2 y y^{\prime } x +y^{2}-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.805 |
|
| 10464 |
\begin{align*}
2 x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 10465 |
\begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 10466 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 10467 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 10468 |
\begin{align*}
y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 10469 |
\begin{align*}
-y+y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ t -1 & 1\le t <2 \\ -t +3 & 2\le t <3 \\ 0 & 3\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.806 |
|
| 10470 |
\begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 y y^{\prime } x +x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.807 |
|
| 10471 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \sec \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 10472 |
\begin{align*}
x^{2} y^{\prime \prime }&=\left (3 x -2 y^{\prime }\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 10473 |
\begin{align*}
y^{2} y^{\prime \prime }+y^{\prime \prime }+2 y {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.807 |
|
| 10474 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=x^{3} {\mathrm e}^{-x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 10475 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+4 x_{2}+4 x_{3} \\
x_{2}^{\prime }&=3 x_{2}+2 x_{3} \\
x_{3}^{\prime }&=2 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 10476 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\
y \left (2\right ) &= 10 \\
y^{\prime }\left (2\right ) &= 15 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 10477 |
\begin{align*}
2 \left (b x +3 a \right ) y-2 x \left (b x +2 a \right ) y^{\prime }+x^{2} \left (b x +a \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.808 |
|
| 10478 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 10479 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x +1 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.808 |
|
| 10480 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (\frac {x}{2}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 10481 |
\begin{align*}
y^{\prime \prime }+9 y&=36 \,{\mathrm e}^{3 x} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 10482 |
\begin{align*}
y&=2 y^{\prime } x +y^{2} {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.808 |
|
| 10483 |
\begin{align*}
x^{\prime }+4 x+3 y&=t \\
y^{\prime }+2 x+5 y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 10484 |
\begin{align*}
x^{2} y^{\prime \prime }&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 10485 |
\begin{align*}
y+y^{\prime }&=\sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 10486 |
\begin{align*}
y^{\prime \prime }&=9 x^{2}+2 x -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 10487 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}+5 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-6 x_{1}-6 x_{2}-5 x_{3} \\
x_{3}^{\prime }&=6 x_{1}+6 x_{2}+5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 10488 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 10489 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{3} \\
x_{2}^{\prime }&=2 x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{3} \\
x_{4}^{\prime }&=-x_{3}+2 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 10490 |
\begin{align*}
y^{\prime }&=\cos \left (x \right )+\sin \left (y\right ) \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\
\end{align*} Series expansion around \(x=\frac {\pi }{2}\). |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 10491 |
\begin{align*}
{y^{\prime }}^{3}+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.809 |
|
| 10492 |
\begin{align*}
x&=\left (x^{2}-9\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 10493 |
\begin{align*}
x^{\prime }&=-3 x+2 y \\
y^{\prime }&=-x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 10494 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| 10495 |
\begin{align*}
y^{\prime \prime }+\left (p +\frac {1}{2}-\frac {x^{2}}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| 10496 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=\sin \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.810 |
|
| 10497 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0<t <\pi \\ \pi & \pi <t \end {array}\right . \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| 10498 |
\begin{align*}
\sin \left (y\right ) y^{\prime \prime }+\cos \left (y\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.810 |
|
| 10499 |
\begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| 10500 |
\begin{align*}
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.810 |
|