| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 8501 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.826 |
|
| 8502 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-p^{2}+x^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.826 |
|
| 8503 |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.826 |
|
| 8504 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{3} \\
x_{2}^{\prime }&=9 x_{1}-x_{2}+2 x_{3} \\
x_{3}^{\prime }&=-9 x_{1}+4 x_{2}-x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 17 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.827 |
|
| 8505 |
\begin{align*}
x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.827 |
|
| 8506 |
\begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.827 |
|
| 8507 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.827 |
|
| 8508 |
\begin{align*}
{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.827 |
|
| 8509 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.827 |
|
| 8510 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=\delta \left (t -3\right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.827 |
|
| 8511 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
y \left (0\right ) &= \alpha \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.828 |
|
| 8512 |
\begin{align*}
x_{1}^{\prime }&=15 x_{1}-32 x_{2}+12 x_{3} \\
x_{2}^{\prime }&=8 x_{1}-17 x_{2}+6 x_{3} \\
x_{3}^{\prime }&=-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.828 |
|
| 8513 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+10 y^{\prime } x +20 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.828 |
|
| 8514 |
\begin{align*}
{\mathrm e}^{x} \left (y^{\prime }+y\right )&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.828 |
|
| 8515 |
\begin{align*}
6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| 8516 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y&=\sinh \left (x \right ) \cos \left (x \right )-\cosh \left (x \right ) \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| 8517 |
\begin{align*}
2 x^{2} \left (1-3 x \right ) y^{\prime \prime }+5 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| 8518 |
\begin{align*}
y^{\prime }&={\mathrm e}^{a x}+a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| 8519 |
\begin{align*}
x^{\prime }&=3 x+2 y+z \\
y^{\prime }&=-2 x-y+3 z \\
z^{\prime }&=x+y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| 8520 |
\begin{align*}
2 y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -\beta \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.830 |
|
| 8521 |
\begin{align*}
u^{\prime }&=\frac {1}{5-2 u} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.830 |
|
| 8522 |
\begin{align*}
x^{\prime }-4 x+3 y&=\sin \left (t \right ) \\
-2 x+y^{\prime }+y&=-2 \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.831 |
|
| 8523 |
\begin{align*}
x^{\prime }+2 x+5 y&=0 \\
-x+y^{\prime }-2 y&=\sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.831 |
|
| 8524 |
\begin{align*}
y^{\prime }+\sqrt {2 x^{2}+1}\, y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.831 |
|
| 8525 |
\begin{align*}
y^{\prime }&=y-x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| 8526 |
\begin{align*}
y^{\prime \prime \prime \prime }+y&=g \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| 8527 |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| 8528 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{2}+1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.832 |
|
| 8529 |
\begin{align*}
\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.832 |
|
| 8530 |
\begin{align*}
y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+7 y^{\prime \prime }-5 y^{\prime }+6 y&=5 \sin \left (x \right )-12 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| 8531 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime } x -{\mathrm e}^{x} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| 8532 |
\begin{align*}
y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=a \sin \left (x n +\alpha \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| 8533 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| 8534 |
\begin{align*}
\sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 \sin \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.832 |
|
| 8535 |
\begin{align*}
x^{\prime }&=2 x+y+3 \,{\mathrm e}^{2 t} \\
y^{\prime }&=-4 x+2 y+{\mathrm e}^{2 t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| 8536 |
\begin{align*}
t^{2} y^{\prime }&=1-2 t y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| 8537 |
\begin{align*}
9 x^{2} y^{\prime \prime }+9 \left (-x^{2}+x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| 8538 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| 8539 |
\begin{align*}
y^{\prime }&=10+3 y-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| 8540 |
\begin{align*}
y y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.833 |
|
| 8541 |
\begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| 8542 |
\begin{align*}
x_{1}^{\prime }&=-x_{3} \\
x_{2}^{\prime }&=2 x_{1} \\
x_{3}^{\prime }&=-x_{1}+2 x_{2}+4 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 7 \\
x_{2} \left (0\right ) &= 5 \\
x_{3} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| 8543 |
\begin{align*}
y^{\prime \prime }+4 y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| 8544 |
\begin{align*}
4 x^{2} y^{\prime \prime }+x \left (x^{2}-4\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| 8545 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x -18 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| 8546 |
\begin{align*}
x^{2} \left (x -y\right ) y^{\prime \prime }+a \left (-y+y^{\prime } x \right )^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.834 |
|
| 8547 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| 8548 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=-8 x_{1}-5 x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| 8549 |
\begin{align*}
2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| 8550 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-p^{2}+x^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| 8551 |
\begin{align*}
y_{1}^{\prime }&=y_{2}+y_{3}+{\mathrm e}^{2 t} \\
y_{2}^{\prime }&=y_{1}+y_{2}-y_{3}+{\mathrm e}^{2 t} \\
y_{3}^{\prime }&=-2 y_{1}+y_{2}+3 y_{3}-{\mathrm e}^{2 t} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 0 \\
y_{3} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| 8552 |
\begin{align*}
y^{\prime }+20 y&=24 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| 8553 |
\begin{align*}
y^{\prime }&=y+{\mathrm e}^{-y}+{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.835 |
|
| 8554 |
\begin{align*}
y&=y^{\prime } x +\frac {1}{y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.835 |
|
| 8555 |
\begin{align*}
2 \left (1-y\right ) y y^{\prime \prime }&=\left (1-2 y\right ) {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.835 |
|
| 8556 |
\begin{align*}
y^{\prime } x +y&=x^{4} {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.835 |
|
| 8557 |
\begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=-x+2 y+4 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.835 |
|
| 8558 |
\begin{align*}
y^{\prime }&=-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.835 |
|
| 8559 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=x+{\mathrm e}^{t}+{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.835 |
|
| 8560 |
\begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✓ |
0.835 |
|
| 8561 |
\begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.835 |
|
| 8562 |
\begin{align*}
\left (x +3\right ) x^{2} y^{\prime \prime }+x \left (5+4 x \right ) y^{\prime }-\left (1-2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.836 |
|
| 8563 |
\begin{align*}
x^{\prime }+x+2 y&=2 \,{\mathrm e}^{-t} \\
y^{\prime }+y+z&=1 \\
z^{\prime }+z&=1 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.836 |
|
| 8564 |
\begin{align*}
y^{\prime }-k y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.836 |
|
| 8565 |
\begin{align*}
2 \sin \left (t \right ) y^{\prime \prime }+\left (1-t \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.837 |
|
| 8566 |
\begin{align*}
{y^{\prime }}^{2}&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.837 |
|
| 8567 |
\begin{align*}
a \cot \left (x \right )^{2} y+\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.837 |
|
| 8568 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2}+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| 8569 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2}-\cos \left (t \right ) \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| 8570 |
\begin{align*}
y^{\prime }&=-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| 8571 |
\begin{align*}
y^{\prime \prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| 8572 |
\begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }-3 \left (x -1\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✗ |
0.838 |
|
| 8573 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| 8574 |
\begin{align*}
-y+y^{\prime }&=10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| 8575 |
\begin{align*}
y^{\prime }&=-2 y+8 \\
y \left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| 8576 |
\begin{align*}
y^{\prime \prime }&={\mathrm e}^{y} y^{\prime } \\
y \left (3\right ) &= 0 \\
y^{\prime }\left (3\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.839 |
|
| 8577 |
\begin{align*}
2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| 8578 |
\begin{align*}
x^{\prime }+x+y&=t^{2} \\
y^{\prime }+y+z&=2 t \\
z^{\prime }+z&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| 8579 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (-4 x^{3}+x \right ) y^{\prime }-x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| 8580 |
\begin{align*}
y^{\prime \prime }+y&=4 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.840 |
|
| 8581 |
\begin{align*}
y^{\prime \prime } x +\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.840 |
|
| 8582 |
\begin{align*}
x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.840 |
|
| 8583 |
\begin{align*}
y_{1}^{\prime }&=-2 y_{1}-y_{2}+y_{3} \\
y_{2}^{\prime }&=-y_{1}-2 y_{2}-y_{3} \\
y_{3}^{\prime }&=y_{1}-y_{2}-2 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.840 |
|
| 8584 |
\begin{align*}
x^{\prime }&=2 x+2 y-z \\
y^{\prime }&=y+z \\
z^{\prime }&=z-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.840 |
|
| 8585 |
\begin{align*}
t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.840 |
|
| 8586 |
\begin{align*}
y^{\prime \prime } x -\left (x -1\right ) y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| 8587 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.841 |
|
| 8588 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.841 |
|
| 8589 |
\begin{align*}
\sin \left (y^{\prime }\right )&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| 8590 |
\begin{align*}
9 \left (1-x \right ) x y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| 8591 |
\begin{align*}
y^{\prime }&=y^{2}-y^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| 8592 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (\frac {1}{2} x +x^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| 8593 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| 8594 |
\begin{align*}
x^{2} y y^{\prime \prime }+\left (-y+y^{\prime } x \right )^{2}-3 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.842 |
|
| 8595 |
\begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y&=t^{2} \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.844 |
|
| 8596 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=x_{1}+2 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+10 x_{2}+2 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 ) &= 13 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.844 |
|
| 8597 |
\begin{align*}
\left (x +1\right ) \left (x^{2}+1\right ) y^{\prime }&=2 x^{2}+x \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.844 |
|
| 8598 |
\begin{align*}
2 y^{\prime \prime }+5 y^{\prime } x +\left (2 x^{2}+4\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.844 |
|
| 8599 |
\begin{align*}
y^{\prime \prime \prime }-a^{2} \left ({y^{\prime }}^{5}+2 {y^{\prime }}^{3}+y^{\prime }\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.844 |
|
| 8600 |
\begin{align*}
a^{4} y+2 a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=8 \cos \left (a x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.844 |
|