| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12401 |
\begin{align*}
y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.054 |
|
| 12402 |
\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*} |
✓ |
✓ |
✓ |
✓ |
1.055 |
|
| 12403 |
\begin{align*}
y^{\prime }&=y^{2}+2 y-3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.055 |
|
| 12404 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }+\left (a \,x^{2}+b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.055 |
|
| 12405 |
\begin{align*}
y^{\prime \prime }+y&=x \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.055 |
|
| 12406 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=8 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.055 |
|
| 12407 |
\begin{align*}
x^{\prime }&=y+\textit {f\_1} \left (t \right ) \\
y^{\prime }&=-x+f_{2} \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.056 |
|
| 12408 |
\begin{align*}
9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y&=x^{4}+x^{2} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.056 |
|
| 12409 |
\begin{align*}
2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=x^{3}+1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.056 |
|
| 12410 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x +\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.056 |
|
| 12411 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }&=\frac {2}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.056 |
|
| 12412 |
\begin{align*}
y^{\prime \prime }-2 a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.056 |
|
| 12413 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.056 |
|
| 12414 |
\begin{align*}
x^{2} y^{\prime \prime }-2 n x y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.056 |
|
| 12415 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=0 \\
y \left (2\right ) &= 10 \\
y^{\prime }\left (2\right ) &= 15 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.057 |
|
| 12416 |
\begin{align*}
4 y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= \beta \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.057 |
|
| 12417 |
\begin{align*}
2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.057 |
|
| 12418 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.057 |
|
| 12419 |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }&=\left (x -1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.057 |
|
| 12420 |
\begin{align*}
x^{2} \left (x +2\right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.058 |
|
| 12421 |
\begin{align*}
6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.058 |
|
| 12422 |
\begin{align*}
3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.058 |
|
| 12423 |
\begin{align*}
y^{\prime \prime }-4 y&=96 x^{2} {\mathrm e}^{2 x}+4 \,{\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.058 |
|
| 12424 |
\begin{align*}
x \left (1-x \right ) y^{\prime \prime }+2 \left (1-2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.058 |
|
| 12425 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.058 |
|
| 12426 |
\begin{align*}
{\mathrm e}^{-y} \left (y^{\prime }+1\right )&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.058 |
|
| 12427 |
\begin{align*}
y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.059 |
|
| 12428 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }&=9 \,{\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.059 |
|
| 12429 |
\begin{align*}
y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -10\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.059 |
|
| 12430 |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=6 x_{1}+4 \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.059 |
|
| 12431 |
\begin{align*}
4 x y^{\prime \prime }+y^{\prime }+8 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.060 |
|
| 12432 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}+f \left (x \right ) y^{\prime }-f^{\prime }\left (x \right ) y-y^{3}&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
1.060 |
|
| 12433 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y&=3 \cos \left (\frac {t}{4}\right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.060 |
|
| 12434 |
\begin{align*}
\left (x +1\right ) y^{\prime \prime }+2 y^{\prime }&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.060 |
|
| 12435 |
\begin{align*}
y^{\prime }&=2 x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.060 |
|
| 12436 |
\begin{align*}
4 \left (x^{2}+1\right )^{2} y^{\prime \prime }+\left (a \,x^{2}+a -3\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.061 |
|
| 12437 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-4 x_{1}+2 x_{2}-2 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-2 x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.061 |
|
| 12438 |
\begin{align*}
2 y^{\prime }+x y^{\prime \prime }&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.061 |
|
| 12439 |
\begin{align*}
z^{\prime }-3 y+2 z&={\mathrm e}^{x} \\
y^{\prime }+2 y-z&={\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.061 |
|
| 12440 |
\begin{align*}
2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.062 |
|
| 12441 |
\begin{align*}
y x -2 y^{2}-\left (x^{2}-3 y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.062 |
|
| 12442 |
\begin{align*}
y^{\prime \prime }-\frac {t}{y}&=\frac {1}{\pi } \\
y \left (0\right ) &= y_{0} \\
y^{\prime }\left (0\right ) &= y_{1} \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
1.062 |
|
| 12443 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \left (1+\cos \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.062 |
|
| 12444 |
\begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| 12445 |
\begin{align*}
1+{y^{\prime }}^{2}&=\frac {1}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| 12446 |
\begin{align*}
y^{\prime \prime }+y-\sin \left (a x \right ) \sin \left (b x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.063 |
|
| 12447 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x^{{3}/{2}} {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| 12448 |
\begin{align*}
y^{\prime \prime }+\left (\frac {16}{3 x}-1\right ) y^{\prime }-\frac {16 y}{3 x^{2}}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| 12449 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{-x}+17 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| 12450 |
\begin{align*}
\left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.063 |
|
| 12451 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✗ |
1.063 |
|
| 12452 |
\begin{align*}
y^{\prime \prime }&=y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.065 |
|
| 12453 |
\begin{align*}
9 y^{\prime \prime }-6 y^{\prime }+y&=\left (4 x^{2}+24 x +18\right ) {\mathrm e}^{x} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| 12454 |
\begin{align*}
y^{\prime \prime }+\frac {\left (1-5 x \right ) y^{\prime }}{-x^{2}+x}-\frac {4 y}{-x^{2}+x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| 12455 |
\begin{align*}
a y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| 12456 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| 12457 |
\begin{align*}
y^{\prime \prime }-2 k y^{\prime }+k^{2} y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| 12458 |
\begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=-2 x-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| 12459 |
\begin{align*}
y^{\prime }&=y^{3}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| 12460 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| 12461 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| 12462 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=\sin \left (t \right )+{\mathrm e}^{2 t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.066 |
|
| 12463 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}+8 x_{2}+9 t \\
x_{2}^{\prime }&=x_{1}+x_{2}+3 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.066 |
|
| 12464 |
\begin{align*}
x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime }&=x^{2} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.066 |
|
| 12465 |
\begin{align*}
4 y^{2} {y^{\prime }}^{2}+2 \left (1+3 x \right ) x y y^{\prime }+3 x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.067 |
|
| 12466 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.067 |
|
| 12467 |
\begin{align*}
a^{2}-x y^{\prime } \sqrt {-a^{2}+x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.067 |
|
| 12468 |
\begin{align*}
x^{\prime }+3 x+4 y&=8 \,{\mathrm e}^{t} \\
-x+y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.068 |
|
| 12469 |
\begin{align*}
9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| 12470 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| 12471 |
\begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=x+2 y+z \\
z^{\prime }&=3 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| 12472 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\mu x} \left (y-b \,{\mathrm e}^{\lambda x}\right )^{2}+b \lambda \,{\mathrm e}^{\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.069 |
|
| 12473 |
\begin{align*}
y&=y {y^{\prime }}^{2}+2 x y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| 12474 |
\begin{align*}
\left (x^{2}+a \right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.069 |
|
| 12475 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| 12476 |
\begin{align*}
y^{\prime \prime }+2 z y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| 12477 |
\begin{align*}
y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| 12478 |
\begin{align*}
y^{\prime \prime }+y&=a \cos \left (b x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.070 |
|
| 12479 |
\begin{align*}
{y^{\prime }}^{2} \left (x^{2}-1\right )-y^{2}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.070 |
|
| 12480 |
\begin{align*}
\left (4 y^{3}-a y-b \right ) y^{\prime \prime }-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.070 |
|
| 12481 |
\begin{align*}
\left (x +2\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.070 |
|
| 12482 |
\begin{align*}
y^{\prime }-y&=2 x -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.070 |
|
| 12483 |
\begin{align*}
y y^{\prime }-2 {y^{\prime }}^{2} x +x y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.071 |
|
| 12484 |
\begin{align*}
x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.071 |
|
| 12485 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }&=9 \,{\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.071 |
|
| 12486 |
\begin{align*}
x \left (1-x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.071 |
|
| 12487 |
\begin{align*}
{y^{\prime }}^{2}&=4 y \\
y \left (a \right ) &= b \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.072 |
|
| 12488 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+\left (\frac {1}{4 x^{2}}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| 12489 |
\begin{align*}
-y^{\prime }+x y^{\prime \prime }&=x^{2} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| 12490 |
\begin{align*}
x^{\prime }&=3 x+2 y+z \\
y^{\prime }&=-2 x-y+3 z \\
z^{\prime }&=x+y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| 12491 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| 12492 |
\begin{align*}
x^{\prime }&=7 x-y+6 z \\
y^{\prime }&=-10 x+4 y-12 z \\
z^{\prime }&=-2 x+y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| 12493 |
\begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| 12494 |
\begin{align*}
y^{\prime }&=3 y+12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| 12495 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| 12496 |
\begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=\sin \left (x \right ) \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| 12497 |
\begin{align*}
8 y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| 12498 |
\begin{align*}
y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| 12499 |
\begin{align*}
y^{\prime }-\frac {1}{\sqrt {\operatorname {a4} \,x^{4}+\operatorname {a3} \,x^{3}+\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| 12500 |
\begin{align*}
y^{\prime \prime }-\left (\frac {1}{x}+2\right ) y^{\prime }+\left (x +\frac {1}{x^{2}}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.073 |
|