| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10401 |
\begin{align*}
y^{\prime \prime }&=a +y x +2 y^{3} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.784 |
|
| 10402 |
\begin{align*}
x^{\prime }&=5 x+3 y \\
y^{\prime }&=4 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.784 |
|
| 10403 |
\begin{align*}
y&=x y^{\prime }+{y^{\prime }}^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.784 |
|
| 10404 |
\begin{align*}
\sin \left (x \right ) y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.784 |
|
| 10405 |
\begin{align*}
x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+x y^{\prime }+y&=\ln \left (x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.784 |
|
| 10406 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.784 |
|
| 10407 |
\begin{align*}
{y^{\prime }}^{3}&=3 x y^{\prime }-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.784 |
|
| 10408 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 10409 |
\begin{align*}
t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 10410 |
\begin{align*}
12 y-7 y^{\prime }+y^{\prime \prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 10411 |
\begin{align*}
\left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 10412 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 10413 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+\left (9+4 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 10414 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (\alpha t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 10415 |
\begin{align*}
z^{\prime }+y+3 z&={\mathrm e}^{x} \\
y^{\prime }+3 y+4 z&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 10416 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 10417 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-x_{2}+2 x_{3}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}+3 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 ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.786 |
|
| 10418 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+3 x_{3} \\
x_{2}^{\prime }&=-4 x_{2} \\
x_{3}^{\prime }&=-3 x_{1}+2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10419 |
\begin{align*}
{y^{\prime }}^{2}-x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10420 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{x}+{\mathrm e}^{-x}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10421 |
\begin{align*}
{y^{\prime }}^{2}-y^{\prime } x y \left (x +y\right )+x^{3} y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10422 |
\begin{align*}
y^{\prime }&=\frac {1}{1-y} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10423 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+x&=5 \sin \left (7 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10424 |
\begin{align*}
y^{\prime }&=2-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10425 |
\begin{align*}
\theta ^{\prime }&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10426 |
\begin{align*}
y^{\prime }-y \,{\mathrm e}^{x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10427 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=\cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10428 |
\begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10429 |
\begin{align*}
x^{3} y^{\prime \prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.786 |
|
| 10430 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}+x_{2}+3 x_{3} \\
x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=3 x_{1}+x_{2}+5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10431 |
\begin{align*}
x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (2 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10432 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+2 x_{2}-x_{3} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=2 x_{1}+3 x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10433 |
\begin{align*}
y+y^{\prime }&=t \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10434 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (a \,x^{3}+\frac {5}{16}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10435 |
\begin{align*}
x^{\prime \prime }-x&={\mathrm e}^{t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10436 |
\begin{align*}
y^{\prime \prime }-10 y^{\prime }+25 y&={\mathrm e}^{5 t} \ln \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10437 |
\begin{align*}
x^{\prime \prime }+x&=5 t^{2} \\
x \left (0\right ) &= 4 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10438 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+x y^{\prime }-y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10439 |
\begin{align*}
g^{\prime \prime }-3 g^{\prime }+2 g&=\delta \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10440 |
\begin{align*}
y^{2} {y^{\prime }}^{2}&=a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| 10441 |
\begin{align*}
y^{\prime \prime }&=-a \,x^{2 a -1} x^{-2 a} y^{\prime }-b^{2} x^{-2 a} y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.788 |
|
| 10442 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+29 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| 10443 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{t}}{t^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.788 |
|
| 10444 |
\begin{align*}
x^{\prime \prime }+25 x&=90 \cos \left (4 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 90 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10445 |
\begin{align*}
y_{1}^{\prime }&=6 y_{1}-5 y_{2}+3 y_{3} \\
y_{2}^{\prime }&=2 y_{1}-y_{2}+3 y_{3} \\
y_{3}^{\prime }&=2 y_{1}+y_{2}+y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10446 |
\begin{align*}
y_{1}^{\prime }&=-y_{1}-4 y_{2}-y_{3} \\
y_{2}^{\prime }&=3 y_{1}+6 y_{2}+y_{3} \\
y_{3}^{\prime }&=-3 y_{1}-2 y_{2}+3 y_{3} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -2 \\
y_{2} \left (0\right ) &= 1 \\
y_{3} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10447 |
\begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+\left (t +1\right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.789 |
|
| 10448 |
\begin{align*}
x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10449 |
\begin{align*}
y^{\prime \prime }&=f \left (x , \frac {y^{\prime }}{y}\right ) y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.789 |
|
| 10450 |
\begin{align*}
x^{\prime }&=1+y \\
y^{\prime }&=1+x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10451 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10452 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10453 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=2 x^{2} {\mathrm e}^{-2 x}+3 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10454 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.789 |
|
| 10455 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+\left (1-\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.789 |
|
| 10456 |
\begin{align*}
x^{\prime }-2 x+3 y&=0 \\
-2 x+y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10457 |
\begin{align*}
y^{\prime \prime \prime }-y&=3 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10458 |
\begin{align*}
y^{\prime }&=\sqrt {x} \\
y \left (4\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| 10459 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-4 x_{2}+x_{3} \\
x_{2}^{\prime }&=4 x_{1}+3 x_{2}+x_{4} \\
x_{3}^{\prime }&=3 x_{3}-4 x_{4} \\
x_{4}^{\prime }&=4 x_{3}+3 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| 10460 |
\begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-2 x_{3} \\
x_{3}^{\prime }&=3 x_{1}+2 x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| 10461 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| 10462 |
\begin{align*}
\left (4 x^{2}+1\right ) y^{\prime \prime }-8 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| 10463 |
\begin{align*}
\left (-4 x^{2}+1\right ) y^{\prime \prime }+8 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| 10464 |
\begin{align*}
x^{\prime }&=-2 x+7 y \\
y^{\prime }&=3 x+2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 9 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| 10465 |
\begin{align*}
y^{\prime }+y^{\prime \prime \prime }&=\sec \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| 10466 |
\begin{align*}
6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.791 |
|
| 10467 |
\begin{align*}
y^{\prime \prime }+9 y&=18 t \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.791 |
|
| 10468 |
\begin{align*}
4 y+y^{\prime \prime }&=\tan \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.791 |
|
| 10469 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+\left (2 x -1\right ) y&=0 \\
y \left (-1\right ) &= 2 \\
y^{\prime }\left (-1\right ) &= -2 \\
\end{align*}
Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
0.791 |
|
| 10470 |
\begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=2 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.791 |
|
| 10471 |
\begin{align*}
x_{1}^{\prime }&=-20 x_{1}+11 x_{2}+13 x_{3} \\
x_{2}^{\prime }&=12 x_{1}-x_{2}-7 x_{3} \\
x_{3}^{\prime }&=-48 x_{1}+21 x_{2}+31 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 10472 |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+y \sin \left (x \right )&=0 \\
y \left (0\right ) &= a_{0} \\
y^{\prime }\left (0\right ) &= a_{1} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 10473 |
\begin{align*}
4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 10474 |
\begin{align*}
x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (x^{2}+3\right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 10475 |
\begin{align*}
y \left (1+{y^{\prime }}^{2}\right )&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 10476 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 10477 |
\begin{align*}
{y^{\prime }}^{2}-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 10478 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 10479 |
\begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 10480 |
\begin{align*}
y^{\prime \prime }-4 y&=\left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 10481 |
\begin{align*}
y_{1}^{\prime }&=4 y_{1}+6 y_{2}+6 y_{3} \\
y_{2}^{\prime }&=y_{1}+3 y_{2}+2 y_{3} \\
y_{3}^{\prime }&=-y_{1}-4 y_{2}-3 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 10482 |
\begin{align*}
4 x^{2} y^{\prime \prime }+8 x^{2} y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 10483 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+9 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 10484 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-5 x_{1}-4 x_{2}-2 x_{3} \\
x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10485 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-3 x_{2}+{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10486 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10487 |
\begin{align*}
\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10488 |
\begin{align*}
\left (x^{2}+x -6\right ) y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10489 |
\begin{align*}
x^{\prime }&=5 x+y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10490 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{2}+1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.793 |
|
| 10491 |
\begin{align*}
{y^{\prime }}^{2}+\left (b x +a y\right ) y^{\prime }+a b x y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10492 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.793 |
|
| 10493 |
\begin{align*}
x^{\prime \prime }+6 x^{\prime }+10 x&={\mathrm e}^{-2 t} \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10494 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10495 |
\begin{align*}
y&=-t y^{\prime }+\frac {{y^{\prime }}^{5}}{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.793 |
|
| 10496 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=2 \,{\mathrm e}^{x} x^{2} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10497 |
\begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.793 |
|
| 10498 |
\begin{align*}
y^{\prime }&=y x \\
y \left (0\right ) &= 5 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10499 |
\begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -1\right )+\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10500 |
\begin{align*}
y^{\prime }&=\left (1-y\right )^{2} y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.794 |
|