| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12401 |
\begin{align*}
y^{\prime }&=y-x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| 12402 |
\begin{align*}
x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| 12403 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| 12404 |
\begin{align*}
{y^{\prime }}^{3}-y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.010 |
|
| 12405 |
\begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }+\left (x^{2}+x -1\right ) y^{\prime }-\left (2+x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.010 |
|
| 12406 |
\begin{align*}
y^{\prime }&=y^{2}-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| 12407 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.010 |
|
| 12408 |
\begin{align*}
t^{2} y^{\prime \prime }+2 y^{\prime } t +\frac {y}{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 12409 |
\begin{align*}
y {y^{\prime }}^{2}-y^{\prime } x +3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 12410 |
\begin{align*}
y^{\prime \prime }+2 y&=x^{3}+x^{2}+{\mathrm e}^{-2 x}+\cos \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 12411 |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (8\right ) &= -4 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.011 |
|
| 12412 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 12413 |
\begin{align*}
x^{\prime }&=5 x-4 y+{\mathrm e}^{3 t} \\
y^{\prime }&=x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 12414 |
\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*} |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 12415 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 12416 |
\begin{align*}
y^{\prime \prime }&=a {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.012 |
|
| 12417 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{2} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.012 |
|
| 12418 |
\begin{align*}
\left (2 x +1\right ) y-x \left (2 x +1\right ) y^{\prime }+x^{2} \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.012 |
|
| 12419 |
\begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }+\left (2 x +\frac {2}{x}\right ) y^{\prime }+2 x^{2} y&=\frac {4 x^{2}+2 x +10}{x^{4}} \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
1.012 |
|
| 12420 |
\begin{align*}
m y^{\prime \prime }+k y&=\cos \left (\omega t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.012 |
|
| 12421 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }&={\mathrm e}^{-4 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.012 |
|
| 12422 |
\begin{align*}
x^{\prime }+2 x+5 y&=0 \\
-x+y^{\prime }-2 y&=\sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 12423 |
\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*} |
✗ |
✓ |
✓ |
✗ |
1.013 |
|
| 12424 |
\begin{align*}
y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 a x +y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.013 |
|
| 12425 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 12426 |
\begin{align*}
-2 y+a \,x^{2} y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.013 |
|
| 12427 |
\begin{align*}
\left (1+3 x \right ) y^{\prime \prime }-3 y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 12428 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.013 |
|
| 12429 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -20 y&=\left (x +1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 12430 |
\begin{align*}
y^{\prime \prime }+2 b y^{\prime }+y&=k \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 12431 |
\begin{align*}
4 x^{2} y^{\prime \prime }+2 x \left (x^{2}+x +4\right ) y^{\prime }+\left (3 x^{2}+5 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.014 |
|
| 12432 |
\begin{align*}
y^{\prime \prime }+y^{\prime } t +y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.014 |
|
| 12433 |
\begin{align*}
y^{\prime \prime }+y&=2 \sin \left (x \right )-3 \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.014 |
|
| 12434 |
\begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.014 |
|
| 12435 |
\begin{align*}
y^{\prime \prime }&={\mathrm e}^{2 y} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.014 |
|
| 12436 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.015 |
|
| 12437 |
\begin{align*}
y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.015 |
|
| 12438 |
\begin{align*}
y^{\prime }+y^{\prime \prime \prime }&=2 x^{2}+4 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.015 |
|
| 12439 |
\begin{align*}
t^{2} y^{\prime \prime }-3 y^{\prime } t +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| 12440 |
\begin{align*}
y^{\prime \prime }+\left (\frac {1}{x}-\frac {1}{3}\right ) y^{\prime }+\left (\frac {1}{x}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| 12441 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }+y^{\prime } x +\frac {y}{x}&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| 12442 |
\begin{align*}
y^{\prime }+a y&=b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| 12443 |
\begin{align*}
f \left (y\right ) y^{\prime }+g \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.017 |
|
| 12444 |
\begin{align*}
x^{2} \left (x -y\right ) y^{\prime \prime }&=a \left (-y+y^{\prime } x \right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.017 |
|
| 12445 |
\begin{align*}
y^{\prime \prime }+y&=x^{3}-1+2 \cos \left (x \right )+\left (2-4 x \right ) {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 12446 |
\begin{align*}
x^{\prime \prime }+4 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 12447 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.018 |
|
| 12448 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \delta \left (x -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.018 |
|
| 12449 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2}+3 \,{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}+2 t \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -{\frac {5}{18}} \\
x_{2} \left (0\right ) &= {\frac {47}{9}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.018 |
|
| 12450 |
\begin{align*}
y^{\prime }&=y-y^{2}-\frac {1}{4} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.018 |
|
| 12451 |
\begin{align*}
3 {y^{\prime }}^{5}-y y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.019 |
|
| 12452 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| 12453 |
\begin{align*}
5 {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.019 |
|
| 12454 |
\begin{align*}
y^{\prime }&=\ln \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| 12455 |
\begin{align*}
\frac {y x +1}{y}+\frac {\left (-x +2 y\right ) y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.020 |
|
| 12456 |
\begin{align*}
x {y^{\prime }}^{2}-2 y y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| 12457 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+l x y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| 12458 |
\begin{align*}
y {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| 12459 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&={\mathrm e}^{2 x} \cos \left ({\mathrm e}^{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| 12460 |
\begin{align*}
2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| 12461 |
\begin{align*}
\left (a x +b y\right ) {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.021 |
|
| 12462 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}-v \left (v -1\right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| 12463 |
\begin{align*}
4 x^{\prime }+9 y^{\prime }+2 x+31 y&={\mathrm e}^{t} \\
3 x^{\prime }+7 y^{\prime }+x+24 y&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| 12464 |
\begin{align*}
{y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.021 |
|
| 12465 |
\begin{align*}
y^{\prime }&=-x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| 12466 |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (0\right ) &= -4 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.022 |
|
| 12467 |
\begin{align*}
y^{\prime \prime }-8 y^{\prime }+15 y&=9 x \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.022 |
|
| 12468 |
\begin{align*}
y^{\prime }+2 y^{\prime \prime } x&=\sqrt {x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.022 |
|
| 12469 |
\begin{align*}
x y^{2} \left ({y^{\prime }}^{2}+2\right )&=2 y^{3} y^{\prime }+x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.022 |
|
| 12470 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.022 |
|
| 12471 |
\begin{align*}
y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.022 |
|
| 12472 |
\begin{align*}
y^{\prime }&=t \ln \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.022 |
|
| 12473 |
\begin{align*}
4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.023 |
|
| 12474 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2}-x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}+3 x_{3} \\
x_{3}^{\prime }&=3 x_{1}-4 x_{2}-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.023 |
|
| 12475 |
\begin{align*}
\frac {x}{x^{2}+y^{2}}+\frac {y}{x^{2}}+\left (\frac {y}{x^{2}+y^{2}}-\frac {1}{x}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.024 |
|
| 12476 |
\begin{align*}
x \left (-1+{y^{\prime }}^{2}\right )&=2 y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.024 |
|
| 12477 |
\begin{align*}
-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.024 |
|
| 12478 |
\begin{align*}
e y^{\prime \prime }&=\frac {P \left (\frac {L}{2}-x \right )}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.024 |
|
| 12479 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{2 x}+\frac {y}{4 x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.024 |
|
| 12480 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+4 y&=\sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.025 |
|
| 12481 |
\begin{align*}
y^{\prime \prime } x -\left (x -1\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.025 |
|
| 12482 |
\begin{align*}
y^{\prime }&=-5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.025 |
|
| 12483 |
\begin{align*}
4 t^{2} y^{\prime \prime }-8 y^{\prime } t +9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| 12484 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x^{2}+x +1\right ) y^{\prime }+x \left (-x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| 12485 |
\begin{align*}
x_{1}^{\prime }&=7 x_{1}-x_{2}+6 x_{3} \\
x_{2}^{\prime }&=-10 x_{1}+4 x_{2}-12 x_{3} \\
x_{3}^{\prime }&=-2 x_{1}+x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| 12486 |
\begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=6 x_{2}-7 x_{3}+3 x_{4} \\
x_{3}^{\prime }&=3 x_{3}-x_{4} \\
x_{4}^{\prime }&=-4 x_{2}+9 x_{3}-3 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| 12487 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| 12488 |
\begin{align*}
y^{\prime \prime }+y-\sin \left (a x \right ) \sin \left (b x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.026 |
|
| 12489 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+5 x_{2}+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\
x_{2}^{\prime }&=-2 x_{1}-2 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.027 |
|
| 12490 |
\begin{align*}
y \left (6 y^{2}-x -1\right )+2 y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.027 |
|
| 12491 |
\begin{align*}
4 x^{2} y^{\prime \prime }+\left (4 x^{4}-5 x \right ) y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.027 |
|
| 12492 |
\begin{align*}
y^{\prime \prime } x +3 y^{\prime }&=3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.027 |
|
| 12493 |
\begin{align*}
{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.027 |
|
| 12494 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{3}^{\prime }&=4 x_{1}-x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.028 |
|
| 12495 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x \left (x +1\right ) y^{\prime }+\left (1-3 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.028 |
|
| 12496 |
\begin{align*}
y_{1}^{\prime }&=-2 y_{1}+2 y_{2}+y_{3}+{\mathrm e}^{-2 t} \\
y_{2}^{\prime }&=-y_{2} \\
y_{3}^{\prime }&=2 y_{1}-2 y_{2}-y_{3}-{\mathrm e}^{-2 t} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= 1 \\
y_{3} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.028 |
|
| 12497 |
\begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+32 y^{\prime \prime }-64 y^{\prime }+64 y&={\mathrm e}^{2 x} \left (\cos \left (2 x \right )-\sin \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.029 |
|
| 12498 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-x_{2}+1 \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.029 |
|
| 12499 |
\begin{align*}
-\left (3+2 x \right ) y+\left (x^{2}+x +1\right ) y^{\prime }+\left (x^{2}+3 x +4\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.029 |
|
| 12500 |
\begin{align*}
t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
1.030 |
|