| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 14401 |
\begin{align*}
y&=x y^{\prime }+a \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.540 |
|
| 14402 |
\begin{align*}
y^{\prime \prime }-\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.541 |
|
| 14403 |
\begin{align*}
y x +x y^{\prime }&=1-y \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.542 |
|
| 14404 |
\begin{align*}
-2 a \left (-2 a \,x^{2}+1\right ) y-4 a x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.542 |
|
| 14405 |
\begin{align*}
y^{\prime }+2 y&=3 \,{\mathrm e}^{-2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.542 |
|
| 14406 |
\begin{align*}
x \left (x -2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.543 |
|
| 14407 |
\begin{align*}
4 y+y^{\prime \prime }&=x \sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.543 |
|
| 14408 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=4 x +\sin \left (x \right )+\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.543 |
|
| 14409 |
\begin{align*}
y^{\prime \prime }+4 y&=t^{2} \sin \left (2 t \right )+\left (6 t +7\right ) \cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.543 |
|
| 14410 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }&=2 \,{\mathrm e}^{2 x} \sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.543 |
|
| 14411 |
\begin{align*}
b x y+a y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.544 |
|
| 14412 |
\begin{align*}
y^{\prime }&=3 y \left (-2+y\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
1.544 |
|
| 14413 |
\begin{align*}
\left (1-x^{2} y^{2}\right ) y^{\prime }&=\left (y x +1\right ) y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.545 |
|
| 14414 |
\begin{align*}
2 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.545 |
|
| 14415 |
\begin{align*}
\left (x^{4} y^{4}+x^{2} y^{2}+y x \right ) y+\left (x^{4} y^{4}-x^{2} y^{2}+y x \right ) x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.545 |
|
| 14416 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
1.545 |
|
| 14417 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+3 x_{2}+2 x_{3}+\sin \left (t \right ) \\
x_{2}^{\prime }&=-x_{1}+2 x_{2}+x_{3} \\
x_{3}^{\prime }&=4 x_{1}-x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| 14418 |
\begin{align*}
-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.546 |
|
| 14419 |
\begin{align*}
y^{\prime \prime }&=-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| 14420 |
\begin{align*}
x^{\prime }&=2 x+y+2 z \\
y^{\prime }&=3 x+6 z \\
z^{\prime }&=-4 x-3 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| 14421 |
\begin{align*}
y^{\prime }-\left (x +y\right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| 14422 |
\begin{align*}
y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| 14423 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
y \left (-1\right ) &= 1 \\
y^{\prime }\left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| 14424 |
\begin{align*}
t y^{\prime \prime }+2 \left (i t -k \right ) y^{\prime }-2 i k y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| 14425 |
\begin{align*}
y^{\prime }+y^{2}+8 y+7&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.547 |
|
| 14426 |
\begin{align*}
3 y^{\prime }-7 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.547 |
|
| 14427 |
\begin{align*}
y^{\prime }&=y^{2} \left (4-y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.547 |
|
| 14428 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.547 |
|
| 14429 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\left (\mu +2 \lambda \right ) x} y^{2}+\left (b \,{\mathrm e}^{\left (\lambda +\mu \right ) x}-\lambda \right ) y+c \,{\mathrm e}^{\mu x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.547 |
|
| 14430 |
\begin{align*}
x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+x^{n -1} a n y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.547 |
|
| 14431 |
\begin{align*}
y^{\prime }&=3 y-4 \,{\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.547 |
|
| 14432 |
\begin{align*}
y^{\prime }+y x&=3 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.547 |
|
| 14433 |
\begin{align*}
n \cos \left (n x +m y\right )-m \sin \left (m x +n y\right )+\left (m \cos \left (n x +m y\right )-n \sin \left (m x +n y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.548 |
|
| 14434 |
\begin{align*}
y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+18 y^{\prime \prime }+30 y^{\prime }+25 y&={\mathrm e}^{-t} \cos \left (2 t \right )+{\mathrm e}^{-2 t} \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.548 |
|
| 14435 |
\begin{align*}
t^{2} y^{\prime \prime }+7 t y^{\prime }+10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.549 |
|
| 14436 |
\begin{align*}
\left (x^{3} c +b \right ) y+a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.549 |
|
| 14437 |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime \prime }&=2 \left (1+y^{2}\right ) \left (x y^{\prime }-y\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.549 |
|
| 14438 |
\begin{align*}
4 y+y^{\prime \prime }&=\sin \left (2 x \right ) \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.549 |
|
| 14439 |
\begin{align*}
\frac {y}{x}+\left (y^{3}+\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.549 |
|
| 14440 |
\begin{align*}
y^{\prime }-\cos \left (b x +a y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| 14441 |
\begin{align*}
x^{\prime }+y^{\prime }-x-6 y&={\mathrm e}^{3 t} \\
x^{\prime }+2 y^{\prime }-2 x-6 y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| 14442 |
\begin{align*}
y {y^{\prime }}^{3}+x&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.551 |
|
| 14443 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (x^{3}+x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.552 |
|
| 14444 |
\begin{align*}
{y^{\prime }}^{4}-\left (y-a \right )^{3} \left (y-b \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.552 |
|
| 14445 |
\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*} |
✓ |
✓ |
✓ |
✓ |
1.553 |
|
| 14446 |
\begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.554 |
|
| 14447 |
\begin{align*}
y^{\prime }&=-1+y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.554 |
|
| 14448 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.555 |
|
| 14449 |
\begin{align*}
4 y+y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.556 |
|
| 14450 |
\begin{align*}
y^{\prime }+2 y x&=x^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.556 |
|
| 14451 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.556 |
|
| 14452 |
\begin{align*}
\sec \left (y\right )^{2} y^{\prime }-3 \tan \left (y\right )&=-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.557 |
|
| 14453 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.557 |
|
| 14454 |
\begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.557 |
|
| 14455 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.558 |
|
| 14456 |
\begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.558 |
|
| 14457 |
\begin{align*}
y^{\prime \prime }-9 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.558 |
|
| 14458 |
\begin{align*}
y^{\prime }&=\sin \left (y x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.558 |
|
| 14459 |
\begin{align*}
y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1}&=t^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.559 |
|
| 14460 |
\begin{align*}
y^{\prime }&=F \left (y \,{\mathrm e}^{-b x}\right ) {\mathrm e}^{b x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.559 |
|
| 14461 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.559 |
|
| 14462 |
\begin{align*}
x^{\prime }&=x+y+z \\
y^{\prime }&=2 x+5 y+3 z \\
z^{\prime }&=3 x+9 y+5 z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= -1 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.559 |
|
| 14463 |
\begin{align*}
-\left (3 x +2\right ) y+x \left (2-x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.560 |
|
| 14464 |
\begin{align*}
x y^{2} y^{\prime \prime }&=\left (a -y^{2}\right ) y^{\prime }+x y {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.560 |
|
| 14465 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.560 |
|
| 14466 |
\begin{align*}
x y^{\prime \prime }-{y^{\prime }}^{2}&=6 x^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.560 |
|
| 14467 |
\begin{align*}
x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.560 |
|
| 14468 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (-v^{2}+x^{2}+1\right ) y-f \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.561 |
|
| 14469 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=\frac {1}{1+{\mathrm e}^{x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.562 |
|
| 14470 |
\begin{align*}
y^{\prime \prime }-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.562 |
|
| 14471 |
\begin{align*}
y^{\prime \prime }+25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.562 |
|
| 14472 |
\begin{align*}
\left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.562 |
|
| 14473 |
\begin{align*}
y^{\prime }-a \left (t \right ) y&=\delta \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.562 |
|
| 14474 |
\begin{align*}
y^{\prime \prime }-y x -x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.563 |
|
| 14475 |
\begin{align*}
x^{\prime }&=a x+10 y \\
y^{\prime }&=-x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.563 |
|
| 14476 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.563 |
|
| 14477 |
\begin{align*}
y^{\prime \prime }&=\frac {2 \left (a x +2 b \right ) y^{\prime }}{x \left (a x +b \right )}-\frac {\left (2 a x +6 b \right ) y}{\left (a x +b \right ) x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.564 |
|
| 14478 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.564 |
|
| 14479 |
\begin{align*}
y^{\prime }&={\mathrm e}^{2 x}+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.565 |
|
| 14480 |
\begin{align*}
y^{\prime \prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.565 |
|
| 14481 |
\begin{align*}
9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.565 |
|
| 14482 |
\begin{align*}
x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.565 |
|
| 14483 |
\begin{align*}
y^{\prime }&=2 x +1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.566 |
|
| 14484 |
\begin{align*}
\left ({\mathrm e}^{t}-1\right ) y^{\prime \prime }+{\mathrm e}^{t} y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
1.566 |
|
| 14485 |
\begin{align*}
-\left (x^{2}+1\right ) y-4 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.566 |
|
| 14486 |
\begin{align*}
8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2}&=-27 x +27 y \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.567 |
|
| 14487 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=\cos \left (x \right )^{2}+{\mathrm e}^{x}+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.567 |
|
| 14488 |
\begin{align*}
5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.568 |
|
| 14489 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{x} x^{4}+x^{3} {\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.569 |
|
| 14490 |
\begin{align*}
x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.569 |
|
| 14491 |
\begin{align*}
x^{2} y y^{\prime \prime }&=a y^{2}+a x y y^{\prime }+2 {y^{\prime }}^{2} x^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.570 |
|
| 14492 |
\begin{align*}
x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.570 |
|
| 14493 |
\begin{align*}
\sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 y \sin \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.570 |
|
| 14494 |
\begin{align*}
\frac {{y^{\prime \prime }}^{2}}{{y^{\prime }}^{2}}+\frac {y y^{\prime \prime }}{y^{\prime }}-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.570 |
|
| 14495 |
\begin{align*}
y&=y^{\prime }+\frac {{y^{\prime }}^{2}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.571 |
|
| 14496 |
\begin{align*}
y^{\prime \prime }&=2 y y^{\prime } \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.571 |
|
| 14497 |
\begin{align*}
\left (t -2\right )^{2} y^{\prime \prime }+5 \left (t -2\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.572 |
|
| 14498 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=2 \sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.572 |
|
| 14499 |
\begin{align*}
\left (-2 x^{2}+1\right ) y+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.572 |
|
| 14500 |
\begin{align*}
{y^{\prime }}^{2}&=4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.572 |
|