| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 15201 |
\begin{align*}
y^{\prime }&=8 \,{\mathrm e}^{4 t}+t \\
y \left (0\right ) &= 12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.448 |
|
| 15202 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=3-4 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.448 |
|
| 15203 |
\begin{align*}
y^{\prime }&=y+3 y^{{1}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.448 |
|
| 15204 |
\begin{align*}
y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.448 |
|
| 15205 |
\begin{align*}
y^{\prime }&=-{\mathrm e}^{t}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.448 |
|
| 15206 |
\begin{align*}
y^{\prime }&=2 x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.448 |
|
| 15207 |
\begin{align*}
{y^{\prime }}^{2}-{y^{\prime }}^{3}&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.448 |
|
| 15208 |
\begin{align*}
4 x \left (a -x \right ) \left (b -x \right ) {y^{\prime }}^{2}&=\left (a b -2 \left (a +b \right ) x +2 x^{2}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.449 |
|
| 15209 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -10 y&=0 \\
y \left (1\right ) &= 5 \\
y^{\prime }\left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.449 |
|
| 15210 |
\begin{align*}
x^{\prime \prime }+x&=0 \\
x \left (\frac {\pi }{2}\right ) &= 0 \\
x^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.449 |
|
| 15211 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.450 |
|
| 15212 |
\begin{align*}
-\left (i x^{2}+p^{2}\right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.450 |
|
| 15213 |
\begin{align*}
y^{\prime } x +a \,x^{\alpha } y^{2}+b y-c \,x^{\beta }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.450 |
|
| 15214 |
\begin{align*}
y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.450 |
|
| 15215 |
\begin{align*}
x&=\ln \left (y^{\prime }\right )+\sin \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.450 |
|
| 15216 |
\begin{align*}
x-y+z^{\prime }&=0 \\
x^{\prime }-y&=1 \\
y^{\prime }-y+z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.450 |
|
| 15217 |
\begin{align*}
\frac {1+2 x y}{x^{\prime }}&=y^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.451 |
|
| 15218 |
\begin{align*}
y-x^{3}+\left (y^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.451 |
|
| 15219 |
\begin{align*}
x^{2} {y^{\prime }}^{2}-\left (2 y x +1\right ) y^{\prime }+1+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.451 |
|
| 15220 |
\begin{align*}
b x y+a y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.451 |
|
| 15221 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }&=3 t +2 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.451 |
|
| 15222 |
\begin{align*}
x {y^{\prime }}^{2}-2 y y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.452 |
|
| 15223 |
\begin{align*}
y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y&={\mathrm e}^{x} \sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.453 |
|
| 15224 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.453 |
|
| 15225 |
\begin{align*}
y^{\prime }&=t +2 y \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.453 |
|
| 15226 |
\begin{align*}
x_{1}^{\prime }&=6 x_{1}+5 x_{2}-4 \cos \left (3 t \right ) \\
x_{2}^{\prime }&=x_{1}+2 x_{2}+8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.453 |
|
| 15227 |
\begin{align*}
4 {y^{\prime }}^{2}&=9 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.454 |
|
| 15228 |
\begin{align*}
y^{\prime \prime }+16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.454 |
|
| 15229 |
\begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.454 |
|
| 15230 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }&=t^{2}-{\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.454 |
|
| 15231 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=4 \,{\mathrm e}^{x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.454 |
|
| 15232 |
\begin{align*}
4 y+y^{\prime \prime }&=x \sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.455 |
|
| 15233 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{10}+y&=k \delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.455 |
|
| 15234 |
\begin{align*}
t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.456 |
|
| 15235 |
\begin{align*}
y^{\prime \prime }+\sqrt {y^{\prime }}+y&=t \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.456 |
|
| 15236 |
\begin{align*}
\left ({y^{\prime }}^{2}+a \left (-y+y^{\prime } x \right )\right ) y^{\prime \prime }-b&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.457 |
|
| 15237 |
\begin{align*}
y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.457 |
|
| 15238 |
\begin{align*}
x_{1}^{\prime }&=11 x_{1}-x_{2}+26 x_{3}+6 x_{4}-3 x_{5} \\
x_{2}^{\prime }&=3 x_{2} \\
x_{3}^{\prime }&=-9 x_{1}-24 x_{3}-6 x_{4}+3 x_{5} \\
x_{4}^{\prime }&=3 x_{1}+9 x_{3}+5 x_{4}-x_{5} \\
x_{5}^{\prime }&=-48 x_{1}-3 x_{2}-138 x_{3}-30 x_{4}+18 x_{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.459 |
|
| 15239 |
\begin{align*}
t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.459 |
|
| 15240 |
\begin{align*}
x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.459 |
|
| 15241 |
\begin{align*}
x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (\left (1-n \right ) x -\left (6-4 n \right ) x^{2}\right ) y^{\prime }+n \left (1-n \right ) x y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.459 |
|
| 15242 |
\begin{align*}
\left (-a^{2}+b^{2}\right ) y+2 a \cot \left (a x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.460 |
|
| 15243 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.460 |
|
| 15244 |
\begin{align*}
\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime \prime }&=2 y x -{\mathrm e}^{y}-x \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.460 |
|
| 15245 |
\begin{align*}
y^{\prime }&=k y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.461 |
|
| 15246 |
\begin{align*}
x^{2}+y+y^{2}-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.463 |
|
| 15247 |
\begin{align*}
{y^{\prime }}^{2}&=1-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.463 |
|
| 15248 |
\begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.463 |
|
| 15249 |
\begin{align*}
t^{2} x^{\prime \prime }+t x^{\prime }+x&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.463 |
|
| 15250 |
\begin{align*}
\left (x -1-y^{2}\right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.464 |
|
| 15251 |
\begin{align*}
x^{\prime \prime }+\omega ^{2} x&=\cos \left (\omega t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.464 |
|
| 15252 |
\begin{align*}
y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.465 |
|
| 15253 |
\begin{align*}
y^{\prime }+f \left (x \right )^{2}&=f^{\prime }\left (x \right )+y^{2} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.465 |
|
| 15254 |
\begin{align*}
-\left (a^{2} x^{2}+2\right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.466 |
|
| 15255 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&={\mathrm e}^{x} \cos \left (2 x \right )+\cos \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.466 |
|
| 15256 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.466 |
|
| 15257 |
\begin{align*}
x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.466 |
|
| 15258 |
\begin{align*}
\left (1+t \right ) y+y^{\prime } t&=t \\
y \left (\ln \left (2\right )\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.467 |
|
| 15259 |
\begin{align*}
-2 y+a \,x^{2} y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.467 |
|
| 15260 |
\begin{align*}
a^{2} y+y^{\prime \prime }&=2 \cos \left (x m \right )+3 \sin \left (x m \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.467 |
|
| 15261 |
\begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.468 |
|
| 15262 |
\begin{align*}
y^{\prime }&=-x +y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.468 |
|
| 15263 |
\begin{align*}
2 \left (1-x \right ) x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.469 |
|
| 15264 |
\begin{align*}
x^{\prime }&=-12 x-7 y \\
y^{\prime }&=19 x+11 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.469 |
|
| 15265 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\left \{\begin {array}{cc} \sin \left (2 t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.470 |
|
| 15266 |
\begin{align*}
y^{\prime \prime }+16 y&=\cot \left (4 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.470 |
|
| 15267 |
\begin{align*}
x^{2} y y^{\prime \prime }+\left (-y+y^{\prime } x \right )^{2}-3 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.470 |
|
| 15268 |
\begin{align*}
2 y+y^{\prime }&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.471 |
|
| 15269 |
\begin{align*}
y^{\prime }&=y x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.471 |
|
| 15270 |
\begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )&=r^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.472 |
|
| 15271 |
\begin{align*}
y^{\prime \prime }+\omega ^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.472 |
|
| 15272 |
\begin{align*}
y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.473 |
|
| 15273 |
\begin{align*}
x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.473 |
|
| 15274 |
\begin{align*}
y^{\prime \prime }&=2 y y^{\prime } \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.475 |
|
| 15275 |
\begin{align*}
{\mathrm e}^{x} \left (y^{3}+x y^{3}+1\right )+3 y^{2} \left (x \,{\mathrm e}^{x}-6\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| 15276 |
\begin{align*}
\left (1+y^{2} x^{2}\right ) y+\left (y^{2} x^{2}-1\right ) x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| 15277 |
\begin{align*}
x^{\prime }&=x \left (1+{\mathrm e}^{t} x\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| 15278 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| 15279 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
y \left (\frac {\pi }{4}\right ) &= 2 \\
y^{\prime }\left (\frac {\pi }{4}\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.478 |
|
| 15280 |
\begin{align*}
\left (-y+y^{\prime } x \right )^{3}+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.478 |
|
| 15281 |
\begin{align*}
\left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+t y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.478 |
|
| 15282 |
\begin{align*}
y^{\prime } x -3 y&=x^{3} \\
y \left (1\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.479 |
|
| 15283 |
\begin{align*}
y^{\prime }&=y \left (y-3\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.480 |
|
| 15284 |
\begin{align*}
y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x \left (a^{2}-x^{2}\right )}&=\frac {x^{2}}{a \left (a^{2}-x^{2}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.480 |
|
| 15285 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.480 |
|
| 15286 |
\begin{align*}
x^{2}-1+2 y+\left (-x^{2}+1\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.480 |
|
| 15287 |
\begin{align*}
y^{\prime }&=x^{2}-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.481 |
|
| 15288 |
\begin{align*}
y^{\prime }&=-{\mathrm e}^{y}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.481 |
|
| 15289 |
\begin{align*}
3 y+y^{\prime }&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
y \left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.481 |
|
| 15290 |
\begin{align*}
y^{\prime \prime }+i y&=\cosh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.482 |
|
| 15291 |
\begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.483 |
|
| 15292 |
\begin{align*}
y^{\prime }&=t -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.483 |
|
| 15293 |
\begin{align*}
y^{\prime }&=x \sec \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.483 |
|
| 15294 |
\begin{align*}
x^{\prime }&=x+y-z \\
y^{\prime }&=y+z-x \\
z^{\prime }&=x-y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.483 |
|
| 15295 |
\begin{align*}
y-\frac {y^{\prime } x}{2}-\frac {x}{2 y^{\prime }}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.483 |
|
| 15296 |
\begin{align*}
x \left (-1+{y^{\prime }}^{2}\right )&=2 y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.483 |
|
| 15297 |
\begin{align*}
x^{\prime }&=\left (t +x\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.484 |
|
| 15298 |
\begin{align*}
y+y^{\prime }&=5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.484 |
|
| 15299 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -8 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.484 |
|
| 15300 |
\begin{align*}
x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.485 |
|