| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 11401 |
\begin{align*}
{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.900 |
|
| 11402 |
\begin{align*}
y^{\prime \prime }-y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| 11403 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (2 x -1\right ) y^{\prime }+x \left (x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| 11404 |
\begin{align*}
y^{2} {y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.901 |
|
| 11405 |
\begin{align*}
x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| 11406 |
\begin{align*}
z^{\prime \prime }-4 z^{\prime }+13 z&=0 \\
z \left (0\right ) &= 7 \\
z^{\prime }\left (0\right ) &= 42 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| 11407 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.901 |
|
| 11408 |
\begin{align*}
y^{\prime \prime }+\cos \left (x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| 11409 |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=\tan \left (t \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| 11410 |
\begin{align*}
y^{\prime \prime }-2 t y^{\prime }+t^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.901 |
|
| 11411 |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=6 x_{1} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (1\right ) &= 1 \\
x_{2} \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| 11412 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{3} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| 11413 |
\begin{align*}
x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| 11414 |
\begin{align*}
y^{\prime \prime }+a^{2} y&=2 \cos \left (m x \right )+3 \sin \left (m x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| 11415 |
\begin{align*}
x y^{\prime \prime }-\left (x +4\right ) y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.902 |
|
| 11416 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=x_{1}+2 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+10 x_{2}+2 x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -1 \\
x_{2} \left (0\right ) &= -4 \\
x_{3} \left (0\right ) &= 13 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| 11417 |
\begin{align*}
y^{\prime }&=5-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| 11418 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }-2 y&=-6 \,{\mathrm e}^{\pi -t} \\
y \left (\pi \right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| 11419 |
\begin{align*}
x y^{\prime \prime }&=2 y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| 11420 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{x}+{\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| 11421 |
\begin{align*}
x^{\prime }&=2 x-\frac {5 y}{2} \\
y^{\prime }&=\frac {9 x}{5}-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| 11422 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| 11423 |
\begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| 11424 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{3} \\
x_{2}^{\prime }&=-2 x_{1}+x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| 11425 |
\begin{align*}
x^{\prime \prime }&=-20 \\
x \left (0\right ) &= 5 \\
x^{\prime }\left (0\right ) &= -15 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.903 |
|
| 11426 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.903 |
|
| 11427 |
\begin{align*}
y^{\prime \prime \prime \prime }-9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= -3 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.903 |
|
| 11428 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.903 |
|
| 11429 |
\begin{align*}
{y^{\prime }}^{2} x -y y^{\prime }+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.904 |
|
| 11430 |
\begin{align*}
y^{\prime \prime }&=\frac {2 y}{\sin \left (x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.904 |
|
| 11431 |
\begin{align*}
y_{1}^{\prime }&=-4 y_{1}-y_{2}+2 \,{\mathrm e}^{t} \\
y_{2}^{\prime }&=y_{1}-2 y_{2}+\sin \left (2 t \right ) \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.904 |
|
| 11432 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\frac {3 y^{\prime }}{x +2}+\frac {\left (1-x \right )^{2} y}{x +3}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.904 |
|
| 11433 |
\begin{align*}
t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.904 |
|
| 11434 |
\begin{align*}
y^{\prime }&=2 x^{2} \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.904 |
|
| 11435 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2}-x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}-x_{3}+t \\
x_{3}^{\prime }&=x_{1}-x_{2}+x_{3}+2 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 2 \\
x_{3} \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.904 |
|
| 11436 |
\begin{align*}
x^{\prime \prime }&=50 \\
x \left (0\right ) &= 20 \\
x^{\prime }\left (0\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| 11437 |
\begin{align*}
\sin \left (t \right ) y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+\frac {y}{t}&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.905 |
|
| 11438 |
\begin{align*}
2 x^{2} \left (-3 x +1\right ) y^{\prime \prime }+5 x y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| 11439 |
\begin{align*}
\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| 11440 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| 11441 |
\begin{align*}
x^{\prime }&=x+2 y+t -1 \\
y^{\prime }&=3 x+2 y-5 t -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| 11442 |
\begin{align*}
x^{\prime }&=x+y-z \\
y^{\prime }&=2 y \\
z^{\prime }&=y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| 11443 |
\begin{align*}
y^{\prime \prime }-9 y&=54 t \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| 11444 |
\begin{align*}
x^{\prime \prime \prime }+4 x^{\prime }&=\sec \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| 11445 |
\begin{align*}
4 i^{\prime \prime }+i&=t^{2}+2 \cos \left (4 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| 11446 |
\begin{align*}
x^{\prime }&=8 y \\
y^{\prime }&=-2 z \\
z^{\prime }&=2 x+8 y-2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| 11447 |
\begin{align*}
y^{\prime \prime }+y&=x \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.906 |
|
| 11448 |
\begin{align*}
y^{\prime \prime }-2 x y^{\prime }+2 y p&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.906 |
|
| 11449 |
\begin{align*}
y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.906 |
|
| 11450 |
\begin{align*}
\left (-3 x^{3}+3 x^{2}\right ) y^{\prime \prime }-\left (5 x^{2}+4 x \right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.906 |
|
| 11451 |
\begin{align*}
x_{1}^{\prime }&=\frac {3 x_{1}}{4}+\frac {29 x_{2}}{4}-\frac {11 x_{3}}{2} \\
x_{2}^{\prime }&=-\frac {3 x_{1}}{4}+\frac {3 x_{2}}{4}-\frac {5 x_{3}}{2} \\
x_{3}^{\prime }&=\frac {5 x_{1}}{4}+\frac {11 x_{2}}{4}-\frac {5 x_{3}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.906 |
|
| 11452 |
\begin{align*}
{y^{\prime }}^{2}-\frac {a^{2}}{x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.907 |
|
| 11453 |
\begin{align*}
x y y^{\prime \prime }+{y^{\prime }}^{2} x -y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.907 |
|
| 11454 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+\left (x^{2}-4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.907 |
|
| 11455 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.907 |
|
| 11456 |
\begin{align*}
{y^{\prime }}^{2}+x&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.907 |
|
| 11457 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+13 y&=4 \,{\mathrm e}^{3 x} \sec \left (2 x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| 11458 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }+10 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| 11459 |
\begin{align*}
y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| 11460 |
\begin{align*}
x^{4} y^{\prime \prime }-x \left (x^{2}+2 y\right ) y^{\prime }+4 y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.908 |
|
| 11461 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+4 x&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| 11462 |
\begin{align*}
x^{\prime }&=-4 x-10 y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| 11463 |
\begin{align*}
y^{\prime }+4 y&=8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| 11464 |
\begin{align*}
x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=x^{2}-x -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.909 |
|
| 11465 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{3}+\cos \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.909 |
|
| 11466 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.909 |
|
| 11467 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=12 t \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.909 |
|
| 11468 |
\begin{align*}
y+\left (y^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| 11469 |
\begin{align*}
y^{\prime \prime }-x y^{\prime }-y x -x^{3}+2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.910 |
|
| 11470 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{3} \cos \left (x \right )+\sin \left (x \right )^{2} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.910 |
|
| 11471 |
\begin{align*}
2 x^{2} y^{\prime \prime }+x y^{\prime }+\left (x -5\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.910 |
|
| 11472 |
\begin{align*}
x^{\prime \prime }+\frac {x^{\prime }}{10}+x&=3 \cos \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| 11473 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| 11474 |
\begin{align*}
x^{\prime \prime }+3 x^{\prime }&={\mathrm e}^{-3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| 11475 |
\begin{align*}
2 x y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| 11476 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 11477 |
\begin{align*}
2 y \left (x \,{\mathrm e}^{x^{2}}+\sin \left (x \right ) \cos \left (x \right ) y\right )+\left (2 \,{\mathrm e}^{x^{2}}+3 y \sin \left (x \right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.911 |
|
| 11478 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\cosh \left (x \right ) \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.911 |
|
| 11479 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 11480 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+4 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 11481 |
\begin{align*}
x^{\prime }+y^{\prime }-x&=-2 t \\
x^{\prime }+y^{\prime }-3 x-y&=t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.911 |
|
| 11482 |
\begin{align*}
y^{\prime \prime }-2 x y^{\prime }-4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 11483 |
\begin{align*}
x^{\prime }&=x-4 y+2 t \\
y^{\prime }&=x-3 y-3 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 11484 |
\begin{align*}
y^{\prime \prime }+4 y&=3 \sin \left (2 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 11485 |
\begin{align*}
y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 11486 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-9 x+6 y+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 11487 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.911 |
|
| 11488 |
\begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (t -2\right )+\operatorname {Heaviside}\left (-3+t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 11489 |
\begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\left (5+x \right ) y^{\prime }-4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 11490 |
\begin{align*}
\left (8-x \right ) x^{2} y^{\prime \prime }+6 x y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.912 |
|
| 11491 |
\begin{align*}
y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.912 |
|
| 11492 |
\begin{align*}
-y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.912 |
|
| 11493 |
\begin{align*}
x^{\prime }&=-3 x+48 y-28 z \\
y^{\prime }&=-4 x+40 y-22 z \\
z^{\prime }&=-6 x+57 y-31 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.912 |
|
| 11494 |
\begin{align*}
x^{\prime \prime }+4 x&=\delta \left (t \right )+\delta \left (t -\pi \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| 11495 |
\begin{align*}
y^{\prime \prime }-y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| 11496 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}+x_{2}-2 x_{3} \\
x_{2}^{\prime }&=4 x_{1}+x_{2} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| 11497 |
\begin{align*}
x^{3} y^{\prime \prime }-a \left (x y^{\prime }-y\right )^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.913 |
|
| 11498 |
\(\left [\begin {array}{ccc} -2 & 5 & 5 \\ -1 & 4 & 5 \\ 3 & -3 & 2 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.913 |
|
| 11499 |
\begin{align*}
x^{\prime \prime }+x&=t \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| 11500 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.913 |
|