| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12501 |
\begin{align*}
x_{1}^{\prime }&=-4 x_{1} \\
x_{2}^{\prime }&=2 x_{1}+5 x_{2}-9 x_{3} \\
x_{3}^{\prime }&=5 x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| 12502 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime }&=3 x^{2} \tan \left (x \right ) \\
y \left (0\right ) &= \frac {\pi }{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| 12503 |
\begin{align*}
16 y+8 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{x}-{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| 12504 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=-8 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| 12505 |
\begin{align*}
x^{\prime }&=2 \sin \left (t \right )^{2} \\
x \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| 12506 |
\begin{align*}
x^{3} x^{\prime \prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.030 |
|
| 12507 |
\begin{align*}
x_{1}^{\prime }&=\frac {4 x_{1}}{3}+\frac {4 x_{2}}{3}-\frac {11 x_{3}}{3} \\
x_{2}^{\prime }&=-\frac {16 x_{1}}{3}-\frac {x_{2}}{3}+\frac {14 x_{3}}{3} \\
x_{3}^{\prime }&=3 x_{1}-2 x_{2}-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| 12508 |
\begin{align*}
x+y^{\prime }&=\sin \left (t \right )+\cos \left (t \right ) \\
x^{\prime }+y&=\cos \left (t \right )-\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| 12509 |
\begin{align*}
5 {y^{\prime }}^{2}+6 y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.030 |
|
| 12510 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.031 |
|
| 12511 |
\begin{align*}
f \left (x \right )^{2} y^{\prime \prime }&=-24 f \left (x \right )^{4}+\left (3 f \left (x \right )^{3}-f \left (x \right )^{2} y+3 f \left (x \right ) f^{\prime }\left (x \right )\right ) y^{\prime } \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.031 |
|
| 12512 |
\begin{align*}
\left (x +1\right ) y^{\prime \prime }-3 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.031 |
|
| 12513 |
\begin{align*}
y^{\prime \prime }-4 y&=\delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| 12514 |
\begin{align*}
y^{\prime \prime }+\alpha ^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| 12515 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| 12516 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}+1 \\
x_{2}^{\prime }&=x_{1}+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| 12517 |
\begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 12518 |
\begin{align*}
x^{\prime }+x+2 y^{\prime }+7 y&={\mathrm e}^{t}+2 \\
-2 x+y^{\prime }+3 y&={\mathrm e}^{t}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 12519 |
\begin{align*}
4 x^{2} y^{\prime \prime }+\left (1-2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 12520 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=18 \,{\mathrm e}^{-t} \sin \left (3 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 12521 |
\begin{align*}
y^{\prime }&=t \sin \left (t^{2}\right ) \\
y \left (\sqrt {\pi }\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 12522 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 12523 |
\begin{align*}
9 y+6 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{-3 x}}{x^{3}} \\
y \left (1\right ) &= 4 \,{\mathrm e}^{-3} \\
y^{\prime }\left (1\right ) &= -2 \,{\mathrm e}^{-3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 12524 |
\begin{align*}
y^{\prime \prime }+4 y&=t \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.034 |
|
| 12525 |
\begin{align*}
y^{\prime \prime }&=4 \sin \left (x \right )-4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.034 |
|
| 12526 |
\begin{align*}
y^{\prime } x +a y^{2}-y+b \,x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.034 |
|
| 12527 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+1&=3 \sin \left (2 x \right )+\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.034 |
|
| 12528 |
\begin{align*}
y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.034 |
|
| 12529 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.035 |
|
| 12530 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.035 |
|
| 12531 |
\begin{align*}
y^{\prime }-a y&={\mathrm e}^{a x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.035 |
|
| 12532 |
\begin{align*}
x^{2} y^{\prime \prime }+x \cos \left (x \right ) y^{\prime }-2 \,{\mathrm e}^{x} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| 12533 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| 12534 |
\begin{align*}
8 x {y^{\prime }}^{3}&=y \left (12 {y^{\prime }}^{2}-9\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.036 |
|
| 12535 |
\begin{align*}
x^{\prime \prime }+4 x^{3}&=0 \\
x \left (0\right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.036 |
|
| 12536 |
\begin{align*}
y^{\prime \prime } x -3 y^{\prime }-5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| 12537 |
\begin{align*}
x^{2} {y^{\prime }}^{2}+3 y y^{\prime } x +3 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.037 |
|
| 12538 |
\begin{align*}
y^{\prime \prime }+\frac {8 y^{\prime }}{3 x}-\left (\frac {2}{3 x^{2}}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.038 |
|
| 12539 |
\begin{align*}
y^{\prime }-3 y&=3+\delta \left (-2+t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.038 |
|
| 12540 |
\begin{align*}
10 x_{1}^{\prime }&=-x_{1}+x_{3} \\
10 x_{2}^{\prime }&=x_{1}-x_{2} \\
10 x_{3}^{\prime }&=x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| 12541 |
\begin{align*}
y_{1}^{\prime }&=-3 y_{1}+y_{2}-3 y_{3} \\
y_{2}^{\prime }&=4 y_{1}-y_{2}+2 y_{3} \\
y_{3}^{\prime }&=4 y_{1}-2 y_{2}+3 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| 12542 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1} \\
x_{2}^{\prime }&=x_{1}+3 x_{2} \\
x_{3}^{\prime }&=3 x_{3} \\
x_{4}^{\prime }&=2 x_{3}+3 x_{4} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
x_{4} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| 12543 |
\begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| 12544 |
\begin{align*}
y^{\prime }&=y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| 12545 |
\begin{align*}
x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (1+y\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.039 |
|
| 12546 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{x} \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| 12547 |
\begin{align*}
y^{\prime }-1&={\mathrm e}^{x +2 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| 12548 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| 12549 |
\begin{align*}
t y^{\prime \prime }-y^{\prime }&=3 t^{2}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| 12550 |
\begin{align*}
y^{\prime }&=2 y x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| 12551 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+3 x_{2} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{3}^{\prime }&=x_{1}+x_{3}+x_{4} \\
x_{4}^{\prime }&=x_{2}+x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| 12552 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=4 x -2+2 \,{\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| 12553 |
\begin{align*}
x^{2} \left ({y^{\prime }}^{6}+3 y^{4}+3 y^{2}+1\right )&=a^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.040 |
|
| 12554 |
\begin{align*}
2 y+y^{\prime }&=3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| 12555 |
\begin{align*}
t y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| 12556 |
\begin{align*}
x^{\prime }&=-10 x+10 y \\
y^{\prime }&=28 x-y \\
z^{\prime }&=-\frac {8 z}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| 12557 |
\begin{align*}
y^{\prime }+2 y&=4 \delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| 12558 |
\begin{align*}
y^{\prime \prime } x +4 y^{\prime }+\frac {12 y}{\left (2+x \right )^{2}}&=0 \\
\end{align*} Series expansion around \(x=-2\). |
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| 12559 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-1\right ) y&=-3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.040 |
|
| 12560 |
\begin{align*}
x^{\prime }+3 x-y^{\prime }-y&=0 \\
2 x^{\prime }-9 x+y^{\prime }+4 y&=15 \,{\mathrm e}^{-3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| 12561 |
\begin{align*}
y^{\prime }&=1-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| 12562 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.041 |
|
| 12563 |
\begin{align*}
\left (x^{2}-6 x \right ) y^{\prime \prime }+4 \left (x -3\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.041 |
|
| 12564 |
\begin{align*}
y^{\prime } t -{y^{\prime }}^{3}&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.041 |
|
| 12565 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}+x_{2}+x_{3}-2 x_{4} \\
x_{2}^{\prime }&=7 x_{1}-4 x_{2}-6 x_{3}+11 x_{4} \\
x_{3}^{\prime }&=5 x_{1}-x_{2}+x_{3}+3 x_{4} \\
x_{4}^{\prime }&=6 x_{1}-2 x_{2}-2 x_{3}+6 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.042 |
|
| 12566 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (1-x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.042 |
|
| 12567 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.042 |
|
| 12568 |
\begin{align*}
\left (1+{y^{\prime }}^{2}\right ) \left (\arctan \left (y^{\prime }\right )+a x \right )+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.042 |
|
| 12569 |
\begin{align*}
y^{\prime \prime }-9 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.042 |
|
| 12570 |
\begin{align*}
x_{1}^{\prime }&=1-x_{2}+x_{3} \\
x_{2}^{\prime }&=2 x_{2}+t \\
x_{3}^{\prime }&=-2 x_{1}-x_{2}+3 x_{3}+{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.042 |
|
| 12571 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.042 |
|
| 12572 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+34 y&={\mathrm e}^{3 t} \tan \left (5 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| 12573 |
\begin{align*}
y^{\prime \prime \prime }+4 y^{\prime }&=\tan \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| 12574 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| 12575 |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=x \,{\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.044 |
|
| 12576 |
\begin{align*}
4 \left (x -4\right )^{2} y^{\prime \prime }+\left (x -4\right ) \left (x -8\right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=4\). |
✓ |
✓ |
✓ |
✓ |
1.045 |
|
| 12577 |
\begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.045 |
|
| 12578 |
\begin{align*}
y^{\prime \prime }+b y^{\prime }+c y&=f \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.045 |
|
| 12579 |
\begin{align*}
x^{\prime \prime }&=x^{3}-x \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.046 |
|
| 12580 |
\begin{align*}
t^{2} y^{\prime \prime }+5 y^{\prime } t -5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.047 |
|
| 12581 |
\begin{align*}
y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.047 |
|
| 12582 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.047 |
|
| 12583 |
\begin{align*}
4 x^{2} y^{\prime \prime }+8 x \left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.047 |
|
| 12584 |
\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*} |
✓ |
✓ |
✓ |
✓ |
1.047 |
|
| 12585 |
\begin{align*}
y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+\csc \left (x \right )^{2} y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.047 |
|
| 12586 |
\begin{align*}
t^{2} y^{\prime \prime }+2 y^{\prime } t -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.047 |
|
| 12587 |
\begin{align*}
3 \left (x +3\right ) x^{2} y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.048 |
|
| 12588 |
\begin{align*}
\left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }&=3 y^{\prime } {y^{\prime \prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.048 |
|
| 12589 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (x^{2}+3\right ) y^{\prime }+6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.048 |
|
| 12590 |
\begin{align*}
y^{\prime }&=-\lambda \,{\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\mu x} y-a \,{\mathrm e}^{\left (\mu -\lambda \right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.048 |
|
| 12591 |
\begin{align*}
x^{\prime }-x&=\operatorname {Heaviside}\left (t -a \right ) \\
x \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.048 |
|
| 12592 |
\begin{align*}
y^{\prime }&=2 y \\
\end{align*} |
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✓ |
✓ |
✓ |
1.049 |
|
| 12593 |
\begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=3 x_{1}+x_{2}-2 x_{3} \\
x_{3}^{\prime }&=2 x_{1}+2 x_{2}+x_{3} \\
\end{align*} |
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✓ |
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✓ |
1.049 |
|
| 12594 |
\begin{align*}
\left (2-3 y\right )^{2} {y^{\prime }}^{2}&=4-4 y \\
\end{align*} |
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✓ |
✓ |
✓ |
1.049 |
|
| 12595 |
\begin{align*}
y^{\prime \prime }+y&=-2 \delta \left (t -\frac {\pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
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✓ |
✓ |
✓ |
1.049 |
|
| 12596 |
\begin{align*}
y^{\prime }-3 y&=2 \,{\mathrm e}^{t} \\
y \left (1\right ) &= {\mathrm e}^{3}-{\mathrm e} \\
\end{align*} Using Laplace transform method. |
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✓ |
1.049 |
|
| 12597 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=2\). |
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✓ |
1.050 |
|
| 12598 |
\begin{align*}
y^{\prime \prime } x +x^{5} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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✓ |
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1.050 |
|
| 12599 |
\begin{align*}
y^{\prime }&=\left (-1+y\right )^{2}-\frac {1}{100} \\
y \left (0\right ) &= 1 \\
\end{align*} |
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✓ |
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✓ |
1.050 |
|
| 12600 |
\begin{align*}
y^{\prime \prime } x +\left (x -6\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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✗ |
1.050 |
|