| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12501 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.073 |
|
| 12502 |
\begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.073 |
|
| 12503 |
\begin{align*}
x_{1}^{\prime }&=x_{2}+f_{1} \left (t \right ) \\
x_{2}^{\prime }&=-x_{1}+f_{2} \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.074 |
|
| 12504 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (-2 x^{2}+x \right ) y^{\prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.074 |
|
| 12505 |
\begin{align*}
4 y+y^{\prime \prime }&=\sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.074 |
|
| 12506 |
\begin{align*}
y^{\prime \prime }-x y^{\prime }+\left (3 x -2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.074 |
|
| 12507 |
\begin{align*}
x^{\prime }+x-5 y&=0 \\
y^{\prime }+4 x+5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.074 |
|
| 12508 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+c y&={\mathrm e}^{i \omega t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.074 |
|
| 12509 |
\begin{align*}
{y^{\prime }}^{2} x +\left (a +x -y\right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.075 |
|
| 12510 |
\begin{align*}
4 x y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.075 |
|
| 12511 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.075 |
|
| 12512 |
\begin{align*}
\left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.075 |
|
| 12513 |
\begin{align*}
y^{\prime \prime }-y^{\prime }+y \,{\mathrm e}^{2 x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.075 |
|
| 12514 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{3} \\
x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.075 |
|
| 12515 |
\begin{align*}
y^{\prime \prime }&=2 t +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.075 |
|
| 12516 |
\begin{align*}
y^{\prime }+y&=2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| 12517 |
\begin{align*}
t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
1.076 |
|
| 12518 |
\begin{align*}
2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| 12519 |
\begin{align*}
4 x^{2} y^{\prime \prime }+3 x y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| 12520 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }&=2 \,{\mathrm e}^{2 x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| 12521 |
\begin{align*}
b x y+a y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.076 |
|
| 12522 |
\begin{align*}
n \left (n +2\right ) y-3 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.076 |
|
| 12523 |
\begin{align*}
3 y-\left (x +3\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.076 |
|
| 12524 |
\begin{align*}
y^{\prime }+y \sqrt {x^{2}+1}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| 12525 |
\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 \(x=0\). |
✗ |
✗ |
✓ |
✗ |
1.076 |
|
| 12526 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=\frac {1}{\left ({\mathrm e}^{x}-1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.076 |
|
| 12527 |
\begin{align*}
x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x&=F \cos \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.077 |
|
| 12528 |
\begin{align*}
y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.077 |
|
| 12529 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.077 |
|
| 12530 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+5 \left (x +1\right ) y^{\prime }+\left (x^{2}-x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.077 |
|
| 12531 |
\begin{align*}
y^{\prime \prime }&=-\frac {a y}{\left (x^{2}-1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.077 |
|
| 12532 |
\begin{align*}
y^{\prime \prime \prime \prime }-11 y^{\prime \prime }+18 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.077 |
|
| 12533 |
\begin{align*}
x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.078 |
|
| 12534 |
\begin{align*}
x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.078 |
|
| 12535 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.078 |
|
| 12536 |
\begin{align*}
4 x y^{\prime \prime }+2 y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.078 |
|
| 12537 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-{\mathrm e}^{t} \\
x_{2}^{\prime }&=2 x_{1}-3 x_{2}+2 x_{3}+6 \,{\mathrm e}^{-t} \\
x_{3}^{\prime }&=x_{1}-2 x_{2}+2 x_{3}+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.079 |
|
| 12538 |
\begin{align*}
x y y^{\prime \prime }&=-y y^{\prime }+{y^{\prime }}^{2} x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.079 |
|
| 12539 |
\begin{align*}
x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.079 |
|
| 12540 |
\begin{align*}
x^{2} y^{\prime \prime }+7 x y^{\prime }-7 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.079 |
|
| 12541 |
\begin{align*}
\left (x +2\right ) y^{\prime \prime }-\left (5+2 x \right ) y^{\prime }+2 y&={\mathrm e}^{x} \left (x +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.079 |
|
| 12542 |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right ) \left (x y^{\prime }-y\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.080 |
|
| 12543 |
\begin{align*}
y^{\prime \prime }-12 y^{\prime }+37 y&={\mathrm e}^{6 t} \sec \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| 12544 |
\begin{align*}
y^{\prime \prime }&=\frac {a}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| 12545 |
\begin{align*}
x^{\prime }&=y+z \\
y^{\prime }&=x+z \\
z^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| 12546 |
\begin{align*}
x^{2} \left (1+3 x \right ) y^{\prime \prime }+x \left (x^{2}+12 x +2\right ) y^{\prime }+2 x \left (x +3\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.081 |
|
| 12547 |
\begin{align*}
x^{\prime }&=2 x-y+\cos \left (t \right ) \\
y^{\prime }&=5 x-2 y+\sin \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.081 |
|
| 12548 |
\begin{align*}
x^{\prime \prime }+2 h x^{\prime }+k^{2} x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.081 |
|
| 12549 |
\begin{align*}
x_{1}^{\prime }&=x_{2}-x_{3}+x_{4} \\
x_{2}^{\prime }&=-x_{2}+x_{4} \\
x_{3}^{\prime }&=x_{3}-x_{4} \\
x_{4}^{\prime }&=2 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.081 |
|
| 12550 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.081 |
|
| 12551 |
\begin{align*}
{y^{\prime }}^{2} x +\left (a +b x -y\right ) y^{\prime }-b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.082 |
|
| 12552 |
\begin{align*}
y^{\prime }+{y^{\prime }}^{3}+2 x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.082 |
|
| 12553 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 4 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.082 |
|
| 12554 |
\begin{align*}
2 x^{\prime }+y^{\prime }+x+5 y&=4 t \\
x^{\prime }+y^{\prime }+2 x+2 y&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.082 |
|
| 12555 |
\begin{align*}
y^{2} {y^{\prime }}^{2}-a^{2}+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.082 |
|
| 12556 |
\begin{align*}
y_{1}^{\prime }&=2 y_{1}-5 y_{2}+2 \cos \left (t \right ) \\
y_{2}^{\prime }&=y_{1}-2 y_{2}+\cos \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.082 |
|
| 12557 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.083 |
|
| 12558 |
\begin{align*}
10 x^{2} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+x \left (66 x^{2}+13 x +13\right ) y^{\prime }-\left (10 x^{2}+4 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.083 |
|
| 12559 |
\begin{align*}
2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.083 |
|
| 12560 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=2 \,{\mathrm e}^{x}-10 \sin \left (x \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.083 |
|
| 12561 |
\begin{align*}
y^{3} y^{\prime \prime }&=-1 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
1.083 |
|
| 12562 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| 12563 |
\begin{align*}
\left (x^{2}+x -6\right ) y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| 12564 |
\begin{align*}
x V^{\prime }&=x^{2}+1 \\
V \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| 12565 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{\frac {x}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| 12566 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| 12567 |
\begin{align*}
\theta ^{\prime \prime }+4 \theta &=15 \cos \left (3 t \right ) \\
\theta \left (0\right ) &= 0 \\
\theta ^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| 12568 |
\begin{align*}
y^{\prime \prime }-\frac {y}{x}&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.084 |
|
| 12569 |
\begin{align*}
t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 12570 |
\begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 12571 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}-x_{3} \\
x_{2}^{\prime }&=3 x_{1}-4 x_{2}-3 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 12572 |
\begin{align*}
2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 12573 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=2 x \\
y \left (0\right ) &= 0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 12574 |
\begin{align*}
t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 12575 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }&=3 x \,{\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 12576 |
\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*} |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| 12577 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+10 x y^{\prime }+20 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| 12578 |
\begin{align*}
y^{\prime \prime }-\left (a^{2} x^{2}+a \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.086 |
|
| 12579 |
\begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=\frac {x}{2}-\frac {3 y}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| 12580 |
\begin{align*}
{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.086 |
|
| 12581 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+2 x_{2}-x_{3} \\
x_{2}^{\prime }&=-2 x_{1}+3 x_{2}-2 x_{3} \\
x_{3}^{\prime }&=-2 x_{1}+4 x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| 12582 |
\begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }-a \,t^{2} y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| 12583 |
\begin{align*}
x^{2} y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+5 y \,{\mathrm e}^{2 x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.087 |
|
| 12584 |
\begin{align*}
4 x^{3} y^{3}+\frac {1}{x}+\left (3 y^{2} x^{4}-\frac {1}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.087 |
|
| 12585 |
\begin{align*}
x^{\prime }+x-z&=0 \\
x+y^{\prime }-y&=0 \\
z^{\prime }+x+2 y-3 z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.087 |
|
| 12586 |
\begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+\left (x +1\right ) y&=\left (x -1\right )^{3} {\mathrm e}^{x} \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -6 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.088 |
|
| 12587 |
\begin{align*}
y^{\prime \prime \prime }-8 y&={\mathrm e}^{i x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.088 |
|
| 12588 |
\begin{align*}
y^{\prime }&=\frac {x +y+F \left (-\frac {-y+x \ln \left (x \right )}{x}\right ) x^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.088 |
|
| 12589 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }&={\mathrm e}^{4 x} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.088 |
|
| 12590 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.089 |
|
| 12591 |
\begin{align*}
4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y&=x^{{7}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.089 |
|
| 12592 |
\begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-v^{2}\right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
1.089 |
|
| 12593 |
\begin{align*}
y^{\prime }&=y^{2}-y \tan \left (x \right )+a \left (1-a \right ) \cot \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.089 |
|
| 12594 |
\begin{align*}
\frac {\left (x^{2}-x \right ) y^{\prime \prime }}{x}+\frac {\left (1+3 x \right ) y^{\prime }}{x}+\frac {y}{x}&=3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.089 |
|
| 12595 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x \left ({\mathrm e}^{-x}-\cos \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| 12596 |
\begin{align*}
x_{1}^{\prime }&=-4 x_{1}+x_{2} \\
x_{2}^{\prime }&=x_{1}-5 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{2}-4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.090 |
|
| 12597 |
\begin{align*}
x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime }&=x^{2} \\
y \left (5\right ) &= 0 \\
y^{\prime }\left (5\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.091 |
|
| 12598 |
\begin{align*}
x y^{\prime \prime }&=-y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.091 |
|
| 12599 |
\begin{align*}
x^{\prime }&=a x+b y \\
y^{\prime }&=c x+d y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.091 |
|
| 12600 |
\begin{align*}
y^{\prime \prime }&=6 \sin \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.091 |
|