| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12601 |
\begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.092 |
|
| 12602 |
\begin{align*}
b \,{\mathrm e}^{y} x +a y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.092 |
|
| 12603 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-8 y&=4 \,{\mathrm e}^{2 x}-21 \,{\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| 12604 |
\begin{align*}
w^{\prime }&=\left (3-w\right ) \left (w+1\right ) \\
w \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.092 |
|
| 12605 |
\begin{align*}
y^{\prime \prime }-2 m y^{\prime }+m^{2} y&=\sin \left (n x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| 12606 |
\begin{align*}
y^{\prime \prime }-\frac {2 y^{\prime }}{y^{3}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.092 |
|
| 12607 |
\begin{align*}
2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (1-t \right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| 12608 |
\begin{align*}
y^{\prime \prime }+9 y&=f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| 12609 |
\begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=1-\operatorname {Heaviside}\left (t -\pi \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. |
✓ |
✓ |
✓ |
✓ |
1.093 |
|
| 12610 |
\begin{align*}
-{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.093 |
|
| 12611 |
\begin{align*}
y^{\prime \prime }&=-\frac {2 \left (x -2\right ) y^{\prime }}{x \left (x -1\right )}+\frac {2 \left (x +1\right ) y}{x^{2} \left (x -1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.093 |
|
| 12612 |
\begin{align*}
2 x^{\prime }+y^{\prime }-3 x-y&=t \\
x^{\prime }+y^{\prime }-4 x-y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.093 |
|
| 12613 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (3 x \right )-\cos \left (\frac {x}{2}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.093 |
|
| 12614 |
\begin{align*}
x^{\prime }&=2 x-y-5 t \\
y^{\prime }&=3 x+6 y-4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.093 |
|
| 12615 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.093 |
|
| 12616 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=-2 x +2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.093 |
|
| 12617 |
\begin{align*}
y^{\prime \prime }+k y&={\mathrm e}^{i \omega t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.093 |
|
| 12618 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (a \,x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.094 |
|
| 12619 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (x -1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.094 |
|
| 12620 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.094 |
|
| 12621 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.094 |
|
| 12622 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.094 |
|
| 12623 |
\begin{align*}
a y^{\prime } \left (x y^{\prime }-y\right )+x y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.095 |
|
| 12624 |
\begin{align*}
x y^{\prime }&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| 12625 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| 12626 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (4 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| 12627 |
\begin{align*}
\left (c +2 b x +a \,x^{2}+y^{2}\right )^{2} y^{\prime \prime }+d y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.095 |
|
| 12628 |
\begin{align*}
y^{\prime }&=\sin \left (x \right ) \left (2 \sec \left (x \right )^{2}-y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.096 |
|
| 12629 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (l \,x^{2}-v^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.096 |
|
| 12630 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.096 |
|
| 12631 |
\begin{align*}
y^{\prime }&=y^{2}-3 y+2 \\
y \left (0\right ) &= {\frac {3}{2}} \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
1.097 |
|
| 12632 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.097 |
|
| 12633 |
\begin{align*}
u^{\prime \prime }+\frac {2 u^{\prime }}{r}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| 12634 |
\begin{align*}
x^{\prime }&=3 x-2 y-6 \\
y^{\prime }&=4 x-y+2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| 12635 |
\begin{align*}
y^{\prime \prime }+3 y&=x^{2}+1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| 12636 |
\begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }+\frac {y}{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| 12637 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2}+3 x_{3}+6 x_{4} \\
x_{2}^{\prime }&=3 x_{1}+6 x_{2}+9 x_{3}+18 x_{4} \\
x_{3}^{\prime }&=5 x_{1}+10 x_{2}+15 x_{3}+30 x_{4} \\
x_{4}^{\prime }&=7 x_{1}+14 x_{2}+21 x_{3}+42 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| 12638 |
\begin{align*}
y^{\prime }&=200 y-2 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| 12639 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| 12640 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\left (5 x +4\right ) {\mathrm e}^{x}+{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| 12641 |
\begin{align*}
y^{\prime \prime }-y^{\prime }+y \,{\mathrm e}^{2 x}&=x \,{\mathrm e}^{2 x}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.099 |
|
| 12642 |
\begin{align*}
y^{\prime }+c y&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| 12643 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=2 x^{2}+{\mathrm e}^{x}+2 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| 12644 |
\begin{align*}
y^{\prime }+20 y&=24 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.100 |
|
| 12645 |
\begin{align*}
x^{\prime }+2 y^{\prime }&=t \\
x^{\prime }-y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.100 |
|
| 12646 |
\begin{align*}
y_{1}^{\prime }&=3 y_{1}+2 y_{2} \\
y_{2}^{\prime }&=3 y_{2}-2 y_{1} \\
y_{3}^{\prime }&=y_{3} \\
y_{4}^{\prime }&=2 y_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.100 |
|
| 12647 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=\cosh \left (x \right ) {\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.101 |
|
| 12648 |
\begin{align*}
\left (-y+a x y^{\prime }\right )^{2}+x y^{\prime \prime }&=b \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.101 |
|
| 12649 |
\begin{align*}
\left (3 x y^{3}-4 y x +y\right ) y^{\prime }+y^{2} \left (y^{2}-2\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.101 |
|
| 12650 |
\begin{align*}
y^{\prime \prime }&=-\frac {a \left (n -1\right ) \sin \left (2 a x \right ) y^{\prime }}{\cos \left (a x \right )^{2}}-\frac {n \,a^{2} \left (\left (n -1\right ) \sin \left (a x \right )^{2}+\cos \left (a x \right )^{2}\right ) y}{\cos \left (a x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.101 |
|
| 12651 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.101 |
|
| 12652 |
\begin{align*}
x^{\prime }+x+2 y^{\prime }+3 y&=0 \\
x^{\prime }-2 x+5 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.101 |
|
| 12653 |
\begin{align*}
2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.101 |
|
| 12654 |
\begin{align*}
y^{\prime \prime } \cos \left (y\right )+\sin \left (y\right ) {y^{\prime }}^{2}&=y^{\prime } \\
y \left (-1\right ) &= \frac {\pi }{6} \\
y^{\prime }\left (-1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.101 |
|
| 12655 |
\begin{align*}
m y^{\prime \prime }+b y^{\prime }+k y&=\cos \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| 12656 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+\left (3 x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| 12657 |
\begin{align*}
4 {y^{\prime }}^{2} x&=\left (3 x -1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| 12658 |
\begin{align*}
y^{\prime \prime }&=a {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| 12659 |
\begin{align*}
{y^{\prime }}^{3}-x y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.102 |
|
| 12660 |
\begin{align*}
2 y^{\prime }+2 y&=x +3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| 12661 |
\begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+32 y^{\prime \prime }-64 y^{\prime }+64 y&={\mathrm e}^{2 x} \left (\cos \left (2 x \right )-\sin \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| 12662 |
\begin{align*}
x +2 y y^{\prime }&={y^{\prime }}^{2} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| 12663 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| 12664 |
\begin{align*}
y_{1}^{\prime }&=5 y_{1}-5 y_{2}-5 y_{3} \\
y_{2}^{\prime }&=-y_{1}+4 y_{2}+2 y_{3} \\
y_{3}^{\prime }&=3 y_{1}-5 y_{2}-3 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| 12665 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x +3\right ) y^{\prime }+\left (x^{2}+x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| 12666 |
\begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| 12667 |
\begin{align*}
y^{\prime \prime }-y&=3 \,{\mathrm e}^{x} x^{2} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| 12668 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=-2 \delta \left (t -2\right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| 12669 |
\begin{align*}
x_{1}^{\prime }&=\frac {x_{1}}{2}-x_{2}-\frac {3 x_{3}}{2} \\
x_{2}^{\prime }&=\frac {3 x_{1}}{2}-2 x_{2}-\frac {3 x_{3}}{2} \\
x_{3}^{\prime }&=-2 x_{1}+2 x_{2}+x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| 12670 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }+x y^{\prime }+\frac {y}{x}&=0 \\
\end{align*}
Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| 12671 |
\begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 0 & 0\le t <4 \\ 3 & 4\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| 12672 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+x y^{\prime }-y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.105 |
|
| 12673 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=8 \sin \left (3 x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.105 |
|
| 12674 |
\begin{align*}
x^{\prime }&=5 x+2 y+5 t \\
y^{\prime }&=3 x+4 y+17 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.105 |
|
| 12675 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.106 |
|
| 12676 |
\begin{align*}
y^{\prime \prime }+8 y^{\prime }&=8 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.106 |
|
| 12677 |
\begin{align*}
3 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.107 |
|
| 12678 |
\begin{align*}
y^{\prime \prime }+2 a \,{\mathrm e}^{\lambda x} y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{\lambda x}+\lambda \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.107 |
|
| 12679 |
\begin{align*}
\left (-b \,x^{2}+a x \right ) y^{\prime \prime }+2 a y^{\prime }+2 b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.107 |
|
| 12680 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2}-3 x_{3}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=x_{1}+x_{2}+2 x_{3} \\
x_{3}^{\prime }&=x_{1}-x_{2}+4 x_{3}-{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.108 |
|
| 12681 |
\begin{align*}
x^{\prime }-x+y&=\sec \left (t \right ) \\
-2 x+y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.108 |
|
| 12682 |
\begin{align*}
x y y^{\prime \prime }&={y^{\prime }}^{3}+y^{\prime } \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
1.108 |
|
| 12683 |
\begin{align*}
x y^{\prime \prime }&=2 y^{\prime } \\
y \left (-1\right ) &= 4 \\
y^{\prime }\left (-1\right ) &= 12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.108 |
|
| 12684 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.108 |
|
| 12685 |
\begin{align*}
-\left (x^{2}+1\right ) y-4 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.108 |
|
| 12686 |
\begin{align*}
y^{\prime \prime }+16 y&=34 \,{\mathrm e}^{x}+16 \cos \left (4 x \right )-8 \sin \left (4 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.109 |
|
| 12687 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-5 x_{2}+x_{3} \\
x_{2}^{\prime }&=4 x_{1}-9 x_{2}-x_{3} \\
x_{3}^{\prime }&=3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.109 |
|
| 12688 |
\begin{align*}
\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime \prime }-a \,\lambda ^{2} {\mathrm e}^{\lambda x} y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.109 |
|
| 12689 |
\begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.109 |
|
| 12690 |
\begin{align*}
y^{\prime \prime }+a^{2} y&=\sin \left (b x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.109 |
|
| 12691 |
\begin{align*}
x \left (-1+{y^{\prime }}^{2}\right )&=2 y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.110 |
|
| 12692 |
\begin{align*}
3 x^{2} y^{\prime \prime }+x \left (3 x^{2}+1\right ) y^{\prime }-2 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.110 |
|
| 12693 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.110 |
|
| 12694 |
\begin{align*}
x^{\prime }&=4 x+3 y+5 \operatorname {Heaviside}\left (t -2\right ) \\
y^{\prime }&=x+6 y+17 \operatorname {Heaviside}\left (t -2\right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.110 |
|
| 12695 |
\begin{align*}
x^{\prime }-3 x-6 y&=27 t^{2} \\
x^{\prime }+y^{\prime }-3 y&=5 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 5 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.110 |
|
| 12696 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.110 |
|
| 12697 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2}+\csc \left (t \right ) \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+\sec \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.111 |
|
| 12698 |
\begin{align*}
x^{2} \left (x^{2}+2 x +1\right ) y^{\prime \prime }+x \left (4 x^{2}+3 x +1\right ) y^{\prime }-x \left (1-2 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.111 |
|
| 12699 |
\begin{align*}
y^{\prime }&=-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| 12700 |
\begin{align*}
x^{\prime }&=x+z \\
y^{\prime }&=x+y \\
z^{\prime }&=-2 x-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.112 |
|