| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12601 |
\begin{align*}
\left (1-x \right ) x^{2} y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| 12602 |
\begin{align*}
x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| 12603 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{-2 x} \sin \left ({\mathrm e}^{-x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| 12604 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| 12605 |
\begin{align*}
\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda -x \right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.734 |
|
| 12606 |
\begin{align*}
3 x^{\prime }+2 y^{\prime }-x+y&=-1+t \\
x^{\prime }+y^{\prime }-x&=t +2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| 12607 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=-8 x_{1}-5 x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| 12608 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \sec \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| 12609 |
\begin{align*}
{y^{\prime }}^{2}+y^{2} y^{\prime } x +y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.734 |
|
| 12610 |
\begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{3 x} \left (1+\sin \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| 12611 |
\begin{align*}
4 y+y^{\prime \prime }&=2 \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| 12612 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.736 |
|
| 12613 |
\begin{align*}
y^{\prime \prime }+t y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.736 |
|
| 12614 |
\begin{align*}
-a \left (2+a \right ) y+4 a x y^{\prime }+4 \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.736 |
|
| 12615 |
\begin{align*}
x^{\prime }+3 x&=\delta \left (-1+t \right )+\operatorname {Heaviside}\left (t -4\right ) \\
x \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| 12616 |
\begin{align*}
2 t^{2} y^{\prime \prime }-3 t y^{\prime }-3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| 12617 |
\begin{align*}
t^{2} \ln \left (t \right ) y^{\prime \prime \prime }-t y^{\prime \prime }+y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.736 |
|
| 12618 | \begin{align*}
\left (x^{2}-1\right ) y^{\prime }&=1 \\
y \left (2\right ) &= 0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.736 |
|
| 12619 |
\begin{align*}
2 n y-2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| 12620 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| 12621 |
\begin{align*}
x^{2} \left (8+x \right ) y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| 12622 |
\begin{align*}
t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| 12623 |
\begin{align*}
2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| 12624 |
\begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y&=t^{2} \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| 12625 |
\begin{align*}
y^{\prime \prime }+9 y&=\csc \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| 12626 |
\begin{align*}
8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.737 |
|
| 12627 |
\begin{align*}
y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| 12628 |
\begin{align*}
-y+y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.737 |
|
| 12629 |
\begin{align*}
4 y x -\left (x^{2}+7\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.737 |
|
| 12630 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2}+2 \,{\mathrm e}^{-t} \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+3 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| 12631 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (x^{n -1} a n +b m \,x^{m -1}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.737 |
|
| 12632 |
\begin{align*}
{y^{\prime }}^{2}-y^{\prime } y+{\mathrm e}^{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.737 |
|
| 12633 |
\begin{align*}
5 {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.738 |
|
| 12634 |
\begin{align*}
y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.738 |
|
| 12635 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=\cos \left (x \right ) x^{3}+\sin \left (x \right )^{2} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.738 |
|
| 12636 |
\begin{align*}
y^{\prime \prime }+y&=3 x^{2}-4 \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.738 |
|
| 12637 | \begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.738 |
|
| 12638 |
\begin{align*}
x^{\prime }&=3 x+y-z \\
y^{\prime }&=x+3 y-z \\
z^{\prime }&=3 x+3 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.738 |
|
| 12639 |
\begin{align*}
s^{\prime \prime }&=5 t^{2}-7 t \\
s \left (0\right ) &= 0 \\
s \left (1\right ) &= {\frac {1}{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.738 |
|
| 12640 |
\begin{align*}
y^{\prime }&=y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.738 |
|
| 12641 |
\begin{align*}
x^{4} {y^{\prime }}^{2}+y^{2} y^{\prime } x -y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.739 |
|
| 12642 |
\begin{align*}
y^{\prime \prime }-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.739 |
|
| 12643 |
\begin{align*}
y_{1}^{\prime }&=y_{2}+y_{4} \\
y_{2}^{\prime }&=y_{1}-y_{3} \\
y_{3}^{\prime }&=y_{4} \\
y_{4}^{\prime }&=y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.739 |
|
| 12644 |
\begin{align*}
y^{\prime }+4 y&=y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.739 |
|
| 12645 |
\begin{align*}
y^{\prime }&=y^{2}-y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.739 |
|
| 12646 |
\begin{align*}
y^{\prime }&=2 y+\delta \left (t -3\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.739 |
|
| 12647 |
\begin{align*}
y^{\prime }&=y^{2}-y-6 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.739 |
|
| 12648 |
\begin{align*}
y^{\prime \prime \prime \prime }+y&=g \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| 12649 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| 12650 |
\begin{align*}
x^{\prime }&=x+2 y+z \\
y^{\prime }&=6 x-y \\
z^{\prime }&=-x-2 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| 12651 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x +b \left (a \,x^{n}-1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.740 |
|
| 12652 |
\begin{align*}
x^{\prime }&=y+z-x \\
y^{\prime }&=x-y+z \\
z^{\prime }&=x+y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| 12653 |
\begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| 12654 |
\begin{align*}
3 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| 12655 |
\begin{align*}
y^{\prime }-9 y&=90 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| 12656 | \begin{align*}
x^{\prime \prime }&=-20 \\
x \left (0\right ) &= 5 \\
x^{\prime }\left (0\right ) &= -15 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.741 |
|
| 12657 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.741 |
|
| 12658 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \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. |
✓ |
✓ |
✓ |
✓ |
0.741 |
|
| 12659 |
\begin{align*}
y^{\prime \prime } x +\left (2 a \,x^{3}-1\right ) y^{\prime }+\left (a^{2} x^{3}+a \right ) x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.741 |
|
| 12660 |
\begin{align*}
f \left (x \right ) y+\left (2+f \left (x \right ) x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.741 |
|
| 12661 |
\begin{align*}
y^{\prime \prime }&=\frac {\left (2 x^{2}-1\right ) y^{\prime }}{x^{3}}-\frac {y}{x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.741 |
|
| 12662 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}-\lambda \right ) y^{\prime }+b \,{\mathrm e}^{2 \lambda x} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.741 |
|
| 12663 |
\begin{align*}
{y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x +x^{2}&=0 \\
y \left (0\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.741 |
|
| 12664 |
\begin{align*}
x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.742 |
|
| 12665 |
\begin{align*}
16 y-7 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.742 |
|
| 12666 |
\begin{align*}
x^{\prime }&=-x \left (1-x\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| 12667 |
\begin{align*}
x^{\prime }-x+y&=\sec \left (t \right ) \\
-2 x+y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| 12668 |
\begin{align*}
-a y-\left (a -\left (2-a \right ) x \right ) y^{\prime }+x \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.743 |
|
| 12669 |
\begin{align*}
x^{2} \left (x -y\right ) y^{\prime \prime }&=a \left (-y+y^{\prime } x \right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.743 |
|
| 12670 |
\begin{align*}
y^{\prime }&=2 \sec \left (x \right ) \tan \left (x \right )-\sin \left (x \right ) y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.743 |
|
| 12671 |
\begin{align*}
x^{\prime }&=x+z \\
y^{\prime }&=x+y \\
z^{\prime }&=-2 x-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| 12672 |
\begin{align*}
2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y x&=x^{2}+2 x \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.743 |
|
| 12673 |
\begin{align*}
4 y+y^{\prime \prime }&=\cot \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| 12674 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| 12675 | \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*} | ✓ | ✓ | ✓ | ✓ | 0.743 |
|
| 12676 |
\begin{align*}
-y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t <4 \\ 0 & 4\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.743 |
|
| 12677 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2}-{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| 12678 |
\begin{align*}
4 x^{2} y^{\prime \prime }+x \left (4 x^{2}+2 x +7\right ) y^{\prime }-\left (-7 x^{2}-4 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| 12679 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| 12680 |
\begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| 12681 |
\begin{align*}
3 x^{\prime }+2 x+y^{\prime }-6 y&=5 \,{\mathrm e}^{t} \\
4 x^{\prime }+2 x+y^{\prime }-8 y&=5 \,{\mathrm e}^{t}+2 t -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| 12682 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-{\mathrm e}^{x} y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| 12683 |
\begin{align*}
y^{\prime }&=5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| 12684 |
\begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x -7 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| 12685 |
\begin{align*}
\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| 12686 |
\begin{align*}
-y+y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ -1+t & 1\le t <2 \\ 3-t & 2\le t <3 \\ 0 & 3\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.744 |
|
| 12687 |
\begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }+\frac {y}{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.745 |
|
| 12688 |
\begin{align*}
y^{\prime } y+\sqrt {16-y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.745 |
|
| 12689 |
\begin{align*}
4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.745 |
|
| 12690 |
\begin{align*}
y^{\prime \prime }+2 a y^{\prime }+a^{2} y&=x^{2} {\mathrm e}^{-a x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.745 |
|
| 12691 |
\begin{align*}
x^{\prime }-3 x-6 y&=9-9 t \\
y^{\prime }+3 x+3 y&=9 t \,{\mathrm e}^{-3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.745 |
|
| 12692 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=\cos \left (x \right ) x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.746 |
|
| 12693 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-3 x_{2} \\
x_{3}^{\prime }&=x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| 12694 | \begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.746 |
|
| 12695 |
\begin{align*}
x^{\prime }&=b \,{\mathrm e}^{t} \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| 12696 |
\begin{align*}
\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y^{\prime } y+y^{2}+a^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.746 |
|
| 12697 |
\begin{align*}
y^{\prime \prime }&=6 \sin \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| 12698 |
\begin{align*}
x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| 12699 |
\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. |
✓ |
✓ |
✓ |
✗ |
0.747 |
|
| 12700 |
\begin{align*}
4 x -2 y^{\prime } y+x {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.747 |
|