| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 13601 |
\begin{align*}
x^{2}+y^{2}+\left (2 y x -3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.540 |
|
| 13602 |
\begin{align*}
y^{\prime }-y x&={\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.542 |
|
| 13603 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -\left (\nu ^{2}+x^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.542 |
|
| 13604 |
\begin{align*}
y^{\prime } x&=2 y+\cos \left (x \right ) x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.543 |
|
| 13605 |
\begin{align*}
\frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.543 |
|
| 13606 |
\begin{align*}
\sqrt {x^{2}+1}\, y^{\prime }&=2 x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.543 |
|
| 13607 |
\begin{align*}
y y^{\prime }+x&=\frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.543 |
|
| 13608 |
\begin{align*}
x +\sin \left (y\right )+\left (x \cos \left (y\right )-2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.543 |
|
| 13609 |
\begin{align*}
y^{\prime }&=1-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.543 |
|
| 13610 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.544 |
|
| 13611 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (-2+t \right )-\operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= -{\frac {2}{3}} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.544 |
|
| 13612 |
\begin{align*}
y^{\prime } t +y&=t \sin \left (t \right ) \\
y \left (\pi \right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.544 |
|
| 13613 |
\begin{align*}
x^{3}+4 y x +y^{2}+\left (2 x^{2}+2 y x +4 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.544 |
|
| 13614 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.544 |
|
| 13615 |
\begin{align*}
R^{\prime }&=\left (1+t \right ) \left (1+R^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.545 |
|
| 13616 |
\begin{align*}
y^{\prime }&=\frac {t}{y-t^{2} y} \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.545 |
|
| 13617 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.545 |
|
| 13618 |
\begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{2 x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.546 |
|
| 13619 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.546 |
|
| 13620 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x -\frac {3}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.546 |
|
| 13621 |
\begin{align*}
4 {y^{\prime }}^{2}-2 \left (y+3 y^{\prime } x \right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.546 |
|
| 13622 |
\begin{align*}
y^{\prime } x&=y+x^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.546 |
|
| 13623 |
\begin{align*}
2 x y^{2}+\frac {x}{y^{2}}+4 x^{2} y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.546 |
|
| 13624 |
\begin{align*}
s^{\prime \prime }&=-9 s \\
s \left (0\right ) &= 9 \\
s^{\prime }\left (0\right ) &= 18 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.546 |
|
| 13625 |
\begin{align*}
y^{\prime \prime }+y&=x +2 \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.546 |
|
| 13626 |
\begin{align*}
5 {y^{\prime \prime \prime }}^{2}-3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.547 |
|
| 13627 |
\begin{align*}
y^{\prime \prime }+y x&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.548 |
|
| 13628 |
\begin{align*}
y^{\prime }-3 y&={\mathrm e}^{3 x}+{\mathrm e}^{-3 x} \\
y \left (5\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.548 |
|
| 13629 |
\begin{align*}
\frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.548 |
|
| 13630 |
\begin{align*}
2 x y^{2}+x^{2} y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.549 |
|
| 13631 |
\begin{align*}
\left (c \,x^{2}+b x +a \right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.549 |
|
| 13632 |
\begin{align*}
y^{\prime \prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.549 |
|
| 13633 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.549 |
|
| 13634 |
\begin{align*}
y^{\prime } t +y&=t \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.549 |
|
| 13635 |
\begin{align*}
y+2 x -y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.551 |
|
| 13636 |
\begin{align*}
y^{\prime }&=\frac {a y+b}{d +c y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.551 |
|
| 13637 |
\begin{align*}
y^{\prime \prime }+2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.551 |
|
| 13638 |
\begin{align*}
y^{\prime }&=-4 t y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.551 |
|
| 13639 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.552 |
|
| 13640 |
\begin{align*}
y^{\prime }&=3+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.552 |
|
| 13641 |
\begin{align*}
t^{2} y^{\prime \prime }-5 y^{\prime } t +9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.553 |
|
| 13642 |
\begin{align*}
y^{\prime \prime } x&=y^{\prime }-2 x^{2} y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.553 |
|
| 13643 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y&=x^{2}+\frac {1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.553 |
|
| 13644 |
\begin{align*}
\left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.555 |
|
| 13645 |
\begin{align*}
y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y+1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.555 |
|
| 13646 |
\begin{align*}
x^{\prime }+\frac {x}{t^{2}}&=\frac {1}{t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.555 |
|
| 13647 |
\begin{align*}
z-\left (-a^{2}+t^{2}\right ) z^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.555 |
|
| 13648 |
\begin{align*}
\sin \left (\ln \left (x \right )\right )-\cos \left (\ln \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.555 |
|
| 13649 |
\begin{align*}
\sqrt {x}\, y^{\prime \prime }+2 y^{\prime } x +3 y&=x \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.555 |
|
| 13650 |
\begin{align*}
y^{\prime }+y&=2 x +2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.556 |
|
| 13651 |
\begin{align*}
2 t \cos \left (y\right )+3 t^{2} y+\left (t^{3}-t^{2} \sin \left (y\right )-y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.557 |
|
| 13652 |
\begin{align*}
y^{\prime } x -4 y&=x^{6} {\mathrm e}^{x} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.557 |
|
| 13653 |
\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*} |
✓ |
✓ |
✓ |
✓ |
2.558 |
|
| 13654 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.558 |
|
| 13655 |
\begin{align*}
y x +x^{2} y^{\prime }&=8 x^{2} \cos \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.558 |
|
| 13656 |
\begin{align*}
4 x y^{2}+y^{\prime }&=5 y^{2} x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.559 |
|
| 13657 |
\begin{align*}
y^{\prime }&=1+2 x +y^{2}+2 x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.559 |
|
| 13658 |
\begin{align*}
y^{\prime }+2 y x&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.559 |
|
| 13659 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.559 |
|
| 13660 |
\begin{align*}
-y+y^{\prime } x&=x \sqrt {x^{2}-y^{2}}\, y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.560 |
|
| 13661 |
\begin{align*}
y^{\prime }&=\frac {3 x}{y+x^{2} y} \\
y \left (0\right ) &= -7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.560 |
|
| 13662 |
\begin{align*}
y^{\prime }&=\tan \left (x \right ) \cot \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.561 |
|
| 13663 |
\begin{align*}
y^{\prime }+2 \sin \left (x \right ) \cos \left (x \right ) y&={\mathrm e}^{-\sin \left (x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.562 |
|
| 13664 |
\begin{align*}
{y^{\prime }}^{3}+y^{\prime }+a -b x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.562 |
|
| 13665 |
\begin{align*}
y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.562 |
|
| 13666 |
\begin{align*}
y&=y^{\prime } x \left (1+y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.563 |
|
| 13667 |
\begin{align*}
y^{\prime } x +y&=x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.563 |
|
| 13668 |
\begin{align*}
x y^{2}-x +\left (y+x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.563 |
|
| 13669 |
\begin{align*}
2 y^{\prime } x -y&=2 \cos \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.563 |
|
| 13670 |
\begin{align*}
\frac {y}{2}+y^{\prime }&=2 \cos \left (t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.564 |
|
| 13671 |
\begin{align*}
2 y+y^{\prime }&=3 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.564 |
|
| 13672 |
\begin{align*}
x \left (x y^{2}+1\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.564 |
|
| 13673 |
\begin{align*}
y^{\prime }&=\frac {x \left (1-x \right )}{y \left (y-2\right )} \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.564 |
|
| 13674 |
\begin{align*}
y^{\prime \prime }+25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.564 |
|
| 13675 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.565 |
|
| 13676 |
\begin{align*}
\left (x +y+2\right ) y^{\prime }&=-x -y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.565 |
|
| 13677 |
\begin{align*}
1+2 x y^{2}+\left (2 x^{2} y+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.565 |
|
| 13678 |
\begin{align*}
x^{2} y^{n} y^{\prime }&=2 y^{\prime } x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.565 |
|
| 13679 |
\begin{align*}
2 y+{\mathrm e}^{-3 x} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.565 |
|
| 13680 |
\begin{align*}
2 y+\left (x +1\right ) y^{\prime }&=\frac {{\mathrm e}^{x}}{x +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.566 |
|
| 13681 |
\begin{align*}
y^{\prime }&=\sin \left (x \right ) \left (y \sec \left (x \right )-2\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.566 |
|
| 13682 |
\begin{align*}
{y^{\prime }}^{3}+\left (\cos \left (x \right ) \cot \left (x \right )-y\right ) {y^{\prime }}^{2}-\left (1+y \cos \left (x \right ) \cot \left (x \right )\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.566 |
|
| 13683 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.566 |
|
| 13684 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}-4 x_{2}+5 x_{3}+9 x_{4} \\
x_{2}^{\prime }&=-2 x_{1}-5 x_{2}+4 x_{3}+12 x_{4} \\
x_{3}^{\prime }&=-2 x_{1}-x_{3}+2 x_{4} \\
x_{4}^{\prime }&=-2 x_{2}+2 x_{3}+3 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.566 |
|
| 13685 |
\begin{align*}
y^{\prime }-y&=x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.566 |
|
| 13686 |
\begin{align*}
x^{3} y^{\prime }&=3-x^{2}+x^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.567 |
|
| 13687 |
\begin{align*}
y^{\prime } x&=y+\cos \left (x \right ) x^{2} \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.567 |
|
| 13688 |
\begin{align*}
\left (1+{\mathrm e}^{y}\right ) \cos \left (x \right )+{\mathrm e}^{y} \sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.567 |
|
| 13689 |
\begin{align*}
u^{\prime \prime }-\left (x +1\right ) u^{\prime }+\left (x -1\right ) u&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.567 |
|
| 13690 |
\begin{align*}
y^{\prime }&=t y+t +y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.567 |
|
| 13691 |
\begin{align*}
x \left (1-\sqrt {x^{2}-y^{2}}\right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.568 |
|
| 13692 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.568 |
|
| 13693 |
\begin{align*}
-y+y^{\prime } t&=t^{3} {\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.568 |
|
| 13694 |
\begin{align*}
y^{\prime }+\frac {3 y}{x}+2&=3 x \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.569 |
|
| 13695 |
\begin{align*}
y^{\prime \prime } x +a y^{\prime }+b \,x^{n} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.569 |
|
| 13696 |
\begin{align*}
-y+y^{\prime }&=\sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.569 |
|
| 13697 |
\begin{align*}
x^{\prime \prime \prime }+a x^{\prime \prime }+b x^{\prime }+c x&=0 \\
x \left (\infty \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.569 |
|
| 13698 |
\begin{align*}
\left (a +x \right ) y^{\prime }+b \,x^{2}+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.570 |
|
| 13699 |
\begin{align*}
z^{\prime }+2 x z&=2 a \,x^{3} z^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.570 |
|
| 13700 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.570 |
|