| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 14601 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&=x \,{\mathrm e}^{-3 x} \sin \left (2 x \right )+x^{2} {\mathrm e}^{-2 x} \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.707 |
|
| 14602 |
\begin{align*}
\left (1-\frac {1}{x}\right ) u^{\prime \prime }+\left (\frac {2}{x}-\frac {2}{x^{2}}-\frac {1}{x^{3}}\right ) u^{\prime }-\frac {u}{x^{4}}&=\frac {2}{x}-\frac {2}{x^{2}}-\frac {2}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.707 |
|
| 14603 |
\begin{align*}
y^{\prime \prime } x&=y^{\prime }+x^{5} \\
y \left (1\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.708 |
|
| 14604 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-5 y&=1 \\
y \left (\infty \right ) &= -{\frac {1}{5}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.708 |
|
| 14605 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=2 x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.708 |
|
| 14606 |
\begin{align*}
-2 \left (1-3 x \right ) y-x \left (1-4 x \right ) y^{\prime }+2 x^{2} y^{\prime \prime }&=x^{3} \left (x +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.709 |
|
| 14607 |
\begin{align*}
t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=2 t^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.710 |
|
| 14608 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.710 |
|
| 14609 |
\begin{align*}
t^{2} y^{\prime \prime }-12 y^{\prime } t +42 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.711 |
|
| 14610 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.712 |
|
| 14611 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.713 |
|
| 14612 |
\begin{align*}
u^{2} v-\left (u^{3}+v^{3}\right ) v^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.713 |
|
| 14613 |
\begin{align*}
y^{\prime \prime }+2 x^{2} y^{\prime }+4 y x&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.714 |
|
| 14614 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.714 |
|
| 14615 |
\begin{align*}
y^{\prime }&=k y+f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.715 |
|
| 14616 |
\begin{align*}
t^{2} y+y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.716 |
|
| 14617 |
\begin{align*}
\sqrt {a^{2}-x^{2}}\, \left (-y y^{\prime }-x {y^{\prime }}^{2}+x y y^{\prime \prime }\right )&=b x {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.716 |
|
| 14618 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c \left (a \,x^{2}+b -c \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.716 |
|
| 14619 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.717 |
|
| 14620 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{2}+b x +2\right ) y^{\prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.717 |
|
| 14621 |
\begin{align*}
y^{\prime \prime }+a^{2} y&=\sec \left (a x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.717 |
|
| 14622 |
\begin{align*}
9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.717 |
|
| 14623 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.718 |
|
| 14624 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x -1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.719 |
|
| 14625 |
\begin{align*}
y^{\prime }&=2 x +F \left (-x^{2}+y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.719 |
|
| 14626 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.719 |
|
| 14627 |
\begin{align*}
y^{\prime } x +y x +y-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.720 |
|
| 14628 |
\begin{align*}
y^{\prime \prime }+9 y&=\csc \left (3 t \right ) \\
y \left (\frac {\pi }{12}\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{12}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.720 |
|
| 14629 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=4 \,{\mathrm e}^{x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.720 |
|
| 14630 |
\begin{align*}
4 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.720 |
|
| 14631 |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.721 |
|
| 14632 |
\begin{align*}
y^{3} y^{\prime \prime }&=-1 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
1.721 |
|
| 14633 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.722 |
|
| 14634 |
\begin{align*}
y^{\prime \prime }&=6 \sin \left (3 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.722 |
|
| 14635 |
\begin{align*}
1-y^{\prime }&=x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.723 |
|
| 14636 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.723 |
|
| 14637 |
\begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.723 |
|
| 14638 |
\begin{align*}
4 y+y^{\prime \prime }&=4 \sec \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.724 |
|
| 14639 |
\begin{align*}
y^{\prime \prime } \sqrt {a^{2}+x^{2}}&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.724 |
|
| 14640 |
\begin{align*}
y^{\prime }+y&=\left \{\begin {array}{cc} 1 & 0\le x \le 1 \\ -1 & 1<x \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.725 |
|
| 14641 |
\begin{align*}
\left (2 y^{3}+5 x^{2} y\right ) y^{\prime }+5 x y^{2}+x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.725 |
|
| 14642 |
\begin{align*}
a y y^{\prime }+2 x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.726 |
|
| 14643 |
\begin{align*}
y^{2}-3 y x -2 x^{2}+\left (y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.726 |
|
| 14644 |
\begin{align*}
i^{\prime }+i&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.726 |
|
| 14645 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.727 |
|
| 14646 |
\begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2}-8 y^{3}-4 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.727 |
|
| 14647 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x -y&=0 \\
y \left (1\right ) &= 8 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.727 |
|
| 14648 |
\begin{align*}
x_{1}^{\prime }&=-5 x_{1}-2 x_{2}-x_{3}+2 x_{4}+3 x_{5} \\
x_{2}^{\prime }&=-3 x_{2} \\
x_{3}^{\prime }&=x_{1}-x_{3}-x_{5} \\
x_{4}^{\prime }&=2 x_{1}+x_{2}-4 x_{4}-2 x_{5} \\
x_{5}^{\prime }&=-3 x_{1}-2 x_{2}-x_{3}+2 x_{4}+x_{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.727 |
|
| 14649 |
\begin{align*}
y^{\prime }&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.727 |
|
| 14650 |
\begin{align*}
{\mathrm e}^{x} \left (y^{\prime }+y\right )&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.727 |
|
| 14651 |
\begin{align*}
x^{\prime \prime }+2 b x^{\prime }+k^{2} x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= v_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.727 |
|
| 14652 |
\begin{align*}
y^{\prime } x -3 y&=x^{3} \\
y \left (1\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.728 |
|
| 14653 |
\begin{align*}
x^{\prime }-2 x+y^{\prime }-2 y&=1 \\
y^{\prime }+z^{\prime }+z&=2 \\
3 x+z^{\prime }+z&=3 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.729 |
|
| 14654 |
\begin{align*}
y^{\prime }&=y x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.729 |
|
| 14655 |
\begin{align*}
x {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.729 |
|
| 14656 |
\begin{align*}
y^{\prime }+y^{2}&=x^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.730 |
|
| 14657 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y&=x^{1+a} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.730 |
|
| 14658 |
\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 \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
1.730 |
|
| 14659 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}-v \left (v -1\right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.730 |
|
| 14660 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.730 |
|
| 14661 |
\begin{align*}
\left (8 {y^{\prime }}^{3}-27\right ) x&=12 y {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.730 |
|
| 14662 |
\begin{align*}
y^{\prime \prime } x -3 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.730 |
|
| 14663 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.730 |
|
| 14664 |
\begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y \left (0\right ) &= 0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.731 |
|
| 14665 |
\begin{align*}
p^{\prime }&=p-p^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.731 |
|
| 14666 |
\begin{align*}
\left (x^{2}-y^{4}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.731 |
|
| 14667 |
\begin{align*}
y^{\prime }&=2 \sqrt {2 x +y-3}-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.731 |
|
| 14668 |
\begin{align*}
y^{\prime \prime }+16 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.731 |
|
| 14669 |
\begin{align*}
\frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.733 |
|
| 14670 |
\begin{align*}
y^{\prime \prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.733 |
|
| 14671 |
\begin{align*}
x {y^{\prime }}^{2}-2 y y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.733 |
|
| 14672 |
\begin{align*}
{y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.734 |
|
| 14673 |
\begin{align*}
y^{2}&=a^{2} \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.734 |
|
| 14674 |
\begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.734 |
|
| 14675 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.735 |
|
| 14676 |
\begin{align*}
4 {y^{\prime }}^{2}-9 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.735 |
|
| 14677 |
\begin{align*}
x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.735 |
|
| 14678 |
\begin{align*}
-y^{\prime }+y^{\prime \prime } x&={\mathrm e}^{x} x^{2} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.736 |
|
| 14679 |
\begin{align*}
y^{\prime \prime } x +\left (x^{n} a +b \right ) y^{\prime }+x^{n -1} a n y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.737 |
|
| 14680 |
\begin{align*}
\left (-a^{2}+x^{2}\right ) y^{\prime \prime }+2 b x y^{\prime }+b \left (b -1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.737 |
|
| 14681 |
\begin{align*}
y+y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.737 |
|
| 14682 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.737 |
|
| 14683 |
\begin{align*}
y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.737 |
|
| 14684 |
\begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.737 |
|
| 14685 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.738 |
|
| 14686 |
\begin{align*}
y^{\prime \prime } x +\left (\frac {1}{2}-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.738 |
|
| 14687 |
\begin{align*}
y^{\prime }&=-x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.738 |
|
| 14688 |
\begin{align*}
4 y^{\prime \prime } x +2 \left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.739 |
|
| 14689 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=g \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.739 |
|
| 14690 |
\begin{align*}
2 x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✓ |
1.740 |
|
| 14691 |
\begin{align*}
x {y^{\prime }}^{2}-2 y y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.740 |
|
| 14692 |
\begin{align*}
t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.740 |
|
| 14693 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.740 |
|
| 14694 |
\begin{align*}
t y^{\prime \prime }-y^{\prime }+4 y t^{3}&=4 t^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.740 |
|
| 14695 |
\begin{align*}
y^{\prime }+2 y x&=x \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.741 |
|
| 14696 |
\begin{align*}
y^{\prime \prime }+16 y&=\left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.741 |
|
| 14697 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y-2 \cos \left (x \right )+2 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.741 |
|
| 14698 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.742 |
|
| 14699 |
\begin{align*}
y^{\prime }&=y-y^{3} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
1.742 |
|
| 14700 |
\begin{align*}
{y^{\prime }}^{2}-y y^{\prime } x +y^{2} \ln \left (a y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.743 |
|