| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 3701 |
\begin{align*}
{\mathrm e}^{t} \left (y-t \right )+\left (1+{\mathrm e}^{t}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.302 |
|
| 3702 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-15 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.302 |
|
| 3703 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=x^{2} \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.302 |
|
| 3704 |
\begin{align*}
\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.302 |
|
| 3705 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{2 t} t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.302 |
|
| 3706 |
\begin{align*}
y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=-12 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x}+10 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| 3707 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| 3708 |
\begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| 3709 |
\begin{align*}
2 y+y^{\prime }&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| 3710 |
\begin{align*}
y^{\prime \prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| 3711 |
\(\left [\begin {array}{cc} 6 & -10 \\ 2 & -3 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.303 |
|
| 3712 |
\begin{align*}
x^{\prime }&=-\frac {x}{2} \\
y^{\prime }&=x-\frac {y}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| 3713 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| 3714 |
\begin{align*}
y^{\prime }&={\mathrm e}^{z -y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| 3715 |
\begin{align*}
x^{2} y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| 3716 |
\begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| 3717 |
\begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.304 |
|
| 3718 |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.304 |
|
| 3719 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.304 |
|
| 3720 |
\(\left [\begin {array}{cc} 8 & -10 \\ 2 & -1 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.304 |
|
| 3721 |
\(\left [\begin {array}{cc} 19 & -10 \\ 21 & -10 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.304 |
|
| 3722 |
\begin{align*}
y^{\left (6\right )}-y&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.304 |
|
| 3723 |
\begin{align*}
2 y^{\prime \prime }-4 y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.304 |
|
| 3724 |
\begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.304 |
|
| 3725 |
\begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.304 |
|
| 3726 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }-4 y&={\mathrm e}^{-4 x}+x \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.304 |
|
| 3727 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.304 |
|
| 3728 |
\begin{align*}
2 y^{\prime \prime }-7 y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.305 |
|
| 3729 |
\begin{align*}
2 y+y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.305 |
|
| 3730 |
\begin{align*}
4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.305 |
|
| 3731 |
\begin{align*}
x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.305 |
|
| 3732 |
\begin{align*}
y^{\prime \prime }&=\left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (x -1\right )^{2}}+\frac {3}{16 \left (x -1\right ) x}\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.305 |
|
| 3733 |
\(\left [\begin {array}{cc} 13 & -15 \\ 6 & -6 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.305 |
|
| 3734 |
\begin{align*}
x^{3}+3 t x^{2} x^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.305 |
|
| 3735 |
\begin{align*}
x^{\prime \prime }+\left (t +1\right ) x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.305 |
|
| 3736 |
\(\left [\begin {array}{cc} 0 & 1 \\ 2 & 0 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.305 |
|
| 3737 |
\begin{align*}
z^{\prime \prime }-7 z^{\prime }-13 z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.305 |
|
| 3738 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2} \\
x_{2}^{\prime }&=x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.305 |
|
| 3739 |
\begin{align*}
x_{1}^{\prime }&=-6 x_{1}-7 x_{2} \\
x_{2}^{\prime }&=7 x_{1}-20 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.305 |
|
| 3740 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=x \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.305 |
|
| 3741 |
\begin{align*}
y^{\prime \prime }+y&=x \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.306 |
|
| 3742 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| 3743 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=8 x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| 3744 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| 3745 |
\begin{align*}
3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| 3746 |
\begin{align*}
u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| 3747 |
\begin{align*}
x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.306 |
|
| 3748 |
\begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| 3749 |
\begin{align*}
y^{\prime \prime }+4 y&={\mathrm e}^{3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| 3750 |
\begin{align*}
a y^{\prime \prime }+b y^{\prime }+\frac {b^{2} y}{4 a}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| 3751 |
\begin{align*}
x y^{\prime }&=y \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.306 |
|
| 3752 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }-4 y&=t^{2} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| 3753 |
\begin{align*}
x y^{\prime \prime }-3 y^{\prime }-5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| 3754 |
\begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| 3755 |
\begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| 3756 |
\begin{align*}
y^{\prime \prime }-9 y^{\prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.307 |
|
| 3757 |
\begin{align*}
y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.307 |
|
| 3758 |
\begin{align*}
x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.307 |
|
| 3759 |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.307 |
|
| 3760 |
\begin{align*}
x^{2} \left (1-4 x \right ) y^{\prime \prime }-\frac {x y^{\prime }}{2}-\frac {3 y x}{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.307 |
|
| 3761 |
\begin{align*}
x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.307 |
|
| 3762 |
\begin{align*}
u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.307 |
|
| 3763 |
\begin{align*}
y^{\prime \prime }&=-\frac {2 \left (x^{2}-1\right ) y^{\prime }}{x \left (x -1\right )^{2}}-\frac {\left (-2 x^{2}+2 x +2\right ) y}{x^{2} \left (x -1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.307 |
|
| 3764 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| 3765 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| 3766 |
\begin{align*}
\tan \left (t \right ) x^{\prime \prime }-3 x^{\prime }+\left (\tan \left (t \right )+3 \cot \left (t \right )\right ) x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.308 |
|
| 3767 |
\begin{align*}
3 y^{\prime \prime }+7 y^{\prime }-6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| 3768 |
\begin{align*}
y^{\prime \prime }+4 y&=20 \,{\mathrm e}^{4 t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 12 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| 3769 |
\begin{align*}
e i u^{\prime \prime \prime \prime }&=\sinh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| 3770 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| 3771 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| 3772 |
\begin{align*}
x^{2} y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| 3773 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| 3774 |
\begin{align*}
25 y^{\prime \prime }-20 y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| 3775 |
\begin{align*}
2 y^{\prime \prime }+7 y^{\prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| 3776 |
\begin{align*}
4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.309 |
|
| 3777 |
\begin{align*}
4 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+3 y&=3 x^{3}-8 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| 3778 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| 3779 |
\begin{align*}
x y^{\prime \prime \prime }+2 y^{\prime \prime }&=6 x \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
y^{\prime \prime }\left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| 3780 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| 3781 |
\begin{align*}
y&=x y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| 3782 |
\begin{align*}
y^{\prime \prime }+4 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| 3783 |
\begin{align*}
5 {b^{\prime \prime \prime \prime }}^{5}+7 {b^{\prime }}^{10}+b^{7}-b^{5}&=p \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.309 |
|
| 3784 |
\begin{align*}
y^{\prime \prime }-2 x y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| 3785 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=\cosh \left (2 x \right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.309 |
|
| 3786 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| 3787 |
\begin{align*}
y^{\prime \prime }-x y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| 3788 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| 3789 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }-40 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| 3790 |
\begin{align*}
y^{\prime \prime }+x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.309 |
|
| 3791 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.310 |
|
| 3792 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.310 |
|
| 3793 |
\begin{align*}
x^{{3}/{2}} y^{\prime }&=a +b \,x^{{3}/{2}} y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.310 |
|
| 3794 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.310 |
|
| 3795 |
\begin{align*}
x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.310 |
|
| 3796 |
\begin{align*}
\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.310 |
|
| 3797 |
\begin{align*}
y^{\prime \prime }-c \,x^{a} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.310 |
|
| 3798 |
\(\left [\begin {array}{cc} 7 & -6 \\ 12 & -10 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.310 |
|
| 3799 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.310 |
|
| 3800 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
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0.310 |
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