| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 15701 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.374 |
|
| 15702 |
\begin{align*}
y+y^{\prime }&={\mathrm e}^{t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.374 |
|
| 15703 |
\begin{align*}
2 y+y^{\prime }&={\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.374 |
|
| 15704 |
\begin{align*}
y^{\prime }+a y^{2}-b \,x^{2 \nu }-c \,x^{\nu -1}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.374 |
|
| 15705 |
\begin{align*}
y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 1 & 1<t \end {array}\right .\right ) y&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.374 |
|
| 15706 |
\begin{align*}
1+y+x^{2} y+\left (x^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.374 |
|
| 15707 |
\begin{align*}
-y+y^{\prime }&={\mathrm e}^{2 t} t \\
y \left (0\right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.374 |
|
| 15708 |
\begin{align*}
x^{2} y^{\prime \prime }-7 y^{\prime } x +25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.375 |
|
| 15709 |
\begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.375 |
|
| 15710 |
\begin{align*}
y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{2 x \left (x^{2}+1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.377 |
|
| 15711 |
\begin{align*}
x^{\prime }-2 x&=3 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.377 |
|
| 15712 |
\begin{align*}
{\mathrm e}^{y} \left (1+y^{\prime }\right )&=1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.378 |
|
| 15713 |
\begin{align*}
y y^{\prime \prime }+a \left (1+{y^{\prime }}^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.378 |
|
| 15714 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=6 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.378 |
|
| 15715 |
\begin{align*}
\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (3 x +5\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
1.378 |
|
| 15716 |
\begin{align*}
-y+y^{\prime }&=8 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.378 |
|
| 15717 |
\begin{align*}
y^{\prime }&=\frac {-1-2 y x}{x^{2}+2 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.381 |
|
| 15718 | \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=0 \\
y \left (2\right ) &= 1 \\
y^{\prime }\left (2\right ) &= -1 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.381 |
|
| 15719 |
\begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=x^{m +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.381 |
|
| 15720 |
\begin{align*}
{y^{\prime \prime }}^{2}+2 y^{\prime \prime } x -y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.381 |
|
| 15721 |
\begin{align*}
-y+y^{\prime } x&=\ln \left (x \right ) x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.382 |
|
| 15722 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{{\mathrm e}^{x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.382 |
|
| 15723 |
\begin{align*}
2 y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.383 |
|
| 15724 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=x^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.383 |
|
| 15725 |
\begin{align*}
t^{2} y^{\prime \prime }+7 t y^{\prime }-7 y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= -22 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.383 |
|
| 15726 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+3 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.383 |
|
| 15727 |
\begin{align*}
y^{\prime }-\frac {2 y}{x}-x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.384 |
|
| 15728 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.384 |
|
| 15729 |
\begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.384 |
|
| 15730 |
\begin{align*}
t^{2} y^{\prime \prime }+\left (-1+t \right ) y^{\prime }-y&={\mathrm e}^{-t} t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.384 |
|
| 15731 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.385 |
|
| 15732 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+\left (x -1\right ) y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.385 |
|
| 15733 |
\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*} |
✓ |
✓ |
✓ |
✓ |
1.385 |
|
| 15734 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{2}-{\mathrm e}^{-x}+{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.385 |
|
| 15735 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.385 |
|
| 15736 |
\begin{align*}
x_{1}^{\prime }&=11 x_{1}-x_{2}+26 x_{3}+6 x_{4}-3 x_{5} \\
x_{2}^{\prime }&=3 x_{2} \\
x_{3}^{\prime }&=-9 x_{1}-24 x_{3}-6 x_{4}+3 x_{5} \\
x_{4}^{\prime }&=3 x_{1}+9 x_{3}+5 x_{4}-x_{5} \\
x_{5}^{\prime }&=-48 x_{1}-3 x_{2}-138 x_{3}-30 x_{4}+18 x_{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.386 |
|
| 15737 | \begin{align*}
y^{\prime }&=2 y \\
y \left (\ln \left (3\right )\right ) &= 3 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.386 |
|
| 15738 |
\begin{align*}
y^{\prime \prime }-\tan \left (x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.386 |
|
| 15739 |
\begin{align*}
3 x^{2} y^{\prime \prime }+x^{6} y^{\prime }+2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.386 |
|
| 15740 |
\begin{align*}
y^{\prime \prime }&=9 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.386 |
|
| 15741 |
\begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.386 |
|
| 15742 |
\begin{align*}
x^{\prime }+2 x&=6 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.386 |
|
| 15743 |
\begin{align*}
{y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.387 |
|
| 15744 |
\begin{align*}
y^{\prime }&={\mathrm e}^{3+t +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.388 |
|
| 15745 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.388 |
|
| 15746 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.388 |
|
| 15747 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }&=18 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.388 |
|
| 15748 |
\begin{align*}
y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=x^{2} {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.388 |
|
| 15749 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (1-x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.388 |
|
| 15750 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y^{\prime }\left (1\right ) &= 3 \\
y^{\prime }\left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.389 |
|
| 15751 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.389 |
|
| 15752 |
\begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (4+2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.389 |
|
| 15753 |
\begin{align*}
y^{\prime } x +y-1&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.390 |
|
| 15754 |
\begin{align*}
y+y^{\prime }&=8 \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.390 |
|
| 15755 |
\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*} |
✓ |
✓ |
✓ |
✓ |
1.391 |
|
| 15756 | \begin{align*}
5 y^{\prime }-y x&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.391 |
|
| 15757 |
\begin{align*}
\left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5+2 x \right ) y^{\prime }+8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.391 |
|
| 15758 |
\begin{align*}
y^{\prime }&=y+{\mathrm e}^{-y}+{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.392 |
|
| 15759 |
\begin{align*}
x^{2} \left (x -a \right )^{2} y^{\prime \prime }+b y&=c \,x^{2} \left (x -a \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.392 |
|
| 15760 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (2\right ) &= -12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.392 |
|
| 15761 |
\begin{align*}
x^{\prime }+y^{\prime }-y&=0 \\
y^{\prime }+2 y+z^{\prime }+2 z&=2 \\
x+z^{\prime }-z&=0 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.392 |
|
| 15762 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \sec \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.392 |
|
| 15763 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.393 |
|
| 15764 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.393 |
|
| 15765 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.393 |
|
| 15766 |
\begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+2 y&={\mathrm e}^{2 x} \left (x^{4}+x +24\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.394 |
|
| 15767 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\left (y-t \right )^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.394 |
|
| 15768 |
\begin{align*}
2 \left (x +y\right ) y^{\prime }+x^{2}+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.394 |
|
| 15769 |
\begin{align*}
y^{\prime } x +y&=2 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.395 |
|
| 15770 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=3 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.395 |
|
| 15771 |
\begin{align*}
y^{\prime }&=x^{2}-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.395 |
|
| 15772 |
\begin{align*}
y^{\prime \prime }&=2 x +\left (x^{2}-y^{\prime }\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.395 |
|
| 15773 |
\begin{align*}
y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.395 |
|
| 15774 |
\begin{align*}
y^{2} y^{\prime } x -y^{3}&=\frac {x^{4}}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.396 |
|
| 15775 |
\begin{align*}
y^{\prime } x -y+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.396 |
|
| 15776 | \begin{align*}
\frac {2 t y}{t^{2}+1}+y^{\prime }&=\frac {1}{t^{2}+1} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.397 |
|
| 15777 |
\begin{align*}
y^{\prime \prime } x&=y^{\prime }-2 {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.397 |
|
| 15778 |
\begin{align*}
x^{\prime }+3 x&=-2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.397 |
|
| 15779 |
\begin{align*}
y^{\prime }&=\frac {y x +a^{2}}{a^{2}-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.397 |
|
| 15780 |
\begin{align*}
\operatorname {a2} y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.398 |
|
| 15781 |
\begin{align*}
\left (-a^{2}+4 b \right ) y+12 x^{5} y^{\prime }+4 x^{6} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.398 |
|
| 15782 |
\begin{align*}
2 y y^{\prime \prime }&=y^{2} \left (1-3 y^{2}\right )+6 {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.398 |
|
| 15783 |
\begin{align*}
a x y+2 y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.398 |
|
| 15784 |
\begin{align*}
x^{\prime \prime }+p \left (t \right ) x^{\prime }+q \left (t \right ) x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.398 |
|
| 15785 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=8 x^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.399 |
|
| 15786 |
\begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{\frac {201 t}{100}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.400 |
|
| 15787 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.401 |
|
| 15788 |
\begin{align*}
4 x^{2} y^{\prime \prime }-\left (4 x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.401 |
|
| 15789 |
\begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.401 |
|
| 15790 |
\begin{align*}
y^{\prime \prime }-f \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.401 |
|
| 15791 |
\begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.401 |
|
| 15792 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.402 |
|
| 15793 |
\begin{align*}
y^{\prime \prime }+\left (\sin \left (x \right )+2 x \right ) y^{\prime }+\cos \left (y\right ) y {y^{\prime }}^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.402 |
|
| 15794 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.402 |
|
| 15795 |
\begin{align*}
4 y+y^{\prime \prime }&=4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.402 |
|
| 15796 | \begin{align*}
y+y^{\prime }&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.403 |
|
| 15797 |
\begin{align*}
x^{\prime \prime }+x&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.403 |
|
| 15798 |
\begin{align*}
\left (1-x \right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.404 |
|
| 15799 |
\begin{align*}
y^{\prime }&=f \left (x \right ) g \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.404 |
|
| 15800 |
\begin{align*}
y-\left (x^{2}+y^{2}+x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.404 |
|