| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 19001 |
\begin{align*}
\left (2+x \right ) y^{\prime }+4 y&=\frac {2 x^{2}+1}{x \left (2+x \right )^{3}} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.535 |
|
| 19002 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x}-\sin \left (y\right )}{x \cos \left (y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.535 |
|
| 19003 |
\begin{align*}
2 y^{\prime } x&=1-y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.535 |
|
| 19004 |
\begin{align*}
1+{\mathrm e}^{t y} \left (t y+1\right )+\left (1+{\mathrm e}^{t y} t^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.537 |
|
| 19005 |
\begin{align*}
x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right )&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.537 |
|
| 19006 |
\begin{align*}
y^{\prime }&=\frac {y \left (b_{2} x +b_{1} \right )}{x \left (a_{1} +a_{2} y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.537 |
|
| 19007 |
\begin{align*}
a y-2 x^{2} \tan \left (x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.538 |
|
| 19008 |
\begin{align*}
y^{\prime }&=3 y-3 x +3+\left (x -y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.539 |
|
| 19009 |
\begin{align*}
y^{\prime } x&=x^{3}+\left (2 x^{2}+1\right ) y+x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.539 |
|
| 19010 |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.539 |
|
| 19011 |
\begin{align*}
\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.539 |
|
| 19012 |
\begin{align*}
y^{\prime }-\frac {\sqrt {x^{2}-1}}{\sqrt {y^{2}-1}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.540 |
|
| 19013 |
\begin{align*}
r^{\prime }&=t -\frac {r}{3 t} \\
r \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.540 |
|
| 19014 |
\begin{align*}
\left (\csc \left (x \right )+\cot \left (x \right )\right ) y^{\prime }+y^{\prime \prime }&=1+a \csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.541 |
|
| 19015 |
\begin{align*}
\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.541 |
|
| 19016 |
\begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
w \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.541 |
|
| 19017 |
\begin{align*}
y^{\prime }+3 t y&=4-4 t^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.541 |
|
| 19018 | \begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.542 |
|
| 19019 |
\begin{align*}
2 x y^{2}+\frac {x}{y^{2}}+4 x^{2} y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.542 |
|
| 19020 |
\begin{align*}
2 y+y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.543 |
|
| 19021 |
\begin{align*}
\left (1+y\right ) y^{\prime }&=x^{2} \left (1-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.544 |
|
| 19022 |
\begin{align*}
a y+2 x^{2} \cot \left (x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.544 |
|
| 19023 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0\le t \le \frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.544 |
|
| 19024 |
\begin{align*}
x^{\prime }&=\ln \left (1+x^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.545 |
|
| 19025 |
\begin{align*}
x y y^{\prime \prime }+x {y^{\prime }}^{2}-y^{\prime } y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.546 |
|
| 19026 |
\begin{align*}
y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x}&=4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.546 |
|
| 19027 |
\begin{align*}
x \left (x +3\right )^{2} y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.547 |
|
| 19028 |
\begin{align*}
2 y x +\left (x^{2}-y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.547 |
|
| 19029 |
\begin{align*}
y^{\prime }&=\csc \left (x \right )+3 \tan \left (x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.549 |
|
| 19030 |
\begin{align*}
x \ln \left (y\right ) y^{\prime }-y \ln \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.549 |
|
| 19031 |
\begin{align*}
y^{\prime }&=\sin \left (2 x \right )-\tan \left (x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.550 |
|
| 19032 |
\begin{align*}
y^{\prime } x&=a x +b y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.550 |
|
| 19033 |
\begin{align*}
2 x^{2} y^{\prime }-2 y^{2}-y x +2 a^{2} x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.550 |
|
| 19034 |
\begin{align*}
\left (p \left (1+p \right )-k^{2} \csc \left (x \right )^{2}\right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.551 |
|
| 19035 |
\begin{align*}
t \cot \left (x\right ) x^{\prime }&=-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.551 |
|
| 19036 |
\begin{align*}
y \sin \left (x \right )+\cos \left (x \right )^{2}-\cos \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.552 |
|
| 19037 | \begin{align*}
y^{\prime }+\frac {3 y}{x}&=x^{2} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.552 |
|
| 19038 |
\begin{align*}
-y+y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.552 |
|
| 19039 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & t <6 \\ 1 & 6\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.552 |
|
| 19040 |
\begin{align*}
y \ln \left (x \right ) \ln \left (y\right )+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.553 |
|
| 19041 |
\begin{align*}
y^{\prime }+c y&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.554 |
|
| 19042 |
\begin{align*}
y^{\prime }&=\sqrt {y^{2}-9} \\
y \left (2\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.555 |
|
| 19043 |
\begin{align*}
y^{\prime }&=2 t y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.556 |
|
| 19044 |
\begin{align*}
m v^{\prime }&=m g -k v^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.556 |
|
| 19045 |
\begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
2.556 |
|
| 19046 |
\begin{align*}
3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.556 |
|
| 19047 |
\begin{align*}
y^{\prime }&=\frac {\cot \left (t \right ) y}{1+y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.556 |
|
| 19048 |
\begin{align*}
\left (x -y\right )^{2} y^{\prime }&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.557 |
|
| 19049 |
\begin{align*}
y^{\prime }&=3 x +y \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.557 |
|
| 19050 |
\begin{align*}
y^{\prime \prime }&=2 k y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.558 |
|
| 19051 |
\begin{align*}
y^{\prime }&=\frac {\left (3+y\right )^{2}}{4 x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.558 |
|
| 19052 |
\begin{align*}
z^{\prime \prime }+\frac {z}{1+z^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.559 |
|
| 19053 |
\begin{align*}
y^{\prime }+a y-b \sin \left (c x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.559 |
|
| 19054 |
\begin{align*}
\left (t +1\right ) y^{\prime }&=4 y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.559 |
|
| 19055 |
\begin{align*}
y^{\prime }+y x&=y^{4} x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.560 |
|
| 19056 | \begin{align*}
y \left (1+y^{2}\right )&=2 \left (1-2 x y^{2}\right ) y^{\prime } \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.561 |
|
| 19057 |
\begin{align*}
\left (y x +1\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.562 |
|
| 19058 |
\begin{align*}
2 x^{3} y^{2}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.562 |
|
| 19059 |
\begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.562 |
|
| 19060 |
\begin{align*}
y^{\prime }&=\frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.562 |
|
| 19061 |
\begin{align*}
-y+y^{\prime }&=2 \,{\mathrm e}^{2 t} t \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.562 |
|
| 19062 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}-x_{2}+4 x_{3}+2 x_{4} \\
x_{2}^{\prime }&=-19 x_{1}-6 x_{2}+6 x_{3}+16 x_{4} \\
x_{3}^{\prime }&=-9 x_{1}-x_{2}+x_{3}+6 x_{4} \\
x_{4}^{\prime }&=-5 x_{1}-3 x_{2}+6 x_{3}+5 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.562 |
|
| 19063 |
\begin{align*}
y^{\prime } x +y&=x y \left (y^{\prime }-1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.563 |
|
| 19064 |
\begin{align*}
y^{\prime }&=x^{2}+3 \cosh \left (x \right )-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.563 |
|
| 19065 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.563 |
|
| 19066 |
\begin{align*}
y^{\prime } x -3 y&=x^{4} {\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.563 |
|
| 19067 |
\begin{align*}
y^{\prime } x&=y+2 \,{\mathrm e}^{-\frac {y}{x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.564 |
|
| 19068 |
\begin{align*}
y^{\prime }&=-\frac {i \left (i x +x^{4}+2 y^{2} x^{2}+y^{4}\right )}{y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.564 |
|
| 19069 |
\begin{align*}
\left (x +a \right ) \left (x +b \right ) y^{\prime }&=y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.565 |
|
| 19070 |
\begin{align*}
3 y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.566 |
|
| 19071 |
\begin{align*}
3 x^{2} y+\left (x^{3}+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.566 |
|
| 19072 |
\begin{align*}
x^{2} y-2 x +\left (\frac {x^{3}}{3}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.566 |
|
| 19073 |
\begin{align*}
y \left (x -y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.567 |
|
| 19074 |
\begin{align*}
y^{\prime }&=\frac {1}{y x +x^{3} y^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.568 |
|
| 19075 | \begin{align*}
y^{\prime }&=F \left (\frac {y}{x +a}\right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 2.568 |
|
| 19076 |
\begin{align*}
y^{\prime } y+x&=\frac {a^{2} \left (-y+y^{\prime } x \right )}{y^{2}+x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.568 |
|
| 19077 |
\begin{align*}
y+y^{3}+4 \left (x y^{2}-1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.569 |
|
| 19078 |
\begin{align*}
y^{\prime }&=\sin \left (x \right )+2 \tan \left (x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.569 |
|
| 19079 |
\begin{align*}
y^{\prime } x&=2 x^{2} y+y \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.569 |
|
| 19080 |
\begin{align*}
x \left ({\mathrm e}^{y}+4\right )&={\mathrm e}^{x +y} y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.569 |
|
| 19081 |
\begin{align*}
\left (x^{2}+1\right ) y y^{\prime }+4&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.569 |
|
| 19082 |
\begin{align*}
x^{2}+1+x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.569 |
|
| 19083 |
\begin{align*}
y^{\prime }&=x^{2}+3 \cosh \left (x \right )+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.570 |
|
| 19084 |
\begin{align*}
t y^{\prime }+y&=t^{3} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.570 |
|
| 19085 |
\begin{align*}
y^{\prime }&=\sin \left (y\right )-\cos \left (x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.570 |
|
| 19086 |
\begin{align*}
x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.570 |
|
| 19087 |
\begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.571 |
|
| 19088 |
\begin{align*}
y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=12 \operatorname {Heaviside}\left (t \right )-12 \operatorname {Heaviside}\left (-1+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.572 |
|
| 19089 |
\begin{align*}
y-y^{\prime } x&=a \left (y^{\prime }+y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.572 |
|
| 19090 |
\begin{align*}
1+y-\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.574 |
|
| 19091 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x -5 y-\ln \left (x \right ) x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.574 |
|
| 19092 |
\begin{align*}
y^{\prime }&=1+x -\left (2 x +1\right ) y+x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.575 |
|
| 19093 |
\begin{align*}
3 y^{2} y^{\prime } x +y^{3}-2 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.575 |
|
| 19094 |
\begin{align*}
e y^{\prime \prime }&=-P L +\left (w L +P \right ) x -\frac {w \left (L^{2}+x^{2}\right )}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.576 |
|
| 19095 | \begin{align*}
x_{1}^{\prime }&=47 x_{1}-8 x_{2}+5 x_{3}-5 x_{4} \\
x_{2}^{\prime }&=-10 x_{1}+32 x_{2}+18 x_{3}-2 x_{4} \\
x_{3}^{\prime }&=139 x_{1}-40 x_{2}-167 x_{3}-121 x_{4} \\
x_{4}^{\prime }&=-232 x_{1}+64 x_{2}+360 x_{3}+248 x_{4} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.577 |
|
| 19096 |
\begin{align*}
y^{\prime }&=1-t +y^{2}-t y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.578 |
|
| 19097 |
\begin{align*}
y^{\prime }&=2 x +F \left (y-x^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.578 |
|
| 19098 |
\begin{align*}
y \ln \left (t \right )+\left (t -3\right ) y^{\prime }&=2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.579 |
|
| 19099 |
\begin{align*}
2 y \cos \left (x \right )+3 \sin \left (x \right ) y^{\prime }&=0 \\
y \left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.579 |
|
| 19100 |
\begin{align*}
a \left (\ln \left (y^{\prime }\right )-y^{\prime }\right )-x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.580 |
|