| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 19001 |
\begin{align*}
y+y^{\prime } x +\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime \prime }+x \left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime \prime }&=f \left (x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.019 |
|
| 19002 |
\begin{align*}
y^{\prime }+2 \tan \left (y\right ) \tan \left (x \right )-1&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.019 |
|
| 19003 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+3 x +2}{-2+y} \\
y \left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.020 |
|
| 19004 |
\begin{align*}
\left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }-3 x y^{2}+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.020 |
|
| 19005 |
\begin{align*}
x^{2} y^{\prime }&=y-y x \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.020 |
|
| 19006 |
\begin{align*}
y^{\prime }&=\sec \left (x \right )^{2} \cot \left (y\right ) \cos \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.022 |
|
| 19007 |
\begin{align*}
y^{\prime }+5 y&={\mathrm e}^{-3 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.022 |
|
| 19008 |
\begin{align*}
y+y^{\prime }&=t \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.022 |
|
| 19009 |
\begin{align*}
y^{\prime }-\tan \left (x \right ) y&=\sec \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.022 |
|
| 19010 |
\begin{align*}
x^{\prime }&=t^{3} \left (1-x\right ) \\
x \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.023 |
|
| 19011 |
\begin{align*}
x^{\prime }+t x&=4 t \\
x \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.023 |
|
| 19012 |
\begin{align*}
y^{\prime }&=x^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.024 |
|
| 19013 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=2 x^{2} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.026 |
|
| 19014 |
\begin{align*}
3 {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.026 |
|
| 19015 |
\begin{align*}
y^{\prime }&=\cot \left (x \right ) y+\sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.026 |
|
| 19016 |
\begin{align*}
y^{\prime }-2 y&=y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.026 |
|
| 19017 |
\begin{align*}
z^{\prime \prime }+\frac {z}{1+z^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.027 |
|
| 19018 |
\begin{align*}
-y+y^{\prime } x&=x^{2} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.027 |
|
| 19019 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.027 |
|
| 19020 |
\begin{align*}
x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.028 |
|
| 19021 |
\begin{align*}
R^{\prime }&=\left (1+t \right ) \left (1+R^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.030 |
|
| 19022 |
\begin{align*}
y^{\prime }&=y^{2} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.030 |
|
| 19023 |
\begin{align*}
x^{2}-y^{\prime } x&=y \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.030 |
|
| 19024 |
\begin{align*}
\left (1+x^{2}+y^{2}\right ) y^{\prime }+2 y x +x^{2}+3&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.031 |
|
| 19025 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-2 \left (x +1\right ) y&=y^{{5}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.032 |
|
| 19026 |
\begin{align*}
y^{\prime } x -2 y&=x^{3} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.032 |
|
| 19027 |
\begin{align*}
x \left (x +1\right ) y^{\prime }&=\left (x +1\right ) \left (x^{2}-1\right )+\left (x^{2}+x -1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.033 |
|
| 19028 |
\begin{align*}
x {y^{\prime }}^{2}+2 y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.033 |
|
| 19029 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+y^{2}-2 y x +1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.033 |
|
| 19030 |
\begin{align*}
x^{\prime }&=\frac {x}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.033 |
|
| 19031 |
\begin{align*}
\left (x -6 y\right )^{2} y^{\prime }+a +2 y x -6 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.035 |
|
| 19032 |
\begin{align*}
4 y y^{\prime \prime }&=a y+b y^{2}+c y^{3}+3 {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.036 |
|
| 19033 |
\begin{align*}
2 x y^{\prime \prime } y^{\prime \prime \prime }&=-a^{2}+{y^{\prime \prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.036 |
|
| 19034 |
\begin{align*}
y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.037 |
|
| 19035 |
\begin{align*}
y^{\prime }&=-x +y \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.037 |
|
| 19036 |
\begin{align*}
2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.038 |
|
| 19037 |
\begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.039 |
|
| 19038 |
\begin{align*}
x^{2} \left (-y+y^{\prime } x \right )&=y \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.040 |
|
| 19039 |
\begin{align*}
x^{3} y^{\prime }&=x^{4}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.040 |
|
| 19040 |
\begin{align*}
y^{\prime \prime }&=-\frac {a \left (n -1\right ) \sin \left (2 a x \right ) y^{\prime }}{\cos \left (a x \right )^{2}}-\frac {n \,a^{2} \left (\left (n -1\right ) \sin \left (a x \right )^{2}+\cos \left (a x \right )^{2}\right ) y}{\cos \left (a x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.042 |
|
| 19041 |
\begin{align*}
3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.042 |
|
| 19042 |
\begin{align*}
\sin \left (\theta \right ) \theta ^{\prime }+\cos \left (\theta \right )-t \,{\mathrm e}^{-t}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.043 |
|
| 19043 |
\begin{align*}
\left ({\mathrm e}^{v}+1\right ) \cos \left (u \right )+{\mathrm e}^{v} \left (1+\sin \left (u \right )\right ) v^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.043 |
|
| 19044 |
\begin{align*}
{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.043 |
|
| 19045 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.043 |
|
| 19046 |
\begin{align*}
4 y^{\prime \prime }-25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.043 |
|
| 19047 |
\begin{align*}
y^{\prime \prime }+9 y&=2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.044 |
|
| 19048 |
\begin{align*}
\left (y^{2}+x y^{2}\right ) y^{\prime }+x^{2}-x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.044 |
|
| 19049 |
\begin{align*}
y^{\prime }-\frac {y-x f \left (x^{2}+a y^{2}\right )}{x +a y f \left (x^{2}+a y^{2}\right )}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.045 |
|
| 19050 |
\begin{align*}
y^{\prime }&=4+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.046 |
|
| 19051 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.046 |
|
| 19052 |
\begin{align*}
y^{\prime \prime }-y^{\prime }+{\mathrm e}^{2 x} y&=x \,{\mathrm e}^{2 x}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.046 |
|
| 19053 |
\begin{align*}
y^{\prime }&=\frac {\cos \left (x \right )}{\sin \left (y\right )} \\
y \left (\pi \right ) &= \frac {\pi }{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.047 |
|
| 19054 |
\begin{align*}
y^{\prime }+4 y&=8 \cos \left (4 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.047 |
|
| 19055 |
\begin{align*}
y^{\prime }+\cot \left (x \right ) y&=2 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.047 |
|
| 19056 |
\begin{align*}
y^{\prime \prime } x -3 y^{\prime }+\frac {3 y}{x}&=2+x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.048 |
|
| 19057 |
\begin{align*}
y^{\prime }+y^{2}&=x^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.048 |
|
| 19058 |
\begin{align*}
y^{\prime }&=\frac {y}{1+t}+4 t^{2}+4 t \\
y \left (1\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.049 |
|
| 19059 |
\begin{align*}
y {y^{\prime }}^{2}&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.050 |
|
| 19060 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=y^{2} x^{2}+y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.050 |
|
| 19061 |
\begin{align*}
y \left (1+y^{2}\right )+x \left (y^{2}-x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.053 |
|
| 19062 |
\begin{align*}
y^{\prime }&=y x +x \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.053 |
|
| 19063 |
\begin{align*}
y^{\prime }&=-\frac {2 x y}{x^{2}+1} \\
y \left (2\right ) &= -5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.053 |
|
| 19064 |
\begin{align*}
2 y y^{\prime } x&=y^{2}-2 x^{3} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.053 |
|
| 19065 |
\begin{align*}
2 y x +y^{2}+\left (2 y x +x^{2}-2 y^{2} x^{2}-2 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.054 |
|
| 19066 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} t & 0\le t \le 3 \\ t +2 & 3<t \end {array}\right . \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
3.054 |
|
| 19067 |
\begin{align*}
x^{2} y^{\prime }+2 y x&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.055 |
|
| 19068 |
\begin{align*}
y^{\prime }-\frac {x}{x^{2}+1}&=-\frac {x y}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.055 |
|
| 19069 |
\begin{align*}
\left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.056 |
|
| 19070 |
\begin{align*}
\left (2 x^{3} y^{3}-x \right ) y^{\prime }+2 x^{3} y^{3}-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.056 |
|
| 19071 |
\begin{align*}
y^{\prime } \cos \left (y\right )&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.056 |
|
| 19072 |
\begin{align*}
t^{2} y^{\prime \prime }+3 y^{\prime } t +5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.056 |
|
| 19073 |
\begin{align*}
y-2 y^{\prime } x -y {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.056 |
|
| 19074 |
\begin{align*}
y^{\prime }&=1+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.057 |
|
| 19075 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=\sin \left (2 x \right ) \\
y \left (\frac {\pi }{4}\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.057 |
|
| 19076 |
\begin{align*}
-a y+y^{\prime }+2 y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.058 |
|
| 19077 |
\begin{align*}
y^{\prime \prime }+\omega ^{2} y&=t \left (\sin \left (\omega t \right )+\cos \left (\omega t \right )\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.058 |
|
| 19078 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=y-2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.058 |
|
| 19079 |
\begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.059 |
|
| 19080 |
\begin{align*}
y^{\prime }+4 y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.060 |
|
| 19081 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.061 |
|
| 19082 |
\begin{align*}
y^{\prime \prime }&=a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.062 |
|
| 19083 |
\begin{align*}
y^{\prime }+y x&=x^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.062 |
|
| 19084 |
\begin{align*}
y^{2}-1+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.063 |
|
| 19085 |
\begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.063 |
|
| 19086 |
\begin{align*}
2 t y+3 t^{2}+\left (t^{2}-1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.063 |
|
| 19087 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x}+\lambda \right ) y^{\prime }-a \lambda \,{\mathrm e}^{2 \lambda x} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.064 |
|
| 19088 |
\begin{align*}
r^{\prime } \sin \left (t \right )+r \cos \left (t \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.064 |
|
| 19089 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.065 |
|
| 19090 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=\delta \left (t -\pi \right )+\delta \left (t -3 \pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.066 |
|
| 19091 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=\delta \left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.068 |
|
| 19092 |
\begin{align*}
\left ({\mathrm e}^{x}+{\mathrm e}^{-x}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.068 |
|
| 19093 |
\begin{align*}
y^{\prime }&=\frac {2-{\mathrm e}^{x}}{3+2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.069 |
|
| 19094 |
\begin{align*}
{\mathrm e}^{2 y}+\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.069 |
|
| 19095 |
\begin{align*}
y^{\prime }&=x y \left (3+y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.069 |
|
| 19096 |
\begin{align*}
x^{2} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.069 |
|
| 19097 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.069 |
|
| 19098 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{5}+y+\frac {y^{3}}{5}&=\cos \left (w t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
3.069 |
|
| 19099 |
\begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.069 |
|
| 19100 |
\begin{align*}
y^{\prime } t&=2 y-t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.069 |
|