| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 18101 |
\begin{align*}
y^{\prime }&=2 y^{2} x^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.435 |
|
| 18102 |
\begin{align*}
y^{\prime }&=\cos \left (x \right )+\tan \left (x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.436 |
|
| 18103 |
\begin{align*}
y^{\prime \prime }&=-\frac {4 \sin \left (3 x \right ) y}{\sin \left (x \right )^{3}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.437 |
|
| 18104 |
\begin{align*}
y^{\prime }&=4 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.439 |
|
| 18105 |
\begin{align*}
y^{\prime }&=1-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.439 |
|
| 18106 |
\begin{align*}
x^{\prime }+2 x y&={\mathrm e}^{-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.440 |
|
| 18107 |
\begin{align*}
5 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.440 |
|
| 18108 |
\begin{align*}
x^{2} y^{\prime }&=a +b x +c \,x^{2}+y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.441 |
|
| 18109 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=\sin \left (2 x \right ) \\
y \left (\frac {\pi }{4}\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.441 |
|
| 18110 |
\begin{align*}
y^{\prime \prime }-a y^{\prime }+b \,{\mathrm e}^{2 a x} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.441 |
|
| 18111 |
\begin{align*}
y^{\prime }+y x&=4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.441 |
|
| 18112 |
\begin{align*}
\left (a \,x^{2}+b x +c \right ) \left (-y+y^{\prime } x \right )-y^{2}+x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.443 |
|
| 18113 |
\begin{align*}
\left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }&=3 x y^{2}-x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.443 |
|
| 18114 |
\begin{align*}
y^{\prime }&=\frac {t^{2}+y^{2}}{1+t +y^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
3.444 |
|
| 18115 |
\begin{align*}
y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.445 |
|
| 18116 |
\begin{align*}
\left (4-y^{2}\right ) y^{\prime }&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.445 |
|
| 18117 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime }+c \left (a \,{\mathrm e}^{\lambda x}+b -c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.446 |
|
| 18118 |
\begin{align*}
\left (2 x -1\right ) \left (-1+y\right )+\left (2+x \right ) \left (x -3\right ) y^{\prime }&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.448 |
|
| 18119 |
\begin{align*}
y^{\prime }&=\frac {y}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.449 |
|
| 18120 |
\begin{align*}
2 x +y \cos \left (y x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.450 |
|
| 18121 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=9 \,{\mathrm e}^{2 t} \operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.451 |
|
| 18122 |
\begin{align*}
2 y+\left (x^{2}+1\right ) \arctan \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.451 |
|
| 18123 |
\begin{align*}
y^{\prime }-\cot \left (x \right ) y+\frac {1}{\sin \left (x \right )}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.452 |
|
| 18124 |
\begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.452 |
|
| 18125 |
\begin{align*}
12 y y^{\prime \prime }-15 {y^{\prime }}^{2}+8 y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.452 |
|
| 18126 |
\begin{align*}
x^{2} y^{\prime \prime }+a x y^{\prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.452 |
|
| 18127 |
\begin{align*}
b \tan \left (x \right )^{2} y-2 \csc \left (2 x \right ) \left (1-a \sin \left (x \right )^{2}\right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.453 |
|
| 18128 |
\begin{align*}
y^{\prime }+\frac {y}{t -3}&=\frac {1}{t -1} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.453 |
|
| 18129 |
\begin{align*}
1+3 x \sin \left (y\right )-x^{2} y^{\prime } \cos \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.453 |
|
| 18130 |
\begin{align*}
3 y^{2} y^{\prime }&=2 x -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.454 |
|
| 18131 |
\begin{align*}
y y^{\prime }+x y^{2}-4 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.454 |
|
| 18132 |
\begin{align*}
y^{\prime }+\tan \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.454 |
|
| 18133 |
\begin{align*}
x^{\prime }&=4 t^{3} x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.454 |
|
| 18134 |
\begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.456 |
|
| 18135 |
\begin{align*}
m y^{\prime \prime }+k y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.457 |
|
| 18136 |
\begin{align*}
-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.458 |
|
| 18137 |
\begin{align*}
m^{\prime }&=-\frac {k}{m^{2}} \\
m \left (0\right ) &= m_{0} \\
\end{align*} |
✓ |
✗ |
✓ |
✓ |
3.459 |
|
| 18138 |
\begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.459 |
|
| 18139 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.460 |
|
| 18140 |
\begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\frac {\operatorname {Heaviside}\left (t -\frac {3}{2}\right )}{2}-\frac {\operatorname {Heaviside}\left (t -\frac {5}{2}\right )}{2} \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.461 |
|
| 18141 |
\begin{align*}
y^{\prime \prime }-16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.461 |
|
| 18142 |
\begin{align*}
y^{\prime } x +y&=x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.462 |
|
| 18143 |
\begin{align*}
x^{\prime }+x \tan \left (t \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.463 |
|
| 18144 |
\begin{align*}
\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.464 |
|
| 18145 |
\begin{align*}
y^{\prime }&=5 \,{\mathrm e}^{x^{2}+20 y}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.464 |
|
| 18146 |
\begin{align*}
y^{\prime }&=\frac {1}{x \left (x y^{2}+1+x \right ) y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.464 |
|
| 18147 |
\begin{align*}
y^{\prime }&=\frac {x}{-y+1+y^{4}+2 y^{2} x^{2}+x^{4}+y^{6}+3 x^{2} y^{4}+3 y^{2} x^{4}+x^{6}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.464 |
|
| 18148 |
\begin{align*}
y^{\prime }+q \left (x \right ) y&=0 \\
y \left (\textit {x\_0} \right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.464 |
|
| 18149 |
\begin{align*}
t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
3.465 |
|
| 18150 |
\begin{align*}
6 y^{2} y^{\prime } x +x +2 y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.466 |
|
| 18151 |
\begin{align*}
y^{\prime }+3 y&=3 y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.467 |
|
| 18152 |
\begin{align*}
3 x^{2}+4 y x +\left (2 x^{2}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.467 |
|
| 18153 |
\begin{align*}
y^{\prime } x&=x^{n} \ln \left (x \right )-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.468 |
|
| 18154 |
\begin{align*}
\sqrt {x^{2}+1}\, y^{\prime }&=2 x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.468 |
|
| 18155 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.469 |
|
| 18156 |
\begin{align*}
x^{2} {\mathrm e}^{y+x^{2}} \left (2 x^{2}+3\right )+4 x +\left (x^{3} {\mathrm e}^{y+x^{2}}-12 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.470 |
|
| 18157 |
\begin{align*}
t^{2} y+y^{\prime }&=t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.470 |
|
| 18158 |
\begin{align*}
y^{\prime } x +y \ln \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.471 |
|
| 18159 |
\begin{align*}
x^{\prime \prime }+64 x&=0 \\
x \left (0\right ) &= {\frac {3}{4}} \\
x^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.471 |
|
| 18160 |
\begin{align*}
y^{\prime }&=a y^{\frac {-1+a}{a}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.472 |
|
| 18161 |
\begin{align*}
3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.472 |
|
| 18162 |
\begin{align*}
y^{\prime }-\frac {2 t y}{t^{2}+1}&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.472 |
|
| 18163 |
\begin{align*}
y^{\prime }-{\mathrm e}^{x} y&=2 x \,{\mathrm e}^{{\mathrm e}^{x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.472 |
|
| 18164 |
\begin{align*}
\left (3 y^{2}+4 y\right ) y^{\prime }+2 x +\cos \left (x \right )&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.473 |
|
| 18165 |
\begin{align*}
x^{4} \left (y^{\prime }+y^{2}\right )+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.473 |
|
| 18166 |
\begin{align*}
x^{\prime }&=-3 x+3 y+z+5 \sin \left (2 t \right ) \\
y^{\prime }&=x-5 y-3 z+5 \cos \left (2 t \right ) \\
z^{\prime }&=-3 x+7 y+3 z+23 \,{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.473 |
|
| 18167 |
\begin{align*}
y^{2}+\left (y x +y^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.474 |
|
| 18168 |
\begin{align*}
y^{\prime }&=t y \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.475 |
|
| 18169 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{5}+y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.475 |
|
| 18170 |
\begin{align*}
2 y y^{\prime }&=y^{2}+t -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.476 |
|
| 18171 |
\begin{align*}
\sqrt {x^{2}+1}\, y^{\prime }-y&=2 \sqrt {x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.477 |
|
| 18172 |
\begin{align*}
y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.478 |
|
| 18173 |
\begin{align*}
\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime }&=2 y x -{\mathrm e}^{y}-x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.478 |
|
| 18174 |
\begin{align*}
x^{\prime }&=3 x+2 y+3 \\
y^{\prime }&=7 x+5 y+2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.478 |
|
| 18175 |
\begin{align*}
\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.478 |
|
| 18176 |
\begin{align*}
\ln \left (y\right ) x +y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.478 |
|
| 18177 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.480 |
|
| 18178 |
\begin{align*}
y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.480 |
|
| 18179 |
\begin{align*}
x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.481 |
|
| 18180 |
\begin{align*}
{\mathrm e}^{t} \sin \left (y\right )+\left (1+{\mathrm e}^{t} \cos \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.481 |
|
| 18181 |
\begin{align*}
y^{\prime }+y x \,{\mathrm e}^{x}&={\mathrm e}^{{\mathrm e}^{x} \left (1-x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.481 |
|
| 18182 |
\begin{align*}
y^{\prime }+y \ln \left (y\right )&=t y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.483 |
|
| 18183 |
\begin{align*}
y^{\prime }+2 y x&=x \,{\mathrm e}^{-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.484 |
|
| 18184 |
\begin{align*}
{\mathrm e}^{y^{2}} \left (2 y y^{\prime }+\frac {2}{x}\right )&=\frac {1}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.484 |
|
| 18185 |
\begin{align*}
y^{\prime }&=a \ln \left (x \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.484 |
|
| 18186 |
\begin{align*}
3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.485 |
|
| 18187 |
\begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.486 |
|
| 18188 |
\begin{align*}
2 y^{\prime \prime } x +6 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.486 |
|
| 18189 |
\begin{align*}
y^{\prime \prime }-2 x^{2} y-x^{4}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.486 |
|
| 18190 |
\begin{align*}
y^{\prime \prime } x -3 y^{\prime }+\frac {3 y}{x}&=2+x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.487 |
|
| 18191 |
\begin{align*}
x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (x -2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.487 |
|
| 18192 |
\begin{align*}
9 y^{2} x^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.488 |
|
| 18193 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.488 |
|
| 18194 |
\begin{align*}
1&=\left ({\mathrm e}^{y}+x \right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.488 |
|
| 18195 |
\begin{align*}
y^{\prime }&=y^{2}-x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.488 |
|
| 18196 |
\begin{align*}
2 x^{2} y+2 y+5+\left (2 x^{3}+2 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.488 |
|
| 18197 |
\begin{align*}
x -2 y x +{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.489 |
|
| 18198 |
\begin{align*}
g \left (y\right )+f \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.491 |
|
| 18199 |
\begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y \left (\pi \right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.491 |
|
| 18200 |
\begin{align*}
y^{\prime }-\frac {3 y}{x^{2}}&=\frac {1}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.492 |
|