| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 22201 |
\begin{align*}
\left (1+\cos \left (\theta \right )\right ) r^{\prime }&=-r \sin \left (\theta \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.691 |
|
| 22202 |
\begin{align*}
y^{\prime } \left (1+\sinh \left (x \right )\right ) \sinh \left (y\right )+\cosh \left (x \right ) \left (\cosh \left (y\right )-1\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.692 |
|
| 22203 |
\begin{align*}
y^{\prime } x&=\left (y x +1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.694 |
|
| 22204 |
\begin{align*}
\left (\operatorname {a0} +\operatorname {a1} \cos \left (x \right )^{2}+\operatorname {a2} \csc \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
9.695 |
|
| 22205 |
\begin{align*}
x +y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.699 |
|
| 22206 |
\begin{align*}
a^{2} {y^{\prime \prime }}^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.700 |
|
| 22207 |
\begin{align*}
y^{\prime }&=\frac {y}{y-y^{3}+2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.702 |
|
| 22208 |
\begin{align*}
y^{\prime } x&=y+x \sin \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.704 |
|
| 22209 |
\begin{align*}
b y+a x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.708 |
|
| 22210 |
\begin{align*}
x^{\prime }&=\frac {2 x}{1+t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.708 |
|
| 22211 |
\begin{align*}
y^{\prime }&=3 x y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.723 |
|
| 22212 |
\begin{align*}
x \left (-y x +1\right )^{2} y^{\prime }+\left (y^{2} x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.724 |
|
| 22213 |
\begin{align*}
x \left (x +y\right ) y^{\prime }&=y \left (x -y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.728 |
|
| 22214 |
\begin{align*}
y^{\prime }&=\frac {2 x y}{3 x^{2}-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.728 |
|
| 22215 |
\begin{align*}
x^{\prime }&=\frac {2 x y +x^{2}}{3 y^{2}+2 x y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.732 |
|
| 22216 |
\begin{align*}
6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.735 |
|
| 22217 |
\begin{align*}
\left ({\mathrm e}^{x^{2}}-k^{2}\right ) x^{3} y-y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.747 |
|
| 22218 |
\begin{align*}
y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.749 |
|
| 22219 |
\begin{align*}
-a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.750 |
|
| 22220 |
\begin{align*}
x^{2} \ln \left (a x \right ) \left (y^{\prime }-y^{2}\right )&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.757 |
|
| 22221 |
\begin{align*}
y^{\prime } x&=2 x -y+a \,x^{n} \left (x -y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.758 |
|
| 22222 |
\begin{align*}
\left (2 x +2 y+3\right ) y^{\prime }&=x +y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.758 |
|
| 22223 |
\begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.761 |
|
| 22224 |
\begin{align*}
\left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (a_{1} x +b_{1} \right ) y+a_{0} x +b_{0}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.763 |
|
| 22225 |
\begin{align*}
t x^{\prime }&=-x+t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.764 |
|
| 22226 |
\begin{align*}
x -y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.766 |
|
| 22227 |
\begin{align*}
y^{\prime }&=\frac {y \left (-\ln \left (x \right )-x \ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right ) x^{2} y\right )}{x \ln \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.770 |
|
| 22228 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \,x^{n} g \left (x \right ) y+x^{n -1} a n +a^{2} x^{2 n} \left (g \left (x \right )-f \left (x \right )\right ) \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
9.771 |
|
| 22229 |
\begin{align*}
y^{\prime } x&=a \,x^{4} y^{3}+\left (b \,x^{2}-1\right ) y+c x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.772 |
|
| 22230 |
\begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.780 |
|
| 22231 |
\begin{align*}
\frac {\left (3 x^{3}-x y^{2}\right ) y^{\prime }}{y^{3}+3 x^{2} y}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.785 |
|
| 22232 |
\begin{align*}
y^{\prime }&=\frac {y^{3}-2 x^{3}}{x y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.789 |
|
| 22233 |
\begin{align*}
2 t x^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.793 |
|
| 22234 |
\begin{align*}
2 x \left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (a \left (2-k \right ) x^{2}+b \left (1-k \right ) x -c k \right ) y^{\prime }+\lambda \,x^{1+k} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.794 |
|
| 22235 |
\begin{align*}
y^{\prime } x -5 y-x \sqrt {y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.797 |
|
| 22236 |
\begin{align*}
3 y^{2} y^{\prime } x&=2 x -y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.813 |
|
| 22237 |
\begin{align*}
x {y^{\prime }}^{2}-y y^{\prime }+a x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.816 |
|
| 22238 |
\begin{align*}
{y^{\prime }}^{2}+y^{2} y^{\prime } x +y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.817 |
|
| 22239 |
\begin{align*}
\left (-x^{2}+1\right ) z^{\prime }-x z&=a x z^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.821 |
|
| 22240 |
\begin{align*}
y^{\prime } x&=\left (-y x +1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.823 |
|
| 22241 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=5-y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.825 |
|
| 22242 |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=y x +x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.828 |
|
| 22243 |
\begin{align*}
y^{\prime }-\sqrt {\frac {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}{b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.833 |
|
| 22244 |
\begin{align*}
\left (x +\frac {x}{x^{2}+y^{2}}\right ) y^{\prime }+y-\frac {y}{x^{2}+y^{2}}&=0 \\
y \left (1\right ) &= \sqrt {3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.836 |
|
| 22245 |
\begin{align*}
1+2 x+\left (-t^{2}+4\right ) x^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.841 |
|
| 22246 |
\begin{align*}
x^{\prime }+t x^{3}+\frac {x}{t}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.845 |
|
| 22247 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+a -y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.849 |
|
| 22248 |
\begin{align*}
y^{\prime }&=\frac {F \left (-\frac {-y^{2}+b}{x^{2}}\right ) x}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.860 |
|
| 22249 |
\begin{align*}
y^{\prime } x&=x^{2 n} f \left (x \right ) y^{2}+\left (a \,x^{n} f \left (x \right )-n \right ) y+f \left (x \right ) b \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.863 |
|
| 22250 |
\begin{align*}
y^{\prime }&=y^{2}+a x \sinh \left (b x \right )^{m} y+a \sinh \left (b x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.870 |
|
| 22251 |
\begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+a y^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
9.877 |
|
| 22252 |
\begin{align*}
y^{\prime } x +x y^{2}-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.877 |
|
| 22253 |
\begin{align*}
y^{\prime }-\frac {6 y}{x}&=7 x \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.883 |
|
| 22254 |
\begin{align*}
\left (a \cot \left (x \right )^{2}+b \cot \left (x \right ) \csc \left (x \right )+c \csc \left (x \right )^{2}\right ) y+k \cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.885 |
|
| 22255 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }-a -y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.888 |
|
| 22256 |
\begin{align*}
3 x \left (x +2 y\right ) y^{\prime }+x^{3}+3 y \left (2 x +y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.890 |
|
| 22257 |
\begin{align*}
{y^{\prime }}^{2}+y^{\prime \prime \prime } y^{\prime }&=2 {y^{\prime \prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.894 |
|
| 22258 |
\begin{align*}
y \left (y+2 x -2\right )-2 \left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.894 |
|
| 22259 |
\begin{align*}
{y^{\prime }}^{3}&=\left (a +b y+c y^{2}\right ) f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.900 |
|
| 22260 |
\begin{align*}
y x +\ln \left (y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.905 |
|
| 22261 |
\begin{align*}
a \,{\mathrm e}^{y}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.910 |
|
| 22262 |
\begin{align*}
\left (x +1\right ) y^{\prime }+y+\left (x +1\right )^{4} y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.912 |
|
| 22263 |
\begin{align*}
4 y^{6}+x^{3}&=6 x y^{5} y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.913 |
|
| 22264 |
\begin{align*}
x^{2 n +1} y^{\prime }-a y^{3}-b \,x^{3 n}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.915 |
|
| 22265 |
\begin{align*}
y^{\prime }&=\frac {2 x^{2}-4 x^{3} y+1+y^{2} x^{4}+x^{6} y^{3}-3 x^{5} y^{2}+3 x^{4} y-x^{3}}{x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.926 |
|
| 22266 |
\begin{align*}
y^{5} x^{2}+{\mathrm e}^{x^{3}} y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.927 |
|
| 22267 |
\begin{align*}
y^{\prime }+\frac {y}{\sqrt {-x^{2}+1}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.930 |
|
| 22268 |
\begin{align*}
a {y^{\prime }}^{3}&=27 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.934 |
|
| 22269 |
\begin{align*}
\left (3-x^{2} y\right ) y^{\prime }&=x y^{2}+4 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.940 |
|
| 22270 |
\begin{align*}
y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.943 |
|
| 22271 |
\begin{align*}
y^{\prime }+y&=\left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right . \\
y \left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.947 |
|
| 22272 |
\begin{align*}
3-y+2 y^{\prime } x&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.951 |
|
| 22273 |
\begin{align*}
x^{\prime }&=\frac {\left (4+2 t \right ) x}{\ln \left (x\right )} \\
x \left (0\right ) &= {\mathrm e} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.952 |
|
| 22274 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime }+6 x^{2} y&=6 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.960 |
|
| 22275 |
\begin{align*}
n y+\left (1-x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.962 |
|
| 22276 |
\begin{align*}
x y^{2}&=-y^{\prime } x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.968 |
|
| 22277 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.977 |
|
| 22278 |
\begin{align*}
y^{\prime }&=\frac {y^{3} {\mathrm e}^{-2 x}}{{\mathrm e}^{-x} y+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.980 |
|
| 22279 |
\begin{align*}
2 x y^{2}+2 x +\left (6 y^{3}+2 y+4 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.986 |
|
| 22280 |
\begin{align*}
\left (a +x \right ) \left (x +b \right ) y^{\prime }&=y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.988 |
|
| 22281 |
\begin{align*}
y^{\prime }&=\frac {x -y+2}{x +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.993 |
|
| 22282 |
\begin{align*}
x^{2} y^{\prime \prime }+a x y^{\prime }+x^{n} \left (b \,x^{n}+c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.997 |
|
| 22283 |
\begin{align*}
2 \left (x +1\right ) y^{\prime }+2 y+\left (x +1\right )^{4} y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.000 |
|
| 22284 |
\begin{align*}
y^{\prime }&=\frac {y^{2} \left (-2 y+2 x^{2}+2 x^{2} y+x^{4} y\right )}{x^{3} \left (x^{2}-y+x^{2} y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.001 |
|
| 22285 |
\begin{align*}
y^{\prime }&=\frac {y \left (-1+\ln \left (x \left (x +1\right )\right ) y x^{4}-\ln \left (x \left (x +1\right )\right ) x^{3}\right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.003 |
|
| 22286 |
\begin{align*}
x^{\prime }&=2 x-3 y \\
y^{\prime }&=x+y+2 z \\
z^{\prime }&=5 y-7 z \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.017 |
|
| 22287 |
\begin{align*}
y^{\prime }&=\lambda \arctan \left (x \right )^{n} y^{2}+a y+a b -b^{2} \lambda \arctan \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.019 |
|
| 22288 |
\begin{align*}
x^{2} y^{\prime }-y^{2}&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.020 |
|
| 22289 |
\begin{align*}
{\mathrm e}^{\frac {x}{y}}-\frac {y y^{\prime }}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.021 |
|
| 22290 |
\begin{align*}
x y \left (-y^{\prime } x +y\right )&=x +y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.021 |
|
| 22291 |
\begin{align*}
t^{2} y^{\prime }+2 t y-y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.023 |
|
| 22292 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \,{\mathrm e}^{\lambda x} f \left (x \right ) y+a \lambda \,{\mathrm e}^{\lambda x} \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
10.024 |
|
| 22293 |
\begin{align*}
y^{\prime }&=\sin \left (y\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.028 |
|
| 22294 |
\begin{align*}
2 t y+y^{2}-t^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.030 |
|
| 22295 |
\begin{align*}
y^{\prime }&=\frac {a^{3}+y^{2} a^{3}+2 a^{2} b x y+b^{2} x^{2} a +y^{3} a^{3}+3 a^{2} b x y^{2}+3 a \,b^{2} x^{2} y+b^{3} x^{3}}{a^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.031 |
|
| 22296 |
\begin{align*}
\sqrt {1+{y^{\prime \prime }}^{2}}\, \left (1-y^{\prime \prime \prime }\right )&=y^{\prime \prime } y^{\prime \prime \prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.036 |
|
| 22297 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime }+x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.046 |
|
| 22298 |
\begin{align*}
2 x y \left (4-y^{2}\right )+\left (-1+y\right ) \left (x^{2}+2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.051 |
|
| 22299 |
\begin{align*}
2 y x -\tan \left (y\right )+\left (x^{2}-x \sec \left (y\right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.054 |
|
| 22300 |
\begin{align*}
\left (x +1\right ) y^{\prime }&=1+y+\left (x +1\right ) \sqrt {1+y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.055 |
|