| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 23701 |
\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*} |
✗ |
✓ |
✓ |
✗ |
9.074 |
|
| 23702 |
\begin{align*}
y y^{\prime } x +x^{6}-2 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.074 |
|
| 23703 |
\begin{align*}
\frac {y}{x}+\cos \left (y\right )+\left (\ln \left (x \right )-x \sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.077 |
|
| 23704 |
\begin{align*}
y^{\prime }&=\frac {-32 y x -72 x^{3}+32 x^{2}-32 x +64 y^{3}+48 y^{2} x^{2}-192 x y^{2}+12 x^{4} y-96 x^{3} y+192 x^{2} y+x^{6}-12 x^{5}+48 x^{4}}{64 y+16 x^{2}-64 x +64} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.078 |
|
| 23705 |
\begin{align*}
9 x -4 y+4-\left (1+2 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.079 |
|
| 23706 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (b \,x^{2}+c x +d \right ) y}{a \,x^{2} \left (x -1\right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.086 |
|
| 23707 |
\begin{align*}
\sqrt {x^{2}-1}\, y^{\prime }-\sqrt {-1+y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.088 |
|
| 23708 |
\begin{align*}
y^{\prime }+{y^{\prime }}^{3}&={\mathrm e}^{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.090 |
|
| 23709 |
\begin{align*}
x +y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.092 |
|
| 23710 |
\begin{align*}
x \left (a +b y\right ) y^{\prime }&=c y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.096 |
|
| 23711 |
\begin{align*}
y^{\prime }&=\frac {y^{{3}/{2}}}{y^{{3}/{2}}+x^{2}-2 y x +y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.096 |
|
| 23712 |
\begin{align*}
\left (10 x^{3} y^{2}+x^{2} y+2 x \right ) y^{\prime }+5 x^{2} y^{3}+x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.099 |
|
| 23713 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+n \left (n -1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
9.099 |
|
| 23714 |
\begin{align*}
4 {y^{\prime }}^{2}-2 \left (y+3 y^{\prime } x \right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.101 |
|
| 23715 |
\begin{align*}
\left (5-2 x -3 y\right ) y^{\prime }+1-2 x -3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.105 |
|
| 23716 |
\begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.114 |
|
| 23717 |
\begin{align*}
x y \left (x^{2}+1\right ) y^{\prime }-y^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.118 |
|
| 23718 |
\begin{align*}
\left (4-x -3 y\right ) y^{\prime }+3-x -3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.121 |
|
| 23719 |
\begin{align*}
\left (2 x^{2} y \ln \left (y\right )-x \right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.124 |
|
| 23720 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.125 |
|
| 23721 |
\begin{align*}
y^{\prime }&=-\frac {x^{2}-1-4 \sqrt {x^{2}-2 x +1+8 y}}{4 \left (x +1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.127 |
|
| 23722 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=\frac {1}{y} \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.134 |
|
| 23723 |
\begin{align*}
x \csc \left (\frac {y}{x}\right )-y+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.141 |
|
| 23724 |
\begin{align*}
x +y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.141 |
|
| 23725 |
\begin{align*}
x^{\prime }&=\tan \left (x\right ) \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.144 |
|
| 23726 |
\begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.145 |
|
| 23727 |
\begin{align*}
x^{\prime \prime }+t^{2} x^{\prime }&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.146 |
|
| 23728 |
\begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.147 |
|
| 23729 |
\begin{align*}
\left (1+a \left (x +y\right )\right )^{n} y^{\prime }+a \left (x +y\right )^{n}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.153 |
|
| 23730 |
\begin{align*}
1+{y^{\prime }}^{2}+2 y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.157 |
|
| 23731 |
\begin{align*}
y^{\prime }&=-y^{3} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.161 |
|
| 23732 |
\begin{align*}
\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime \prime }+2 \sin \left (x \right ) y^{\prime }-\left (\cos \left (x \right )+\sin \left (x \right )\right ) y&={\mathrm e}^{x} \left (\cos \left (x \right )-\sin \left (x \right )\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.167 |
|
| 23733 |
\begin{align*}
a \,{\mathrm e}^{y}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.170 |
|
| 23734 |
\begin{align*}
2 \sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=y^{3} \left (\cos \left (x \right ) x -\sin \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.171 |
|
| 23735 |
\begin{align*}
y^{\prime }&=\frac {\left ({\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x +x^{3}\right ) {\mathrm e}^{\frac {y}{x}}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.175 |
|
| 23736 |
\begin{align*}
y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.177 |
|
| 23737 |
\begin{align*}
y^{2} x^{2}-y+\left (2 x^{3} y+x \right ) y^{\prime }&=0 \\
y \left (2\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.183 |
|
| 23738 |
\begin{align*}
x^{2} y^{\prime }+\cos \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {5 \pi }{4} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
9.183 |
|
| 23739 |
\begin{align*}
y \left ({\mathrm e}^{x}+2 y x \right )-{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.184 |
|
| 23740 |
\begin{align*}
y^{\prime }&=\frac {-18 y x -6 x^{3}-18 x +27 y^{3}+27 y^{2} x^{2}+9 x^{4} y+x^{6}}{27 y+9 x^{2}+27} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.185 |
|
| 23741 |
\begin{align*}
y+2&=\left (2 x +y-4\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.189 |
|
| 23742 |
\begin{align*}
\left (x +2 y+y^{2}\right ) y^{\prime }+y \left (1+y\right )+\left (x +y\right )^{2} y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.190 |
|
| 23743 |
\begin{align*}
y^{\prime }&=\frac {\left (x +1\right )^{2}-2 y}{2 y} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
9.193 |
|
| 23744 |
\begin{align*}
y y^{\prime } x&=x^{2}-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.207 |
|
| 23745 |
\begin{align*}
x^{5} y^{\prime }+y^{5}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.207 |
|
| 23746 |
\begin{align*}
y^{\prime }&=\frac {t^{2}+y^{2}}{t y} \\
y \left ({\mathrm e}\right ) &= 2 \,{\mathrm e} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.212 |
|
| 23747 |
\begin{align*}
\left (x -a \right ) \left (-b +x \right ) y^{\prime }+k \left (y-a \right ) \left (y-b \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.216 |
|
| 23748 |
\begin{align*}
y+7+\left (2 x +y+3\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.218 |
|
| 23749 |
\begin{align*}
x -2 y+3&=\left (x -2 y+1\right ) y^{\prime } \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.222 |
|
| 23750 |
\begin{align*}
\left (x^{2} \left (-a^{2}+1\right )+y^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+x^{2}+\left (-a^{2}+1\right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.223 |
|
| 23751 |
\begin{align*}
\left ({\mathrm e}^{x^{2}}-k^{2}\right ) x^{3} y-y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.226 |
|
| 23752 |
\begin{align*}
y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.231 |
|
| 23753 |
\begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
9.232 |
|
| 23754 |
\begin{align*}
x +y+\left (x +2 y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.233 |
|
| 23755 |
\begin{align*}
\frac {y}{t}+\ln \left (y\right )+\left (\frac {t}{y}+\ln \left (t \right )\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.235 |
|
| 23756 |
\begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.239 |
|
| 23757 |
\begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2}+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.240 |
|
| 23758 |
\begin{align*}
y^{\prime \prime }+\left (\frac {1}{2 x}-2\right ) y^{\prime }-\frac {35 y}{16 x^{2}}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
9.240 |
|
| 23759 |
\begin{align*}
y^{\prime \prime }&=y^{3}-y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.242 |
|
| 23760 |
\begin{align*}
\left (6 x -2 y\right ) y^{\prime }&=2+3 x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.243 |
|
| 23761 |
\begin{align*}
y x -\left (y^{4}+x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.243 |
|
| 23762 |
\begin{align*}
2 x +2 y-1+\left (x +y-2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.244 |
|
| 23763 |
\begin{align*}
y^{\prime }&=\frac {\left (1+t \right )^{2}}{\left (1+y\right )^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.244 |
|
| 23764 |
\begin{align*}
x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.244 |
|
| 23765 |
\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*} |
✓ |
✓ |
✓ |
✗ |
9.245 |
|
| 23766 |
\begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=x^{2}+16 \ln \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.246 |
|
| 23767 |
\begin{align*}
y^{\prime } x +y \left (1+y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.247 |
|
| 23768 |
\begin{align*}
y^{\prime }&=\tan \left (a x +b y+c \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.247 |
|
| 23769 |
\begin{align*}
y^{\prime }&=2 \sqrt {2 x +y-3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.253 |
|
| 23770 |
\begin{align*}
y^{\prime }&=\frac {2 y^{8}}{y^{5}+2 y^{6}+2 y^{2}+16 y^{4} x +32 y^{6} x^{2}+2+24 x y^{2}+96 x^{2} y^{4}+128 x^{3} y^{6}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.260 |
|
| 23771 |
\begin{align*}
x^{\prime }+t x^{3}+\frac {x}{t}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.263 |
|
| 23772 |
\begin{align*}
y^{\prime }&=\sqrt {\sin \left (y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.263 |
|
| 23773 |
\begin{align*}
y y^{\prime }+x +f \left (x^{2}+y^{2}\right ) g \left (x \right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.265 |
|
| 23774 |
\begin{align*}
\left (1+y^{2}\right ) \cos \left (x \right )&=2 \left (1+\sin \left (x \right )^{2}\right ) y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.267 |
|
| 23775 |
\begin{align*}
y^{\prime }&=\frac {y}{y^{3}-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.270 |
|
| 23776 |
\begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.276 |
|
| 23777 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.278 |
|
| 23778 |
\begin{align*}
x^{\prime \prime }+36 x&=0 \\
x \left (0\right ) &= 5 \\
x \left (\frac {\pi }{12}\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.279 |
|
| 23779 |
\begin{align*}
y y^{\prime } \sin \left (x \right )^{2}+y^{2} \cos \left (x \right ) \sin \left (x \right )-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.283 |
|
| 23780 |
\begin{align*}
\frac {\sin \left (\frac {x}{y}\right )}{y}-\frac {y \cos \left (\frac {y}{x}\right )}{x^{2}}+1+\left (\frac {\cos \left (\frac {y}{x}\right )}{x}-\frac {x \sin \left (\frac {x}{y}\right )}{y^{2}}+\frac {1}{y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.288 |
|
| 23781 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.288 |
|
| 23782 |
\begin{align*}
x^{2} y^{\prime }+y x +\sqrt {y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.294 |
|
| 23783 |
\begin{align*}
x \left (x +6 y^{2}\right ) y^{\prime }+y x -3 y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.297 |
|
| 23784 |
\begin{align*}
-y+y^{\prime } x&=x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.300 |
|
| 23785 |
\begin{align*}
y^{\prime } x&=x \tan \left (\frac {y}{x}\right )+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.302 |
|
| 23786 |
\begin{align*}
y^{\prime }&=\left (4 x +y+2\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.308 |
|
| 23787 |
\begin{align*}
x^{2} \left (y^{\prime }+y^{2}\right )-7 y x +7&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.309 |
|
| 23788 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=\frac {y^{2}}{x} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.309 |
|
| 23789 |
\begin{align*}
y^{\prime }&=x \sqrt {y} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.310 |
|
| 23790 |
\begin{align*}
y^{\prime \prime } x +\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.313 |
|
| 23791 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.314 |
|
| 23792 |
\begin{align*}
2 x -y+\left (-x +2 y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.319 |
|
| 23793 |
\begin{align*}
y^{\prime }&=\sqrt {y^{2}-9} \\
y \left (2\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.328 |
|
| 23794 |
\begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.330 |
|
| 23795 |
\begin{align*}
\left (y+2\right ) x +y \left (2+x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.332 |
|
| 23796 |
\begin{align*}
y^{\prime }-y x&=y^{{3}/{2}} x \\
y \left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.333 |
|
| 23797 |
\begin{align*}
\left (-2+2 y\right ) y^{\prime }&=2 x -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.334 |
|
| 23798 |
\begin{align*}
y^{\prime } x&=y+x \sec \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.336 |
|
| 23799 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \left ({\mathrm e}^{x}-{\mathrm e}^{y}\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
9.343 |
|
| 23800 |
\begin{align*}
y^{\prime \prime }+\sin \left (y\right )&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= \beta \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
9.351 |
|