| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 23701 |
\begin{align*}
y^{\prime }&=\frac {-4 y x +x^{3}+2 x^{2}-4 x -8}{-8 y+2 x^{2}+4 x -8} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.661 |
|
| 23702 |
\begin{align*}
4 x -y+\left (6 y-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.667 |
|
| 23703 |
\begin{align*}
\cos \left (x \right ) y+\left (2 y-\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.667 |
|
| 23704 |
\begin{align*}
1+\left (2 y-x^{2}\right ) {y^{\prime }}^{2}-2 x^{2} y {y^{\prime }}^{2}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
10.668 |
|
| 23705 |
\begin{align*}
y^{\prime \prime }+\sin \left (y\right )&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= \beta \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
10.668 |
|
| 23706 |
\begin{align*}
y^{\prime }&=\left (y-{\mathrm e}^{x}\right )^{2}+{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.676 |
|
| 23707 |
\begin{align*}
y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=12 \operatorname {Heaviside}\left (t \right )-12 \operatorname {Heaviside}\left (t -1\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. |
✓ |
✓ |
✓ |
✓ |
10.677 |
|
| 23708 |
\begin{align*}
-4 \cos \left (x \right ) y+4 \sin \left (x \right ) \cos \left (x \right )+\sec \left (x \right )^{2}+\left (4 y-4 \sin \left (x \right )\right ) y^{\prime }&=0 \\
y \left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.685 |
|
| 23709 |
\begin{align*}
y^{\prime \prime }-\left (x -1\right ) y^{\prime }+x^{2} y&=\tan \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
10.687 |
|
| 23710 |
\begin{align*}
\sqrt {1-y^{2}}+\left (x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.689 |
|
| 23711 |
\begin{align*}
y^{\prime }&=\sqrt {\frac {\ln \left (y+1\right )}{\sin \left (x \right )}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.690 |
|
| 23712 |
\begin{align*}
w^{\prime }&=3 w^{3}-12 w^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.692 |
|
| 23713 |
\begin{align*}
y x -\left (x^{2}+2 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.698 |
|
| 23714 |
\begin{align*}
y^{\prime }&=1-\frac {y}{x} \\
y \left (-\frac {1}{2}\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.704 |
|
| 23715 |
\begin{align*}
y^{\prime }&=\frac {-3 x^{2}-2 y^{2}}{4 y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.707 |
|
| 23716 |
\begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.707 |
|
| 23717 |
\begin{align*}
x \left (x^{2} y^{\prime }+2 y x \right ) y^{\prime \prime }+4 {y^{\prime }}^{2} x +8 x y y^{\prime }+4 y^{2}-1&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
10.712 |
|
| 23718 |
\begin{align*}
x^{2} y^{\prime }&=y^{2}+y x -x^{2} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.716 |
|
| 23719 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
10.722 |
|
| 23720 |
\begin{align*}
x y^{\prime }+x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.726 |
|
| 23721 |
\begin{align*}
x^{3}+y^{3}&=3 x y^{2} y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.731 |
|
| 23722 |
\begin{align*}
y^{\prime }&=y \left (y^{2}+y \,{\mathrm e}^{-x^{2}}+{\mathrm e}^{-2 x^{2}}\right ) {\mathrm e}^{2 x^{2}} x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.732 |
|
| 23723 |
\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*} |
✓ |
✓ |
✓ |
✗ |
10.740 |
|
| 23724 |
\begin{align*}
y+\left (1-a \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
10.741 |
|
| 23725 |
\begin{align*}
x^{\prime }&=2 x-3 y \\
y^{\prime }&=x+y+2 z \\
z^{\prime }&=5 y-7 z \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.743 |
|
| 23726 |
\begin{align*}
y+x y^{\prime }+\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*} |
✗ |
✓ |
✓ |
✗ |
10.744 |
|
| 23727 |
\begin{align*}
y^{\prime }&=\frac {x +2 y}{x +2 y+3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.744 |
|
| 23728 |
\begin{align*}
{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{4}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
10.750 |
|
| 23729 |
\begin{align*}
2 x y^{\prime }+4 y+a +\sqrt {a^{2}-4 b -4 c y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.751 |
|
| 23730 |
\begin{align*}
x y^{\prime }&=y+x \sin \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.758 |
|
| 23731 |
\begin{align*}
x^{n} y^{\prime \prime }+\left (a \,x^{n -1}+b x \right ) y^{\prime }+\left (a -1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
10.758 |
|
| 23732 |
\begin{align*}
x y^{\prime }&=a x +b y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.760 |
|
| 23733 |
\begin{align*}
x +y {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.760 |
|
| 23734 |
\begin{align*}
y^{\prime }&=\frac {x +y+4}{x +y-6} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.762 |
|
| 23735 |
\begin{align*}
y^{\prime }-\frac {2 y}{x +1}&=\left (x +1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.763 |
|
| 23736 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (-2\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.764 |
|
| 23737 |
\begin{align*}
y^{\prime } \sqrt {x \left (1-x \right ) \left (-a x +1\right )}&=\sqrt {y \left (1-y\right ) \left (1-a y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.766 |
|
| 23738 |
\begin{align*}
\left (y^{\prime }+1\right )^{3}&=\left (y^{\prime }-y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.766 |
|
| 23739 |
\begin{align*}
x -y+1+\left (2 y-2 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.767 |
|
| 23740 |
\begin{align*}
\cos \left (x \right ) y+\left (2 y-\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.767 |
|
| 23741 |
\begin{align*}
y \left (x -y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.768 |
|
| 23742 |
\begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=4 \cos \left (\ln \left (x +1\right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.775 |
|
| 23743 |
\begin{align*}
2 x +y-\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.779 |
|
| 23744 |
\begin{align*}
x y^{\prime }+2&=x^{3} \left (-1+y\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.780 |
|
| 23745 |
\begin{align*}
y^{\prime }&=\frac {\left (y x +1\right )^{3}}{x^{5}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.782 |
|
| 23746 |
\begin{align*}
y^{\prime }&=-\frac {x}{4 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.782 |
|
| 23747 |
\begin{align*}
\left (a +b +x +y\right )^{2} y^{\prime }&=2 \left (y+a \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.787 |
|
| 23748 |
\begin{align*}
y y^{\prime }+y x&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.792 |
|
| 23749 |
\begin{align*}
\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.796 |
|
| 23750 |
\begin{align*}
2 x y y^{\prime }&=y^{2}-2 x^{3} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.796 |
|
| 23751 |
\begin{align*}
x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x^{4} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.797 |
|
| 23752 |
\begin{align*}
\ln \left (y t \right )+\frac {t y^{\prime }}{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.802 |
|
| 23753 |
\begin{align*}
y^{\prime }&=\frac {-8 y x -x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.803 |
|
| 23754 |
\begin{align*}
y^{2}-x^{2}+x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.808 |
|
| 23755 |
\begin{align*}
{| y^{\prime }|}+{| y|}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.814 |
|
| 23756 |
\begin{align*}
\frac {2 t^{2} y \cos \left (t^{2}\right )-\sin \left (t^{2}\right ) y}{t^{2}}+\frac {\left (2 y t +\sin \left (t^{2}\right )\right ) y^{\prime }}{t}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.822 |
|
| 23757 |
\begin{align*}
y^{\prime }&=\frac {3 x^{5}+3 x^{2} y^{2}}{2 x^{3} y-2 y^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.822 |
|
| 23758 |
\begin{align*}
y-t y^{\prime }&=2 y^{2} \ln \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.825 |
|
| 23759 |
\begin{align*}
x y^{\prime }+x \tan \left (\frac {y}{x}\right )-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.833 |
|
| 23760 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (\frac {1}{2}\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.834 |
|
| 23761 |
\begin{align*}
y^{\prime }&=\frac {x +1+2 x^{6} \sqrt {1+4 x^{2} y}}{2 x^{3} \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
10.836 |
|
| 23762 |
\begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }&=\left (b +y\right ) \left (x +\sqrt {a^{2}+x^{2}}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.839 |
|
| 23763 |
\begin{align*}
\left (2 x +2 y+1\right ) y^{\prime }&=x +y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.839 |
|
| 23764 |
\begin{align*}
2 x y y^{\prime }+y^{2}&=-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.841 |
|
| 23765 |
\begin{align*}
3 x^{2} y y^{\prime }+1+2 x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.845 |
|
| 23766 |
\begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.851 |
|
| 23767 |
\begin{align*}
2 n y-2 x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
10.855 |
|
| 23768 |
\begin{align*}
a y \left (-1+y\right ) y^{\prime \prime }+\left (b y+c \right ) {y^{\prime }}^{2}+h \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.856 |
|
| 23769 |
\begin{align*}
y^{\prime }&=x \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.871 |
|
| 23770 |
\begin{align*}
y^{\prime }&=25+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.872 |
|
| 23771 |
\begin{align*}
x^{\prime }&=k \left (a -x\right ) \left (b -x\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.875 |
|
| 23772 |
\begin{align*}
y^{\prime }&=\frac {150 x^{3}+125 \sqrt {x}+125+125 y^{2}-100 x^{3} y-500 y \sqrt {x}+20 x^{6}+200 x^{{7}/{2}}+500 x +125 y^{3}-150 x^{3} y^{2}-750 y^{2} \sqrt {x}+60 x^{6} y+600 y x^{{7}/{2}}+1500 y x -8 x^{9}-120 x^{{13}/{2}}-600 x^{4}-1000 x^{{3}/{2}}}{125 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.876 |
|
| 23773 |
\begin{align*}
x y^{\prime }+y \ln \left (x \right )&=\ln \left (y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.879 |
|
| 23774 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \,x^{n} g \left (x \right ) y+a n \,x^{n -1}+a^{2} x^{2 n} \left (g \left (x \right )-f \left (x \right )\right ) \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
10.881 |
|
| 23775 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=x y \left (1+a y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.882 |
|
| 23776 |
\begin{align*}
{y^{\prime }}^{2} x +x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.888 |
|
| 23777 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=2 x^{{3}/{2}} \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.891 |
|
| 23778 |
\begin{align*}
\left (2 y-6 x \right ) y^{\prime }-y+3 x +2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.893 |
|
| 23779 |
\begin{align*}
x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.897 |
|
| 23780 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}-a b \,x^{n} {\mathrm e}^{\lambda x} y+b n \,x^{n -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.898 |
|
| 23781 |
\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*} |
✓ |
✓ |
✓ |
✗ |
10.900 |
|
| 23782 |
\begin{align*}
y^{\prime }&=\frac {y}{x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.907 |
|
| 23783 |
\begin{align*}
y^{\prime }&=1-\frac {y}{x} \\
y \left (\frac {3}{2}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.910 |
|
| 23784 |
\begin{align*}
\left (1-y^{2}\right ) {y^{\prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.911 |
|
| 23785 |
\begin{align*}
2 x y^{2}+\frac {x}{y^{2}}+4 x^{2} y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.912 |
|
| 23786 |
\begin{align*}
\left (-x +y\right ) y^{\prime }&=y-x +8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.917 |
|
| 23787 |
\begin{align*}
y t +y^{\prime }&=t y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.927 |
|
| 23788 |
\begin{align*}
\left (y y^{\prime }+n x \right )^{2}&=\left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
10.938 |
|
| 23789 |
\begin{align*}
3 x^{2} y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.939 |
|
| 23790 |
\begin{align*}
y^{\prime }&=\frac {\left (-y^{2}+4 a x \right )^{3}}{\left (-y^{2}+4 a x -1\right ) y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.945 |
|
| 23791 |
\begin{align*}
x^{2} \left ({y^{\prime }}^{2}-y^{2}\right )+y^{2}&=x^{4}+2 x y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.946 |
|
| 23792 |
\begin{align*}
y^{\prime }&=x^{2} y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.948 |
|
| 23793 |
\begin{align*}
y^{\prime }&=t^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
10.951 |
|
| 23794 |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.951 |
|
| 23795 |
\begin{align*}
x y^{\prime }-y+x \sec \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.956 |
|
| 23796 |
\begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.958 |
|
| 23797 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y&=2 x^{4} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.961 |
|
| 23798 |
\begin{align*}
2 y+x \left (x^{2} \ln \left (y\right )-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.962 |
|
| 23799 |
\begin{align*}
t \cot \left (x\right ) x^{\prime }&=-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.963 |
|
| 23800 |
\begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.963 |
|