| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 14801 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (a \,x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.786 |
|
| 14802 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.786 |
|
| 14803 |
\begin{align*}
y y^{\prime }&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.786 |
|
| 14804 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.787 |
|
| 14805 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.787 |
|
| 14806 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.787 |
|
| 14807 |
\begin{align*}
y^{\prime } x -3 y&=x^{3} \\
y \left (1\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.789 |
|
| 14808 |
\begin{align*}
y y^{\prime \prime }&=y^{2} y^{\prime }+{y^{\prime }}^{2} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.789 |
|
| 14809 |
\begin{align*}
z^{\prime }+5 y-2 z&=x \\
y^{\prime }+4 y+z&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.789 |
|
| 14810 |
\begin{align*}
y&=x \left (1+y^{\prime }\right )+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.789 |
|
| 14811 |
\begin{align*}
y^{\prime } x&=x^{3}+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.789 |
|
| 14812 |
\begin{align*}
a y y^{\prime \prime }+b y&=c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.790 |
|
| 14813 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }&=18 x -10 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.790 |
|
| 14814 |
\begin{align*}
y^{\prime }&=y^{2}-y-6 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.790 |
|
| 14815 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.791 |
|
| 14816 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }&=x +{\mathrm e}^{-4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.792 |
|
| 14817 |
\begin{align*}
i^{\prime }+2 i&=10 \,{\mathrm e}^{-2 t} \\
i \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.792 |
|
| 14818 |
\begin{align*}
5 {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.792 |
|
| 14819 |
\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*} |
✓ |
✓ |
✓ |
✓ |
1.793 |
|
| 14820 |
\begin{align*}
\frac {x+y \,{\mathrm e}^{y}}{x^{\prime }}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.794 |
|
| 14821 |
\begin{align*}
9 x^{2} y^{\prime \prime }-3 x \left (2 x^{2}+11\right ) y^{\prime }+\left (10 x^{2}+13\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.794 |
|
| 14822 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=\frac {1}{{\mathrm e}^{x}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.796 |
|
| 14823 |
\begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.796 |
|
| 14824 |
\begin{align*}
y^{\prime \prime }&=\operatorname {g3} \left (x \right )+\operatorname {g2} \left (x \right ) y+\operatorname {g1} \left (x \right ) y^{2}+\operatorname {g0} \left (x \right ) y^{3}+\left (\operatorname {f1} \left (x \right )+\operatorname {f0} \left (x \right ) y\right ) y^{\prime } \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.796 |
|
| 14825 |
\begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.796 |
|
| 14826 |
\begin{align*}
\left (1-y\right ) y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.796 |
|
| 14827 |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=2 x_{3} \\
x_{3}^{\prime }&=3 x_{4} \\
x_{4}^{\prime }&=4 x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.797 |
|
| 14828 |
\begin{align*}
2 y+y^{\prime }&={\mathrm e}^{-x^{2}-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.797 |
|
| 14829 |
\begin{align*}
x_{1}^{\prime }&=2 x_{2} \\
x_{2}^{\prime }&=-2 x_{1} \\
x_{3}^{\prime }&=-3 x_{4} \\
x_{4}^{\prime }&=3 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
x_{4} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.797 |
|
| 14830 |
\begin{align*}
5 {y^{\prime }}^{2}+6 y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.798 |
|
| 14831 |
\begin{align*}
1+y^{\prime }&=2 y \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.799 |
|
| 14832 |
\begin{align*}
x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.799 |
|
| 14833 |
\begin{align*}
3 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.799 |
|
| 14834 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=\frac {1}{{\mathrm e}^{x}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.799 |
|
| 14835 |
\begin{align*}
y^{\prime }&=2 y x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.799 |
|
| 14836 |
\begin{align*}
{y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.799 |
|
| 14837 |
\begin{align*}
4 y^{\prime \prime }&=\left (x^{2}+a \right ) y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.800 |
|
| 14838 |
\begin{align*}
x^{\prime }&=-14 x+39 y+78 \sinh \left (t \right ) \\
y^{\prime }&=-6 x+16 y+6 \cosh \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.800 |
|
| 14839 |
\begin{align*}
{y^{\prime }}^{2}+2 \left (1-x \right ) y^{\prime }-2 x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.801 |
|
| 14840 |
\begin{align*}
x \left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.801 |
|
| 14841 |
\begin{align*}
x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.801 |
|
| 14842 |
\begin{align*}
y^{\prime \prime }&=\left (1+2 \tan \left (x \right )^{2}\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.802 |
|
| 14843 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=x^{3} {\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.802 |
|
| 14844 |
\begin{align*}
y^{\prime } x -y f \left (y x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.803 |
|
| 14845 |
\begin{align*}
y y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.803 |
|
| 14846 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x -y&=0 \\
y \left (4\right ) &= 0 \\
y^{\prime }\left (4\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.803 |
|
| 14847 |
\begin{align*}
y^{\prime }+y x&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.803 |
|
| 14848 |
\begin{align*}
-2 y+a \,x^{2} y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.804 |
|
| 14849 |
\begin{align*}
y \left (6 y^{2}-x -1\right )+2 y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.805 |
|
| 14850 |
\begin{align*}
\left (x +1\right ) y^{\prime }+y \left (-x +y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.805 |
|
| 14851 |
\begin{align*}
x^{\prime }&={\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.805 |
|
| 14852 |
\begin{align*}
y a \,x^{3}-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.806 |
|
| 14853 |
\begin{align*}
\left (a \,x^{2}+b x +c \right )^{2} y^{\prime \prime }+\left (2 a x +k \right ) \left (a \,x^{2}+b x +c \right ) y^{\prime }+m y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.806 |
|
| 14854 |
\begin{align*}
y^{\prime }&=\tan \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.806 |
|
| 14855 |
\begin{align*}
y^{\prime }-x&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.806 |
|
| 14856 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.807 |
|
| 14857 |
\begin{align*}
y^{\prime }&=3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.809 |
|
| 14858 |
\begin{align*}
3 x^{2} y^{\prime \prime }-2 y^{\prime } x -8 y&=3 x +5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.809 |
|
| 14859 |
\begin{align*}
y^{\prime \prime }+9 y&=5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.810 |
|
| 14860 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (a \,x^{2}+b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.810 |
|
| 14861 |
\begin{align*}
x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }-x \left (x^{2}+3\right ) y^{\prime }-2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.811 |
|
| 14862 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+{\mathrm e}^{c t} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-2 x_{3} \\
x_{3}^{\prime }&=3 x_{1}+2 x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.811 |
|
| 14863 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.811 |
|
| 14864 |
\begin{align*}
y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.811 |
|
| 14865 |
\begin{align*}
x^{3}-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.812 |
|
| 14866 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (1-x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.812 |
|
| 14867 |
\begin{align*}
\left (-a^{2}+4 b \right ) y+12 x^{5} y^{\prime }+4 x^{6} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.813 |
|
| 14868 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }-b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.813 |
|
| 14869 |
\begin{align*}
x^{\prime }&=2 x+4 y-2 z-2 \sinh \left (t \right ) \\
y^{\prime }&=4 x+2 y-2 z+10 \cosh \left (t \right ) \\
z^{\prime }&=-x+3 y+z+5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.813 |
|
| 14870 |
\begin{align*}
w^{\prime }&=\left (3-w\right ) \left (w+1\right ) \\
w \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.813 |
|
| 14871 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{x^{2}}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.813 |
|
| 14872 |
\begin{align*}
y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 a x +y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.814 |
|
| 14873 |
\begin{align*}
x^{2} y^{\prime }&=y^{2} x^{2}+a \ln \left (x \right )^{2}+b \ln \left (x \right )+c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.815 |
|
| 14874 |
\begin{align*}
N^{\prime }&=N-9 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.815 |
|
| 14875 |
\begin{align*}
y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.815 |
|
| 14876 |
\begin{align*}
-y+2 y^{\prime } x +x^{2} \ln \left (x \right ) y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=2 x^{3} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.816 |
|
| 14877 |
\begin{align*}
y^{\prime \prime }&=-\frac {b^{2} y}{\left (a^{2}+x^{2}\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.816 |
|
| 14878 |
\begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )-4 y y^{\prime }-4 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.816 |
|
| 14879 |
\begin{align*}
y^{\prime }&=-\frac {1}{2 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.817 |
|
| 14880 |
\begin{align*}
y^{\prime }&=\left (a +b x +y\right )^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.819 |
|
| 14881 |
\begin{align*}
x^{\prime }&=-7 x+10 y+18 \,{\mathrm e}^{t} \\
y^{\prime }&=-10 x+9 y+37 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.819 |
|
| 14882 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y&=\tan \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.820 |
|
| 14883 |
\begin{align*}
y^{\prime }&=2 \sqrt {y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.820 |
|
| 14884 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.821 |
|
| 14885 |
\begin{align*}
y^{\prime }&=\left (x^{2}+y^{2}\right )^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.822 |
|
| 14886 |
\begin{align*}
y^{\prime }&=t +2 y \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.822 |
|
| 14887 |
\begin{align*}
2 x^{2} y+x^{3} y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.823 |
|
| 14888 |
\begin{align*}
-y+\left (x +1\right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.823 |
|
| 14889 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.823 |
|
| 14890 |
\begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=x^{{1}/{4}} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.823 |
|
| 14891 |
\begin{align*}
x +2 y y^{\prime }&=x {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.825 |
|
| 14892 |
\begin{align*}
y^{\prime \prime }&=f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.825 |
|
| 14893 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +29 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.825 |
|
| 14894 |
\begin{align*}
y^{\prime }-y&=2 x -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.826 |
|
| 14895 |
\begin{align*}
y^{\prime \prime }+w^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.827 |
|
| 14896 |
\begin{align*}
y^{\prime }&=a y^{2}+2 a b \tan \left (x \right ) y+b \left (a b -1\right ) \tan \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.827 |
|
| 14897 |
\begin{align*}
y^{\prime }-3 y&=12 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.827 |
|
| 14898 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=\frac {2}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.828 |
|
| 14899 |
\begin{align*}
y^{\prime \prime }&=\frac {y^{\prime }}{x +1}-\frac {\left (1+3 x \right ) y}{4 x^{2} \left (x +1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.828 |
|
| 14900 |
\begin{align*}
y^{\prime }&=\frac {x^{3}+2 y}{x^{3}+x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.828 |
|