| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 14101 |
\begin{align*}
a^{2} y+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.747 |
|
| 14102 |
\begin{align*}
y^{\prime }&=\frac {t^{2}}{\left (t^{3}+1\right ) y} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✗ |
✓ |
✓ |
2.747 |
|
| 14103 |
\begin{align*}
y^{\prime }&=1+x +y+y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.748 |
|
| 14104 |
\begin{align*}
{y^{\prime }}^{2}-y y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.748 |
|
| 14105 |
\begin{align*}
4 y x +3 y^{2}-x +x \left (x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.748 |
|
| 14106 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-x +y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.749 |
|
| 14107 |
\begin{align*}
y^{\prime }&=1-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.750 |
|
| 14108 |
\begin{align*}
y+2 y^{3} y^{\prime }&=\left (x +4 y \ln \left (y\right )\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.750 |
|
| 14109 |
\begin{align*}
x^{2} y^{\prime }+x \left (2+x \right ) y&=x \left (1-{\mathrm e}^{-2 x}\right )-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.750 |
|
| 14110 |
\begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.750 |
|
| 14111 |
\begin{align*}
y^{\prime }&=x^{3} y^{3}-y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.750 |
|
| 14112 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x +1 \\
y \left (0\right ) &= 1 \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.750 |
|
| 14113 |
\begin{align*}
y^{\prime }&=y \left (2-y\right ) \left (4-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.751 |
|
| 14114 |
\begin{align*}
x^{3}+\frac {y}{x}+\left (y^{2}+\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.752 |
|
| 14115 |
\begin{align*}
y^{\prime }&=\frac {y+t}{t -y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.753 |
|
| 14116 |
\begin{align*}
y^{\prime }&=\frac {\left (1-y \,{\mathrm e}^{y x}\right ) {\mathrm e}^{-y x}}{x} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.753 |
|
| 14117 |
\begin{align*}
6 y^{\prime } y^{2} x +x +2 y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.753 |
|
| 14118 |
\begin{align*}
y^{2}+3+\left (2 y x -4\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.753 |
|
| 14119 |
\begin{align*}
1+s^{2}-\sqrt {t}\, s^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.753 |
|
| 14120 |
\begin{align*}
2 \cos \left (x \right ) y-1+\sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.753 |
|
| 14121 |
\begin{align*}
x_{1}^{\prime }&=47 x_{1}-8 x_{2}+5 x_{3}-5 x_{4} \\
x_{2}^{\prime }&=-10 x_{1}+32 x_{2}+18 x_{3}-2 x_{4} \\
x_{3}^{\prime }&=139 x_{1}-40 x_{2}-167 x_{3}-121 x_{4} \\
x_{4}^{\prime }&=-232 x_{1}+64 x_{2}+360 x_{3}+248 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.754 |
|
| 14122 |
\begin{align*}
3 y^{\prime } y^{2} x&=3 x^{4}+y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.755 |
|
| 14123 |
\begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} 4 & 0\le t <2 \\ 0 & 2\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.755 |
|
| 14124 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.755 |
|
| 14125 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=2 \,{\mathrm e}^{x}-10 \sin \left (x \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.755 |
|
| 14126 |
\begin{align*}
y^{\prime }+2 y \left (1-x \sqrt {y}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.756 |
|
| 14127 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{t} y}{1+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.756 |
|
| 14128 |
\begin{align*}
3 \left (2-y\right ) y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.757 |
|
| 14129 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.757 |
|
| 14130 |
\begin{align*}
y^{\prime }&=\cos \left (x \right )+\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.758 |
|
| 14131 |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.758 |
|
| 14132 |
\begin{align*}
y^{\prime }+1-x&=y \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.760 |
|
| 14133 |
\begin{align*}
\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.760 |
|
| 14134 |
\begin{align*}
y^{\prime }&=z \\
z^{\prime }&=w \\
w^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.760 |
|
| 14135 |
\begin{align*}
3 y+y^{\prime }&=-10 \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.762 |
|
| 14136 |
\begin{align*}
y^{\prime }&=\sin \left (x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.763 |
|
| 14137 |
\begin{align*}
y^{\prime }&=a \,x^{n -1}+b \,x^{2 n}+c y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.763 |
|
| 14138 |
\begin{align*}
x^{\prime \prime }-3 x^{\prime }+2 x&=\sin \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.764 |
|
| 14139 |
\begin{align*}
\frac {y^{2}}{\left (x -y\right )^{2}}-\frac {1}{x}+\left (\frac {1}{y}-\frac {x^{2}}{\left (x -y\right )^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.764 |
|
| 14140 |
\begin{align*}
y^{\prime \prime }+x^{4} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.765 |
|
| 14141 |
\begin{align*}
y y^{\prime \prime }&=-b y^{2}-a y y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.765 |
|
| 14142 |
\begin{align*}
\left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.765 |
|
| 14143 |
\begin{align*}
y^{3}+4 \,{\mathrm e}^{x} y+\left (2 \,{\mathrm e}^{x}+3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.766 |
|
| 14144 |
\begin{align*}
y^{\prime }-\tan \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.766 |
|
| 14145 |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.766 |
|
| 14146 |
\begin{align*}
2 y^{\prime } x -y+\ln \left (y^{\prime }\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.766 |
|
| 14147 |
\begin{align*}
x^{3} y^{\prime }+3+\left (3-2 x \right ) x^{2} y-x^{6} y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.767 |
|
| 14148 |
\begin{align*}
y^{\prime }&=y-y^{3} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
2.767 |
|
| 14149 |
\begin{align*}
x^{\prime \prime }+x^{\prime }&=3 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.767 |
|
| 14150 |
\begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.767 |
|
| 14151 |
\begin{align*}
y^{\prime } x +y&=3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.767 |
|
| 14152 |
\begin{align*}
x^{\prime \prime }&=\frac {1}{\sqrt {t +4}} \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.768 |
|
| 14153 |
\begin{align*}
y&=y^{\prime } x -\sqrt {y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.768 |
|
| 14154 |
\begin{align*}
y+\left (y^{2} {\mathrm e}^{y}-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.768 |
|
| 14155 |
\begin{align*}
y^{\prime }&=16 y-8 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.768 |
|
| 14156 |
\begin{align*}
-y+y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.770 |
|
| 14157 |
\begin{align*}
3 x^{2} y y^{\prime }+1+2 x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.771 |
|
| 14158 |
\begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }-y \cos \left (x \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.771 |
|
| 14159 |
\begin{align*}
2 x^{2}-{\mathrm e}^{x} y-{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.771 |
|
| 14160 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & \operatorname {otherwise} \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.773 |
|
| 14161 |
\begin{align*}
y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.773 |
|
| 14162 |
\begin{align*}
y^{\prime }+\frac {y}{t -3}&=\frac {1}{t -1} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.773 |
|
| 14163 |
\begin{align*}
y^{\prime }+\sin \left (x \right ) y&=2 x \,{\mathrm e}^{\cos \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.773 |
|
| 14164 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.774 |
|
| 14165 |
\begin{align*}
y^{\prime }+4 y&={\mathrm e}^{-4 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.774 |
|
| 14166 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}-x_{2}+4 x_{3}+2 x_{4} \\
x_{2}^{\prime }&=-19 x_{1}-6 x_{2}+6 x_{3}+16 x_{4} \\
x_{3}^{\prime }&=-9 x_{1}-x_{2}+x_{3}+6 x_{4} \\
x_{4}^{\prime }&=-5 x_{1}-3 x_{2}+6 x_{3}+5 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.774 |
|
| 14167 |
\begin{align*}
y \left (6 y^{2}-x -1\right )+2 y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.775 |
|
| 14168 |
\begin{align*}
y^{\prime }+\frac {y \left (x +y\right )}{x +2 y-1}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.775 |
|
| 14169 |
\begin{align*}
u v-2 v+\left (-u^{2}+u \right ) v^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.775 |
|
| 14170 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (2 x^{2}-3 x \right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.776 |
|
| 14171 |
\begin{align*}
\left (-2 x^{2}+1\right ) y+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.776 |
|
| 14172 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1+x^{2}-y \,\operatorname {arccot}\left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.777 |
|
| 14173 |
\begin{align*}
y^{\prime }&=a \,x^{n} {\mathrm e}^{2 \lambda x} y^{2}+\left (b \,x^{n} {\mathrm e}^{\lambda x}-\lambda \right ) y+c \,x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.777 |
|
| 14174 |
\begin{align*}
5 y x +4 y^{2}+1+\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.777 |
|
| 14175 |
\begin{align*}
y^{\prime \prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.778 |
|
| 14176 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.778 |
|
| 14177 |
\begin{align*}
y^{\prime \prime }&=x^{2} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.778 |
|
| 14178 |
\begin{align*}
x \left (3+5 x -12 x y^{2}+4 x^{2} y\right ) y^{\prime }+\left (3+10 x -8 x y^{2}+6 x^{2} y\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.780 |
|
| 14179 |
\begin{align*}
x^{\prime }&=\ln \left (x^{2}+1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.781 |
|
| 14180 |
\begin{align*}
3 \left (-1+y\right ) x +y+2+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.781 |
|
| 14181 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.782 |
|
| 14182 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.782 |
|
| 14183 |
\begin{align*}
y^{\prime }-\left (x +y\right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.782 |
|
| 14184 |
\begin{align*}
y^{\prime }-\tan \left (x \right ) y&=8 \sin \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.783 |
|
| 14185 |
\begin{align*}
x^{2} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.783 |
|
| 14186 |
\begin{align*}
6 x^{2} y-\left (x^{3}+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.783 |
|
| 14187 |
\begin{align*}
y^{\prime } x +3 y-10 x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.783 |
|
| 14188 |
\begin{align*}
y^{\prime }&=3 \left (y+7\right ) x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.784 |
|
| 14189 |
\begin{align*}
t r^{\prime }+r&=t \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.784 |
|
| 14190 |
\begin{align*}
y^{\prime }+\frac {2 x y}{x^{2}+1}&=4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.785 |
|
| 14191 |
\begin{align*}
y^{\prime } x -y f \left (y x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.785 |
|
| 14192 |
\begin{align*}
y^{\prime \prime }+a \,x^{n} y^{\prime }+b \,x^{n -1} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.785 |
|
| 14193 |
\begin{align*}
-y+y^{\prime } x&=2 x^{2} y \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.786 |
|
| 14194 |
\begin{align*}
y^{\prime }&=\sqrt {1-t^{2}-y^{2}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.786 |
|
| 14195 |
\begin{align*}
4 y^{\prime \prime }-25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.786 |
|
| 14196 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+3 x^{3} y&=6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.787 |
|
| 14197 |
\begin{align*}
y^{\prime }&=x \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.787 |
|
| 14198 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right ) \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.787 |
|
| 14199 |
\begin{align*}
y^{2} {y^{\prime }}^{3}-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.787 |
|
| 14200 |
\begin{align*}
y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (b \,x^{2 n}+c \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.788 |
|