| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 17101 |
\begin{align*}
y^{\prime }&=-y^{2}+y x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.916 |
|
| 17102 |
\begin{align*}
y^{\prime }&=x \,{\mathrm e}^{y^{2}-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.918 |
|
| 17103 |
\begin{align*}
y {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.918 |
|
| 17104 |
\begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.918 |
|
| 17105 |
\begin{align*}
y^{\prime \prime }-\left (n \left (n +1\right ) k^{2} \operatorname {JacobiSN}\left (x , k\right )^{2}+b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.920 |
|
| 17106 |
\begin{align*}
2 x^{2}+8 y x +y^{2}+\left (2 x^{2}+\frac {x y^{3}}{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.921 |
|
| 17107 |
\begin{align*}
x^{\prime }&=-x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.921 |
|
| 17108 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}-4 x_{2}+5 x_{3}+9 x_{4} \\
x_{2}^{\prime }&=-2 x_{1}-5 x_{2}+4 x_{3}+12 x_{4} \\
x_{3}^{\prime }&=-2 x_{1}-x_{3}+2 x_{4} \\
x_{4}^{\prime }&=-2 x_{2}+2 x_{3}+3 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.921 |
|
| 17109 |
\begin{align*}
x^{2} {y^{\prime }}^{2}+2 a x y^{\prime }+a^{2}+x^{2}-2 a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.923 |
|
| 17110 |
\begin{align*}
\left (1+\sqrt {x +y}\right ) y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.923 |
|
| 17111 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}-\ln \left (y\right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.924 |
|
| 17112 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+2&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.924 |
|
| 17113 |
\begin{align*}
y^{\prime }&=1+\frac {1}{x}-\frac {1}{y^{2}+2}-\frac {1}{x \left (y^{2}+2\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.924 |
|
| 17114 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.924 |
|
| 17115 |
\begin{align*}
y^{\prime }&=\sin \left (x \right ) y+{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.925 |
|
| 17116 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.926 |
|
| 17117 |
\begin{align*}
y^{\prime }+y&=2 \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.926 |
|
| 17118 |
\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*} |
✓ |
✓ |
✓ |
✗ |
2.928 |
|
| 17119 |
\begin{align*}
\left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }-3 x y^{2}+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.928 |
|
| 17120 |
\begin{align*}
y^{\prime }-\frac {2 y}{x}&=-x^{2}+1 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.928 |
|
| 17121 |
\begin{align*}
y^{\prime } \sin \left (y\right )&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.929 |
|
| 17122 |
\begin{align*}
y^{\prime }+a y^{2}-b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.929 |
|
| 17123 |
\begin{align*}
2 y y^{\prime }-x y^{2}-x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.929 |
|
| 17124 |
\begin{align*}
y-1-y x +y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.930 |
|
| 17125 |
\begin{align*}
y^{\prime }&={\mathrm e}^{3 y+2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.931 |
|
| 17126 |
\begin{align*}
i^{\prime }&=p \left (t \right ) i \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.933 |
|
| 17127 |
\begin{align*}
y^{\prime }&=-\frac {2 x y}{x^{2}+1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.933 |
|
| 17128 |
\begin{align*}
y^{\prime }+\cot \left (x \right ) y&=2 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.935 |
|
| 17129 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=-10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.937 |
|
| 17130 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.937 |
|
| 17131 |
\begin{align*}
y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.937 |
|
| 17132 |
\begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.938 |
|
| 17133 |
\begin{align*}
L i^{\prime }+R i&=e \\
i \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.938 |
|
| 17134 |
\begin{align*}
y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.939 |
|
| 17135 |
\begin{align*}
y^{\prime }&=\frac {y}{x \left (-1+F \left (y x \right ) y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.939 |
|
| 17136 |
\begin{align*}
x \left (x -1\right ) y^{\prime }+y&=x^{2} \left (2 x -1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.939 |
|
| 17137 |
\begin{align*}
y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.940 |
|
| 17138 |
\begin{align*}
2 x^{2} y+x^{3} y^{\prime }&=10 \sin \left (x \right ) \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.940 |
|
| 17139 |
\begin{align*}
y y^{\prime }&=x y^{2}-9 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.941 |
|
| 17140 |
\begin{align*}
-y+y^{\prime } x&=x^{2} {\mathrm e}^{-x^{2}} \\
y \left (3\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.941 |
|
| 17141 |
\begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.941 |
|
| 17142 |
\begin{align*}
y^{\prime } x -y+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.941 |
|
| 17143 |
\begin{align*}
2 y x +y^{2}+\left (2 y x +x^{2}-2 y^{2} x^{2}-2 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.942 |
|
| 17144 |
\begin{align*}
x {y^{\prime }}^{2}+y y^{\prime }-y^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.942 |
|
| 17145 |
\begin{align*}
y^{\prime \prime }-\alpha ^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.942 |
|
| 17146 |
\begin{align*}
z^{\prime }&=z \tan \left (y \right )+\sin \left (y \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.943 |
|
| 17147 |
\begin{align*}
y^{\prime }&=-x^{2}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.943 |
|
| 17148 |
\begin{align*}
v^{\prime }+2 u v&=2 u \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.943 |
|
| 17149 |
\begin{align*}
m y^{\prime \prime }+k y&=F \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.943 |
|
| 17150 |
\begin{align*}
r^{\prime }&=\frac {r^{2}}{x} \\
r \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.944 |
|
| 17151 |
\begin{align*}
y^{2}+y x -y^{\prime } x&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.944 |
|
| 17152 |
\begin{align*}
x \left (x^{2}+1\right ) y^{\prime }+2 y&=\left (x^{2}+1\right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.944 |
|
| 17153 |
\begin{align*}
y^{\prime }&=\frac {x +y+2}{x +1} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.945 |
|
| 17154 |
\begin{align*}
\left (a +x^{2}+y^{2}\right ) y y^{\prime }+x \left (y^{2}+x^{2}-a \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.947 |
|
| 17155 |
\begin{align*}
y+2 y^{\prime }&=3 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.948 |
|
| 17156 |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{x -1}-\frac {x y}{x -1}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.948 |
|
| 17157 |
\begin{align*}
\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.950 |
|
| 17158 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{2 x}+b \,{\mathrm e}^{x}+c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.951 |
|
| 17159 |
\begin{align*}
y^{\prime } x&=\left (-2 x^{2}+1\right ) \tan \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.951 |
|
| 17160 |
\begin{align*}
\left (1+y\right ) y^{\prime \prime }&=3 {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.952 |
|
| 17161 |
\begin{align*}
x^{\prime }&=k \left (A -x\right )^{2} \\
x \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.954 |
|
| 17162 |
\begin{align*}
\left (x -y\right ) y^{\prime \prime }-h \left (y^{\prime }\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.954 |
|
| 17163 |
\begin{align*}
3 y^{\prime }+\frac {y \left (a^{2}+x^{2}\right )}{x \left (-a^{2}+x^{2}\right )}&=\frac {x \left (-a^{2}+3 x^{2}\right )}{y^{2} \left (-a^{2}+x^{2}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.954 |
|
| 17164 |
\begin{align*}
y^{\prime }&=\frac {\left (-1+y \ln \left (x \right )\right )^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.955 |
|
| 17165 |
\begin{align*}
y^{\prime }-\sqrt {3}\, y&=\sin \left (t \right )+\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.955 |
|
| 17166 |
\begin{align*}
y^{\prime }+5 y&=3 \,{\mathrm e}^{-5 t} \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.957 |
|
| 17167 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{5}+y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.957 |
|
| 17168 |
\begin{align*}
y&=x {y^{\prime }}^{2}+y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.958 |
|
| 17169 |
\begin{align*}
y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.959 |
|
| 17170 |
\begin{align*}
x \left (x^{3}-1\right ) y^{\prime }-2 x y^{2}+y+x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.959 |
|
| 17171 |
\begin{align*}
y^{\prime }-2 y x&=3 x \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.959 |
|
| 17172 |
\begin{align*}
y^{\prime } x +y&=3 y x \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.960 |
|
| 17173 |
\begin{align*}
x^{4} \left (y^{\prime }-y^{2}\right )&=a +b \,{\mathrm e}^{\frac {k}{x}}+c \,{\mathrm e}^{\frac {2 k}{x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.960 |
|
| 17174 |
\begin{align*}
x_{1}^{\prime }&=x_{2}+x_{4} \\
x_{2}^{\prime }&=-x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{2}+x_{3} \\
x_{4}^{\prime }&=x_{1}-x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.960 |
|
| 17175 |
\begin{align*}
2 x +x {y^{\prime }}^{2}&=2 y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.961 |
|
| 17176 |
\begin{align*}
L y^{\prime }+R y&=E \sin \left (\omega x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.961 |
|
| 17177 |
\begin{align*}
-y-3 y^{\prime } x +\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.961 |
|
| 17178 |
\begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.961 |
|
| 17179 |
\begin{align*}
y^{\prime }&=1+\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.961 |
|
| 17180 |
\begin{align*}
y^{\prime }&=y+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.962 |
|
| 17181 |
\begin{align*}
y^{\prime }-\frac {y}{t}&=\ln \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.963 |
|
| 17182 |
\begin{align*}
y^{4} {y^{\prime }}^{3}-6 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.963 |
|
| 17183 |
\begin{align*}
y^{\prime }&=-y+3 t \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.963 |
|
| 17184 |
\begin{align*}
R^{\prime }&=\frac {R}{t}+t \,{\mathrm e}^{-t} \\
R \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.964 |
|
| 17185 |
\begin{align*}
y+y^{\prime }&=2-{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.964 |
|
| 17186 |
\begin{align*}
y^{\prime }&=\left (x -y\right )^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.967 |
|
| 17187 |
\begin{align*}
x^{6} {y^{\prime }}^{2}-2 y^{\prime } x -4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.968 |
|
| 17188 |
\begin{align*}
y^{\prime }&={\mathrm e}^{2 y+10 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.968 |
|
| 17189 |
\begin{align*}
z^{\prime \prime }+z-2 z^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.969 |
|
| 17190 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x +12\right ) y&=x^{2}+x \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.969 |
|
| 17191 |
\begin{align*}
y^{\prime }-5 y&={\mathrm e}^{x} x^{2}-x \,{\mathrm e}^{5 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.970 |
|
| 17192 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.971 |
|
| 17193 |
\begin{align*}
\cos \left (y\right ) y^{\prime }&=-\frac {t \sin \left (y\right )}{t^{2}+1} \\
y \left (1\right ) &= \frac {\pi }{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.972 |
|
| 17194 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=4 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.973 |
|
| 17195 |
\begin{align*}
a x y^{\prime \prime }+\left (b x +3 a \right ) y^{\prime }+3 b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.973 |
|
| 17196 |
\begin{align*}
x^{6} {y^{\prime }}^{2}&=8 y^{\prime } x +16 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.974 |
|
| 17197 |
\begin{align*}
2 y-6 x +\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.974 |
|
| 17198 |
\begin{align*}
y^{\prime } x +y&=x \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.975 |
|
| 17199 |
\begin{align*}
x {y^{\prime }}^{2}-y y^{\prime }+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.975 |
|
| 17200 |
\begin{align*}
x^{2} \left (y^{\prime }+y^{2}\right )-x \left (2+x \right ) y+x +2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.976 |
|