| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 26201 |
\begin{align*}
y^{\prime }&=a \tan \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
369.077 |
|
| 26202 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (A \,x^{2}+B x +C \right ) y^{\prime }}{\left (x -a \right ) \left (-b +x \right ) \left (x -c \right )}-\frac {\left (\operatorname {DD} x +E \right ) y}{\left (x -a \right ) \left (-b +x \right ) \left (x -c \right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
370.119 |
|
| 26203 |
\begin{align*}
y^{\prime }&=\frac {y^{4}+2 x y^{3}-3 y^{2} x^{2}-2 x^{3} y}{2 y^{2} x^{2}-2 x^{3} y-2 x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
372.370 |
|
| 26204 |
\begin{align*}
x \left (x -1\right ) \left (x -a \right ) y^{\prime \prime }+\left (\left (\alpha +\beta +1\right ) x^{2}-\left (\alpha +\beta +1+a \left (\gamma +d \right )-a \right ) x +a \gamma \right ) y^{\prime }+\left (\alpha \beta x -q \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
382.410 |
|
| 26205 |
\begin{align*}
x^{4} y \left (3 y+2 y^{\prime } x \right )+x^{2} \left (4 y+3 y^{\prime } x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
386.216 |
|
| 26206 |
\begin{align*}
y^{\prime }&=\sqrt {25-y^{2}} \\
y \left (-4\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
386.914 |
|
| 26207 |
\begin{align*}
\left (\operatorname {c1} \,x^{4}+\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+x \left (\operatorname {b0} \,x^{2}+\operatorname {a0} \right ) y^{\prime }+\left (a^{2}-x^{2}\right )^{2} \left (b^{2}-x^{2}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
387.141 |
|
| 26208 |
\begin{align*}
x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
400.057 |
|
| 26209 |
\begin{align*}
x \left (2 x^{3}+y^{3}\right ) y^{\prime }&=\left (2 x^{3}-x^{2} y+y^{3}\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
409.238 |
|
| 26210 |
\begin{align*}
\left (2 x^{3}-x^{2} y+y^{3}\right ) y-x \left (2 x^{3}+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
409.511 |
|
| 26211 |
\begin{align*}
y^{\prime \prime }&=\frac {\left (2 b c \,x^{c} \left (x^{2}-1\right )+2 \left (-1+a \right ) x^{2}-2 a \right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (b^{2} c^{2} x^{2 c} \left (x^{2}-1\right )+b c \,x^{c +2} \left (2 a -c -1\right )-b c \,x^{c} \left (2 a -c +1\right )+x^{2} \left (a \left (-1+a \right )-v \left (v +1\right )\right )-a \left (1+a \right )\right ) y}{x^{2} \left (x^{2}-1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
413.648 |
|
| 26212 |
\begin{align*}
2 \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+3 \left (3 a \,x^{2}+2 b x +c \right ) y^{\prime }+\left (6 a x +2 b +\lambda \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
416.360 |
|
| 26213 |
\begin{align*}
\left (x -1\right ) \left (x -2\right ) y^{\prime \prime }-\left (2 x -3\right ) y^{\prime }+y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
416.378 |
|
| 26214 |
\begin{align*}
y^{\prime }&=y^{2}-x \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
445.490 |
|
| 26215 |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime }+\alpha y^{2}+\beta x y+\frac {b \left (a +\beta \right )}{\alpha }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
451.221 |
|
| 26216 |
\begin{align*}
y+x y^{2}-\left (x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
471.696 |
|
| 26217 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }-\left (-\lambda ^{2}+x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
473.723 |
|
| 26218 |
\begin{align*}
\left (\operatorname {c1} x +\operatorname {c0} \right ) y+\left (\operatorname {b2} \,x^{2}+\operatorname {b1} x +\operatorname {b0} \right ) y^{\prime }+\left (\operatorname {a1} -x \right ) \left (\operatorname {a2} -x \right ) \left (\operatorname {a3} -x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
478.043 |
|
| 26219 |
\begin{align*}
2 \left (y^{\prime } x +y\right )^{3}-y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
479.025 |
|
| 26220 |
\begin{align*}
x \left (\left (m -1\right ) \left (A x +B \right ) y+m \left (d \,x^{2}+e x +F \right )\right ) y^{\prime }&=\left (A \left (1-n \right ) x -B n \right ) y^{2}+\left (d \left (2-n \right ) x^{2}+e \left (1-n \right ) x -F n \right ) y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
490.552 |
|
| 26221 |
\begin{align*}
x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
497.112 |
|
| 26222 |
\begin{align*}
2 x^{3} {y^{\prime }}^{3}+6 x^{2} y {y^{\prime }}^{2}-\left (1-6 y x \right ) y y^{\prime }+2 y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
504.702 |
|
| 26223 |
\begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }+y&=\frac {6+x}{x^{2}} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
509.012 |
|
| 26224 |
\begin{align*}
\left (a \sqrt {1+{y^{\prime }}^{2}}-y^{\prime } x \right ) y^{\prime \prime }-{y^{\prime }}^{2}-1&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
524.511 |
|
| 26225 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2}+\sin \left (t \right ) \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+\tan \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -1 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
530.147 |
|
| 26226 |
\begin{align*}
x^{\prime \prime }&=x-x^{3} \\
x \left (0\right ) &= \frac {\sqrt {2}}{2} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
552.603 |
|
| 26227 |
\begin{align*}
y^{\prime }&=a \cot \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
586.570 |
|
| 26228 |
\begin{align*}
{y^{\prime }}^{3}+\left (2+x \right ) {\mathrm e}^{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
590.660 |
|
| 26229 |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime }+\alpha y^{2}+\beta x y+\gamma &=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
597.354 |
|
| 26230 |
\begin{align*}
c y+b x y^{\prime }+\left (a \,x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
612.651 |
|
| 26231 |
\begin{align*}
-x^{\prime \prime }&=\arctan \left (x\right ) \\
x \left (0\right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
616.861 |
|
| 26232 |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime \prime }+\left (2 n +1\right ) a x y^{\prime }+c y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
651.777 |
|
| 26233 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x -\left (v +2\right ) \left (v -1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
653.674 |
|
| 26234 |
\begin{align*}
y y^{\prime }-y&=\frac {A}{\sqrt {x}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
702.291 |
|
| 26235 |
\begin{align*}
y^{\prime } x +y&=y^{\prime } \sqrt {y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
748.331 |
|
| 26236 |
\begin{align*}
a y+y y^{\prime }+y^{\prime \prime }&=y^{3} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
833.285 |
|
| 26237 |
\begin{align*}
{y^{\prime }}^{4} x -2 y {y^{\prime }}^{3}+12 x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
874.486 |
|
| 26238 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\left (\alpha \gamma +\beta \right ) x +\beta \lambda \right ) y^{\prime }-\left (x \alpha +\beta \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
885.732 |
|
| 26239 |
\begin{align*}
y^{\prime \prime }&=a \sqrt {b y^{2}+{y^{\prime }}^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
938.819 |
|
| 26240 |
\begin{align*}
y y^{\prime }-y&=\frac {2 a^{2}}{\sqrt {8 a^{2}+x^{2}}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
952.985 |
|
| 26241 |
\begin{align*}
y^{\prime \prime }&=a \sqrt {b y^{2}+{y^{\prime }}^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1039.573 |
|
| 26242 |
\begin{align*}
y^{\prime \prime }&=-\left (\frac {1-\operatorname {a1} -\operatorname {b1}}{x -\operatorname {c1}}+\frac {1-\operatorname {a2} -\operatorname {b2}}{x -\operatorname {c2}}+\frac {1-\operatorname {a3} -\operatorname {b3}}{x -\operatorname {c3}}\right ) y^{\prime }-\frac {\left (\frac {\operatorname {a1} \operatorname {b1} \left (\operatorname {c1} -\operatorname {c3} \right ) \left (\operatorname {c1} -\operatorname {c2} \right )}{x -\operatorname {c1}}+\frac {\operatorname {a2} \operatorname {b2} \left (\operatorname {c2} -\operatorname {c1} \right ) \left (\operatorname {c2} -\operatorname {c3} \right )}{x -\operatorname {c2}}+\frac {\operatorname {a3} \operatorname {b3} \left (\operatorname {c3} -\operatorname {c2} \right ) \left (\operatorname {c3} -\operatorname {c1} \right )}{x -\operatorname {c3}}\right ) y}{\left (x -\operatorname {c1} \right ) \left (x -\operatorname {c2} \right ) \left (x -\operatorname {c3} \right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1052.560 |
|
| 26243 |
\begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{2+2 y^{4}-4 y^{2} x^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 y^{2} x^{4}-2 x^{6}}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{2+2 y^{4}-4 y^{2} x^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 y^{2} x^{4}-2 x^{6}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1093.359 |
|
| 26244 |
\begin{align*}
y^{\prime }-y y^{\prime \prime }&=n \sqrt {{y^{\prime }}^{2}+a^{2} y^{\prime \prime }} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1118.642 |
|
| 26245 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (\lambda ^{3}+x^{3}\right ) y^{\prime }-\left (\lambda ^{2}-\lambda x +x^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1133.063 |
|
| 26246 |
\begin{align*}
y {y^{\prime \prime }}^{2}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1150.613 |
|
| 26247 |
\begin{align*}
y y^{\prime }-y&=A \sqrt {x}+2 A^{2}+\frac {B}{\sqrt {x}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
1173.286 |
|
| 26248 |
\begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {3 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
1176.888 |
|
| 26249 |
\begin{align*}
y^{\prime \prime }&=-\left (\frac {\left (1-\operatorname {al1} -\operatorname {bl1} \right ) \operatorname {b1}}{\operatorname {b1} x -\operatorname {a1}}+\frac {\left (1-\operatorname {al2} -\operatorname {bl2} \right ) \operatorname {b2}}{\operatorname {b2} x -\operatorname {a2}}+\frac {\left (1-\operatorname {al3} -\operatorname {bl3} \right ) \operatorname {b3}}{\operatorname {b3} x -\operatorname {a3}}\right ) y^{\prime }-\frac {\left (\frac {\operatorname {al1} \operatorname {bl1} \left (\operatorname {a1} \operatorname {b2} -\operatorname {a2} \operatorname {b1} \right ) \left (-\operatorname {a1} \operatorname {b3} +\operatorname {a3} \operatorname {b1} \right )}{\operatorname {b1} x -\operatorname {a1}}+\frac {\operatorname {al2} \operatorname {bl2} \left (\operatorname {a2} \operatorname {b3} -\operatorname {a3} \operatorname {b2} \right ) \left (\operatorname {a1} \operatorname {b2} -\operatorname {a2} \operatorname {b1} \right )}{\operatorname {b2} x -\operatorname {a2}}+\frac {\operatorname {al3} \operatorname {bl3} \left (-\operatorname {a1} \operatorname {b3} +\operatorname {a3} \operatorname {b1} \right ) \left (\operatorname {a2} \operatorname {b3} -\operatorname {a3} \operatorname {b2} \right )}{\operatorname {b3} x -\operatorname {a3}}\right ) y}{\left (\operatorname {b1} x -\operatorname {a1} \right ) \left (\operatorname {b2} x -\operatorname {a2} \right ) \left (\operatorname {b3} x -\operatorname {a3} \right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1271.608 |
|
| 26250 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (x^{2} \left (\left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right )+\left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )+\left (x^{2}-\operatorname {a3} \right ) \left (x^{2}-\operatorname {a1} \right )\right )-\left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )\right ) y^{\prime }}{x \left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )}-\frac {\left (A \,x^{2}+B \right ) y}{x \left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1297.271 |
|
| 26251 |
\begin{align*}
y y^{\prime }-y&=A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (n +1\right ) \left (n +3\right ) A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
1321.608 |
|
| 26252 |
\begin{align*}
y y^{\prime }-y&=A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (2 n +3\right ) A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
1347.311 |
|
| 26253 |
\begin{align*}
\left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (a -x \right ) \left (b -x \right ) \left (c -x \right ) \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (a -x \right )^{2} \left (b -x \right )^{2} \left (c -x \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1450.929 |
|
| 26254 |
\begin{align*}
y y^{\prime }-y&=2 A^{2}-A \sqrt {x} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
1461.714 |
|
| 26255 |
\begin{align*}
{y^{\prime }}^{4} x -2 y {y^{\prime }}^{3}+12 x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1521.023 |
|
| 26256 |
\begin{align*}
y y^{\prime }-y&=-\frac {x}{4}+\frac {6 A \left (\sqrt {x}+8 A +\frac {5 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1579.085 |
|
| 26257 |
\begin{align*}
y y^{\prime }-y&=-\frac {6 x}{25}+\frac {6 A \left (2 \sqrt {x}+7 A +\frac {4 A^{2}}{\sqrt {x}}\right )}{25} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1594.700 |
|