| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 18201 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.492 |
|
| 18202 |
\begin{align*}
x^{8} {y^{\prime }}^{2}+3 y^{\prime } x +9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.493 |
|
| 18203 |
\begin{align*}
\left (a^{2}+b^{2}\right )^{2} y-4 a b y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.493 |
|
| 18204 |
\begin{align*}
y^{\prime \prime }-y x -x^{6}+64&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.493 |
|
| 18205 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=\tan \left (x \right )-2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.495 |
|
| 18206 |
\begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.495 |
|
| 18207 |
\begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (0\right ) &= \pi \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
3.495 |
|
| 18208 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.495 |
|
| 18209 |
\begin{align*}
y^{2} {y^{\prime }}^{3}-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
3.496 |
|
| 18210 |
\begin{align*}
y^{\prime }&=\frac {-y+x y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.496 |
|
| 18211 |
\begin{align*}
2 y^{\prime } x +y^{3} {\mathrm e}^{-2 x}&=2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.497 |
|
| 18212 |
\begin{align*}
x^{\prime }&=\frac {x-t +1}{x-t +2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.497 |
|
| 18213 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.497 |
|
| 18214 |
\begin{align*}
2 x y^{2}+x^{2} y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.498 |
|
| 18215 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.499 |
|
| 18216 |
\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*} |
✓ |
✓ |
✓ |
✓ |
3.499 |
|
| 18217 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.499 |
|
| 18218 |
\begin{align*}
6 x +y^{2}+y \left (2 x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.499 |
|
| 18219 |
\begin{align*}
y^{\prime }-\operatorname {R1} \left (x , \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}\right ) \operatorname {R2} \left (y, \sqrt {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.500 |
|
| 18220 |
\begin{align*}
\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.500 |
|
| 18221 |
\begin{align*}
y^{\prime }&=y^{2}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.501 |
|
| 18222 |
\begin{align*}
y^{\prime }-\tan \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.502 |
|
| 18223 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.503 |
|
| 18224 |
\begin{align*}
y^{4} y^{\prime }&=t +2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.503 |
|
| 18225 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.504 |
|
| 18226 |
\begin{align*}
\sin \left (x \right ) y^{\prime \prime }+\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime }+\left (-\cos \left (x \right )+\sin \left (x \right )\right ) y&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.505 |
|
| 18227 |
\begin{align*}
y^{\prime \prime }+\omega ^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.505 |
|
| 18228 |
\begin{align*}
y^{\prime }&=t \left (3-y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.506 |
|
| 18229 |
\begin{align*}
x^{2} y^{\prime \prime }+\sin \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.506 |
|
| 18230 |
\begin{align*}
x^{\prime }&=-t^{2} x^{2} \\
x \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.506 |
|
| 18231 |
\begin{align*}
2 y x +x^{2}+x^{4}-\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.506 |
|
| 18232 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -c^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.507 |
|
| 18233 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.509 |
|
| 18234 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.510 |
|
| 18235 |
\begin{align*}
-y+y^{\prime }&={\mathrm e}^{4 t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.510 |
|
| 18236 |
\begin{align*}
x^{2}+y^{2}-x^{2} y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.510 |
|
| 18237 |
\begin{align*}
y^{\prime \prime }&=\left (1+y\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.510 |
|
| 18238 |
\begin{align*}
y^{\prime }&=x \left (x^{2}-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.511 |
|
| 18239 |
\begin{align*}
y^{\prime }-\frac {2 y}{t}&=2 t^{2} \\
y \left (-2\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.513 |
|
| 18240 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=8 x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.515 |
|
| 18241 |
\begin{align*}
y^{\prime }-x y^{2}-3 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.515 |
|
| 18242 |
\begin{align*}
y^{\prime }&=1+\left (t -y\right )^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.515 |
|
| 18243 |
\begin{align*}
y y^{\prime }&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.516 |
|
| 18244 |
\begin{align*}
y^{\prime }&=16 y-8 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.516 |
|
| 18245 |
\begin{align*}
\left (x +1\right ) y^{\prime }-n y&={\mathrm e}^{x} \left (x +1\right )^{n +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.516 |
|
| 18246 |
\begin{align*}
y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
3.517 |
|
| 18247 |
\begin{align*}
y^{\prime }+3 y x&=6 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.517 |
|
| 18248 |
\begin{align*}
y+x y^{2}-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.517 |
|
| 18249 |
\begin{align*}
\left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+\left (2 a x +c \right ) \left (a \,x^{2}+b \right ) y^{\prime }+k y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.518 |
|
| 18250 |
\begin{align*}
2 \left (1-x \right ) x \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime }&=f \left (x \right ) \left (\left (1-y\right ) \left (x -y\right ) y\right )^{{3}/{2}}-y^{2} \left (1-y^{2}\right )+2 \left (1-y\right ) y \left (x^{2}+y-2 y x \right ) y^{\prime }+\left (1-x \right ) x \left (x -2 y-2 y x +3 y^{2}\right ) {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
3.519 |
|
| 18251 |
\begin{align*}
{y^{\prime }}^{2}-4 y^{3}+a y+b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.519 |
|
| 18252 |
\begin{align*}
-y+y^{\prime } x&=\left (1+y^{2}\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.520 |
|
| 18253 |
\begin{align*}
t x^{\prime }+x \ln \left (t \right )&=t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.520 |
|
| 18254 |
\begin{align*}
y^{\prime } x +2 y-\cos \left (x \right ) x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.520 |
|
| 18255 |
\begin{align*}
4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.523 |
|
| 18256 |
\begin{align*}
y^{\prime }+5 y&={\mathrm e}^{-3 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.525 |
|
| 18257 |
\begin{align*}
y^{\prime } x -3 y&=x^{3} \\
y \left (1\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.527 |
|
| 18258 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=\sec \left (\ln \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.527 |
|
| 18259 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.528 |
|
| 18260 |
\begin{align*}
x y^{2}+y+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.529 |
|
| 18261 |
\begin{align*}
\sin \left (x \right )+y y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.529 |
|
| 18262 |
\begin{align*}
\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.530 |
|
| 18263 |
\begin{align*}
y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.531 |
|
| 18264 |
\begin{align*}
y^{\prime }&=t y \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.531 |
|
| 18265 |
\begin{align*}
y^{\prime }+\frac {y}{1-x}+x -x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.532 |
|
| 18266 |
\begin{align*}
x {y^{\prime }}^{2}-2 y y^{\prime }+a x&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
3.532 |
|
| 18267 |
\begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.532 |
|
| 18268 |
\begin{align*}
\tan \left (x \right ) y^{\prime }+y&=\cot \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.533 |
|
| 18269 |
\begin{align*}
y^{\prime }+\cot \left (t \right ) y&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.533 |
|
| 18270 |
\begin{align*}
x^{4}-x +y-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.535 |
|
| 18271 |
\begin{align*}
2 y+y^{\prime }&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.535 |
|
| 18272 |
\begin{align*}
\left ({\mathrm e}^{x}+1\right ) y y^{\prime }&=\left (1+y\right ) {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.535 |
|
| 18273 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime }&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.535 |
|
| 18274 |
\begin{align*}
2 x^{2} \left (2+x \right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.536 |
|
| 18275 |
\begin{align*}
6+2 y&=y y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.536 |
|
| 18276 |
\begin{align*}
y^{\prime \prime }&=a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.536 |
|
| 18277 |
\begin{align*}
y \left (6 y^{2}-x -1\right )+2 y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.536 |
|
| 18278 |
\begin{align*}
1-y^{\prime } x&=\ln \left (y\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.537 |
|
| 18279 |
\begin{align*}
y^{\prime } x +y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.538 |
|
| 18280 |
\begin{align*}
\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.538 |
|
| 18281 |
\begin{align*}
y^{\prime }&=\frac {\sin \left (\sqrt {x}\right )}{\sqrt {y}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.539 |
|
| 18282 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.539 |
|
| 18283 |
\begin{align*}
x \left (x^{2}-y^{2}-x \right )-y \left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.539 |
|
| 18284 |
\begin{align*}
1+{\mathrm e}^{t y} \left (t y+1\right )+\left (1+{\mathrm e}^{t y} t^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.540 |
|
| 18285 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=x^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.540 |
|
| 18286 |
\begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.540 |
|
| 18287 |
\begin{align*}
y y^{\prime }+x \,{\mathrm e}^{x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.542 |
|
| 18288 |
\begin{align*}
x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right )&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
3.543 |
|
| 18289 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 x y^{2}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.544 |
|
| 18290 |
\begin{align*}
\frac {1}{y}-\frac {x y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.544 |
|
| 18291 |
\begin{align*}
2 y+y^{\prime }&=\frac {x}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.546 |
|
| 18292 |
\begin{align*}
t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.546 |
|
| 18293 |
\begin{align*}
y+y^{\prime }&=2-{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.546 |
|
| 18294 |
\begin{align*}
y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.547 |
|
| 18295 |
\begin{align*}
y^{\prime }&=\sqrt {\left (y+2\right ) \left (-1+y\right )} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.547 |
|
| 18296 |
\begin{align*}
y^{\prime } x +3 y&=2 x^{5} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.548 |
|
| 18297 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 2 & 0\le t \le 3 \\ 3 t -7 & 3<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.549 |
|
| 18298 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-2 y x&=-x^{3}+x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.549 |
|
| 18299 |
\begin{align*}
y x -\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.549 |
|
| 18300 |
\begin{align*}
\cot \left (x \right ) y^{\prime }+y&=\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.550 |
|