| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 16901 |
\begin{align*}
1+v^{2}+\left (u^{2}+1\right ) v v^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.327 |
|
| 16902 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.328 |
|
| 16903 |
\begin{align*}
y y^{\prime \prime }-a {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.328 |
|
| 16904 |
\begin{align*}
y^{\prime } x +\left (2 x^{2}+1\right ) y&=x^{3} {\mathrm e}^{-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.329 |
|
| 16905 |
\begin{align*}
\left (x -1\right ) y^{\prime }+3 y&=\frac {1+\left (x -1\right ) \sec \left (x \right )^{2}}{\left (x -1\right )^{3}} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.329 |
|
| 16906 |
\begin{align*}
y^{\prime }+2 y x&=x \,{\mathrm e}^{-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.329 |
|
| 16907 |
\begin{align*}
x^{2} y^{\prime }+2 y x -x +1&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.332 |
|
| 16908 |
\begin{align*}
y^{\prime \prime }+a_{1} \left (t \right ) y^{\prime }+a_{0} \left (t \right ) y&=f \left (t \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
4.332 |
|
| 16909 |
\begin{align*}
\left (-x^{2}+y\right ) y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.333 |
|
| 16910 |
\begin{align*}
{y^{\prime }}^{3} \sin \left (x \right )-\left (\sin \left (x \right ) y-\cos \left (x \right )^{2}\right ) {y^{\prime }}^{2}-\left (y \cos \left (x \right )^{2}+\sin \left (x \right )\right ) y^{\prime }+\sin \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.333 |
|
| 16911 |
\begin{align*}
4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.333 |
|
| 16912 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.333 |
|
| 16913 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.334 |
|
| 16914 |
\begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.334 |
|
| 16915 |
\begin{align*}
x^{\prime }&=\sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.335 |
|
| 16916 |
\begin{align*}
x^{2} y+\left (x +1\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.335 |
|
| 16917 |
\begin{align*}
y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.336 |
|
| 16918 |
\begin{align*}
y^{\prime \prime }+y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.336 |
|
| 16919 |
\begin{align*}
t^{2} s^{\prime \prime }-t s^{\prime }&=1-\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.339 |
|
| 16920 |
\begin{align*}
y y^{\prime }&=x -1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.340 |
|
| 16921 |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }&=\left (x -1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.340 |
|
| 16922 |
\begin{align*}
v v^{\prime }&=\frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.341 |
|
| 16923 |
\begin{align*}
2 y^{\prime \prime }-3 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.341 |
|
| 16924 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+y&=0 \\
y \left (2\right ) &= 1 \\
y^{\prime }\left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.343 |
|
| 16925 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-15 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.343 |
|
| 16926 |
\begin{align*}
\left (\operatorname {b2} \,x^{2}+\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.345 |
|
| 16927 |
\begin{align*}
3 x^{2} \left (1+\ln \left (y\right )\right )+\left (\frac {x^{3}}{y}-2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.346 |
|
| 16928 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.346 |
|
| 16929 |
\begin{align*}
y^{\prime }&=\frac {x +y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.347 |
|
| 16930 |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.347 |
|
| 16931 |
\begin{align*}
y^{\prime \prime }-9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.348 |
|
| 16932 |
\begin{align*}
\frac {y^{\prime }}{x}&=y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.352 |
|
| 16933 |
\begin{align*}
2 y x -y+\left (x^{2}+x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.352 |
|
| 16934 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.353 |
|
| 16935 |
\begin{align*}
\sqrt {\left (a +x \right ) \left (x +b \right )}\, \left (2 y^{\prime }-3\right )+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.353 |
|
| 16936 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.353 |
|
| 16937 |
\begin{align*}
t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.353 |
|
| 16938 |
\begin{align*}
\sqrt {-x^{2}+1}\, y^{2} y^{\prime }&=\arcsin \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.355 |
|
| 16939 |
\begin{align*}
\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime \prime }-x {y^{\prime }}^{2} \sin \left (y\right )+2 \left (\cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }&=\sin \left (x \right ) y \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
4.356 |
|
| 16940 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\sec \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.356 |
|
| 16941 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=72 x^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.357 |
|
| 16942 |
\begin{align*}
y^{\prime \prime }+x^{2} y&=0 \\
y \left (0\right ) &= y_{0} \\
y^{\prime }\left (0\right ) &= \operatorname {yd}_{0} \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.357 |
|
| 16943 |
\begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.358 |
|
| 16944 |
\begin{align*}
y^{\prime \prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.358 |
|
| 16945 |
\begin{align*}
x^{2} y^{\prime }&=y x +y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.359 |
|
| 16946 |
\begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.360 |
|
| 16947 |
\begin{align*}
\left (a +x \right )^{2} y^{\prime }&=2 \left (a +x \right ) \left (b +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.360 |
|
| 16948 |
\begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } t +6 y&=2 t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.361 |
|
| 16949 |
\begin{align*}
y^{\prime } x +y&=3 y x \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.362 |
|
| 16950 |
\begin{align*}
y^{\prime } x +y&=a \left (-x^{2}+1\right ) y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.362 |
|
| 16951 |
\begin{align*}
y^{\prime }&=2 y^{{2}/{3}} \\
y \left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.362 |
|
| 16952 |
\begin{align*}
t^{2} x^{\prime \prime }-t x^{\prime }-3 x&=0 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.362 |
|
| 16953 |
\begin{align*}
x^{3}+x y^{2}-y+\left (x^{2} y+y^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.362 |
|
| 16954 |
\begin{align*}
t^{2} y^{\prime \prime }-y^{\prime } t -2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.364 |
|
| 16955 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.364 |
|
| 16956 |
\begin{align*}
x^{\prime \prime }-4 x^{\prime }+4 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.364 |
|
| 16957 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.364 |
|
| 16958 |
\begin{align*}
y^{\prime }-y x&=\sqrt {y}\, x \,{\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.365 |
|
| 16959 |
\begin{align*}
x^{\prime }+t x^{3}+\frac {x}{t}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.366 |
|
| 16960 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.367 |
|
| 16961 |
\begin{align*}
x^{2}+y-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.368 |
|
| 16962 |
\begin{align*}
4 y+y^{\prime \prime }&=\sin \left (x \right )^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.368 |
|
| 16963 |
\begin{align*}
y^{2}+2 t y y^{\prime }+3 t^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.368 |
|
| 16964 |
\begin{align*}
y^{\prime } x +a +x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.369 |
|
| 16965 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.370 |
|
| 16966 |
\begin{align*}
y^{\prime }&=\frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \\
y \left (0\right ) &= 100 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.372 |
|
| 16967 |
\begin{align*}
t y^{\prime \prime }+2 y^{\prime }+t y&=-t \\
y \left (\pi \right ) &= -1 \\
y^{\prime }\left (\pi \right ) &= -\frac {1}{\pi } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.372 |
|
| 16968 |
\begin{align*}
2 x^{\prime \prime }+5 x^{\prime }-12 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.372 |
|
| 16969 |
\begin{align*}
3 y^{\prime \prime } x -4 y^{\prime }+\frac {5 y}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.372 |
|
| 16970 |
\begin{align*}
\left (1-t \right ) y^{\prime \prime }+y^{\prime } t -y&=2 \left (t -1\right ) {\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.373 |
|
| 16971 |
\begin{align*}
y^{\prime }&=\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x \right ) y}{x \left (x +1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.373 |
|
| 16972 |
\begin{align*}
y^{\prime \prime }-y^{\prime }&={\mathrm e}^{2 x} \sin \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.375 |
|
| 16973 |
\begin{align*}
y^{\prime }&=\sqrt {x +y+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.376 |
|
| 16974 |
\begin{align*}
y^{\prime } x&=y^{2}-y \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
4.376 |
|
| 16975 |
\begin{align*}
y^{\prime \prime }&=2 a y^{\prime }-\left (a^{2}-\omega ^{2}\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.378 |
|
| 16976 |
\begin{align*}
y y^{\prime }+4 x \left (x +1\right )+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.379 |
|
| 16977 |
\begin{align*}
4 y^{\prime \prime }+17 y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.380 |
|
| 16978 |
\begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y&=x^{{7}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.381 |
|
| 16979 |
\begin{align*}
3 y^{\prime } x +y+x^{2} y^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.381 |
|
| 16980 |
\begin{align*}
-\left (5+4 x \right ) y+32 y^{\prime } x +16 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.382 |
|
| 16981 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{8 y}}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.382 |
|
| 16982 |
\begin{align*}
y^{\prime } x&=y^{2}-y \\
y \left (2\right ) &= {\frac {1}{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.383 |
|
| 16983 |
\begin{align*}
a \csc \left (x \right )^{2} y+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.384 |
|
| 16984 |
\begin{align*}
y^{\prime }&=\frac {\left (t^{2}-4\right ) \left (1+y\right ) {\mathrm e}^{y}}{\left (t -1\right ) \left (3-y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.385 |
|
| 16985 |
\begin{align*}
y^{\prime }-\frac {4 t y}{4 t^{2}+1}&=4 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.385 |
|
| 16986 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (6 x +4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.386 |
|
| 16987 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }&={\mathrm e}^{x}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.386 |
|
| 16988 |
\begin{align*}
y^{\prime \prime } x +\left (x +3\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.386 |
|
| 16989 |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{3}+\frac {2}{3 x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.387 |
|
| 16990 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.389 |
|
| 16991 |
\begin{align*}
y^{2}+y x +1+\left (x^{2}+y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.390 |
|
| 16992 |
\begin{align*}
y^{\prime }&=\frac {1+3 x}{2 y} \\
y \left (-2\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.391 |
|
| 16993 |
\begin{align*}
2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.391 |
|
| 16994 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -20 y&=\left (x +1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.391 |
|
| 16995 |
\begin{align*}
y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\
y \left (3\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.393 |
|
| 16996 |
\begin{align*}
\left (x^{2} y^{3}+y x \right ) y^{\prime }-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.393 |
|
| 16997 |
\begin{align*}
y^{\prime }&=-y^{3}+\left (a x +b \right ) y^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.393 |
|
| 16998 |
\begin{align*}
1+2 x+\left (-t^{2}+4\right ) x^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.394 |
|
| 16999 |
\begin{align*}
\left (x -y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.394 |
|
| 17000 |
\begin{align*}
a^{2} y+y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.395 |
|