| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 17301 |
\begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \left (2+x y^{\prime }-4 y^{2} y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.747 |
|
| 17302 |
\begin{align*}
y^{\prime \prime }+y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.747 |
|
| 17303 |
\begin{align*}
y^{\prime }&=-y x +1 \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.747 |
|
| 17304 |
\begin{align*}
y^{\prime }&=y+y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.748 |
|
| 17305 |
\begin{align*}
y^{\prime }&=\left (t -y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.748 |
|
| 17306 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.749 |
|
| 17307 |
\begin{align*}
x y^{\prime }&=\left (-2 x^{2}+1\right ) \tan \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.749 |
|
| 17308 |
\(\left [\begin {array}{ccc} 3 & 2 & 0 \\ 2 & 0 & i \\ 0 & -i & 0 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
2.749 |
|
| 17309 |
\begin{align*}
x \left (-x^{3}+1\right ) y^{\prime }&=2 x -\left (-4 x^{3}+1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.750 |
|
| 17310 |
\begin{align*}
\left (y^{2}+a \sin \left (x \right )\right ) y^{\prime }&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.750 |
|
| 17311 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{k x} y^{2}+b y+c \,{\mathrm e}^{s x}+d \,{\mathrm e}^{-k x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.750 |
|
| 17312 |
\begin{align*}
x \left (x -1\right ) \left (x +1\right )^{2} y^{\prime \prime }+2 x \left (x -3\right ) \left (x +1\right ) y^{\prime }-2 \left (x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.751 |
|
| 17313 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.751 |
|
| 17314 |
\begin{align*}
{\mathrm e}^{x} \left (x^{2}+y^{2}+2 x \right )+2 y \,{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.753 |
|
| 17315 |
\begin{align*}
-\left (-x^{2}+2\right ) y+x^{3} y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.754 |
|
| 17316 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.754 |
|
| 17317 |
\begin{align*}
x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.755 |
|
| 17318 |
\begin{align*}
3 y+y^{\prime }&=27 t^{2}+9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.755 |
|
| 17319 |
\begin{align*}
\left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.756 |
|
| 17320 |
\begin{align*}
2 y-x y \ln \left (x \right )-2 x \ln \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.756 |
|
| 17321 |
\begin{align*}
y^{\prime \prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.756 |
|
| 17322 |
\begin{align*}
x_{1}^{\prime }&=23 x_{1}-18 x_{2}-16 x_{3} \\
x_{2}^{\prime }&=-8 x_{1}+6 x_{2}+7 x_{3}+9 x_{4} \\
x_{3}^{\prime }&=34 x_{1}-27 x_{2}-26 x_{3}-9 x_{4} \\
x_{4}^{\prime }&=-26 x_{1}+21 x_{2}+25 x_{3}+12 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.757 |
|
| 17323 |
\begin{align*}
x y^{\prime }-3 y+y^{2}&=4 x^{2}-4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.757 |
|
| 17324 |
\begin{align*}
t y^{\prime }+y&={\mathrm e}^{t} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.758 |
|
| 17325 |
\begin{align*}
y^{\prime }+2 x y \left (1-a \,x^{2} y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.759 |
|
| 17326 |
\begin{align*}
y^{\prime }+y&=\left \{\begin {array}{cc} 1 & 0\le x <2 \\ 0 & 0<x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.759 |
|
| 17327 |
\begin{align*}
V^{\prime }\left (x \right )+2 y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.759 |
|
| 17328 |
\begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.760 |
|
| 17329 |
\begin{align*}
x^{2}+y-x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.760 |
|
| 17330 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.761 |
|
| 17331 |
\begin{align*}
4 y+y^{\prime \prime }&=8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.763 |
|
| 17332 |
\begin{align*}
x y^{\prime }+2+\left (-x +3\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.764 |
|
| 17333 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\frac {y}{4}&=-\frac {x^{2}}{2}+\frac {1}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.765 |
|
| 17334 |
\begin{align*}
y+y^{\prime }&=2 \cos \left (t \right )+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.765 |
|
| 17335 |
\begin{align*}
y+\left (-4+t \right ) t y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.766 |
|
| 17336 |
\begin{align*}
y^{\prime }&=\cos \left (x -y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.766 |
|
| 17337 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.766 |
|
| 17338 |
\begin{align*}
\frac {2 x}{y}-\frac {y}{x^{2}+y^{2}}+\left (-\frac {x^{2}}{y^{2}}+\frac {x}{x^{2}+y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.767 |
|
| 17339 |
\begin{align*}
y^{\prime }+y \cot \left (x \right )&=\cos \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.767 |
|
| 17340 |
\begin{align*}
y^{\prime }&=t^{4} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.767 |
|
| 17341 |
\begin{align*}
y+\frac {y^{3}}{3}+\frac {x^{2}}{2}+\frac {\left (x y^{2}+x \right ) y^{\prime }}{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.767 |
|
| 17342 |
\begin{align*}
r^{\prime }&=r \cot \left (\theta \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.770 |
|
| 17343 |
\begin{align*}
y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.770 |
|
| 17344 |
\begin{align*}
y^{\prime }&=-\frac {2 x}{3}+1+y^{2}+\frac {2 x^{2} y}{3}+\frac {x^{4}}{9}+y^{3}+x^{2} y^{2}+\frac {x^{4} y}{3}+\frac {x^{6}}{27} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.770 |
|
| 17345 |
\begin{align*}
y^{\prime }&=-2+3 y-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.770 |
|
| 17346 |
\begin{align*}
\left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0} x +b_{0}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.771 |
|
| 17347 |
\begin{align*}
{\mathrm e}^{x} \left (y^{3}+x y^{3}+1\right )+3 y^{2} \left (x \,{\mathrm e}^{x}-6\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.772 |
|
| 17348 |
\begin{align*}
x^{2} y^{\prime \prime }+7 x y^{\prime }+8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.772 |
|
| 17349 |
\begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.772 |
|
| 17350 |
\begin{align*}
y^{\prime }&=a +b x +c y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.773 |
|
| 17351 |
\begin{align*}
y^{\prime }&=10+3 y-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.773 |
|
| 17352 |
\begin{align*}
y^{\prime \prime }-2 \,{\mathrm e}^{x} y^{\prime }+y \,{\mathrm e}^{2 x}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.773 |
|
| 17353 |
\begin{align*}
2 y t +\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\
y \left (-3\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.774 |
|
| 17354 |
\begin{align*}
y^{\prime \prime }&=-\frac {f^{\prime }\left (x \right ) y^{\prime }}{2 f \left (x \right )}-\frac {g \left (x \right ) y}{f \left (x \right )} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.774 |
|
| 17355 |
\begin{align*}
3 x +y-2+\left (x -1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.775 |
|
| 17356 |
\begin{align*}
\left ({\mathrm e}^{2 y}+x \right ) {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.776 |
|
| 17357 |
\begin{align*}
y+2 x -x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.777 |
|
| 17358 |
\begin{align*}
-2 y+y^{\prime }&=\cos \left (\omega t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.777 |
|
| 17359 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime }+3 y x&=x \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.778 |
|
| 17360 |
\begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2}+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.778 |
|
| 17361 |
\begin{align*}
x y^{2} y^{\prime }&=x^{2}+y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.778 |
|
| 17362 |
\begin{align*}
3 x^{5} y^{2}+x^{3} y^{\prime }&=2 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.779 |
|
| 17363 |
\begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+b^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.779 |
|
| 17364 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{2 c}+b \,x^{c -1}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.779 |
|
| 17365 |
\begin{align*}
x +2 y-x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.779 |
|
| 17366 |
\begin{align*}
x^{2} y^{\prime }+2 y x&=\sinh \left (x \right ) \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.780 |
|
| 17367 |
\begin{align*}
y^{\prime }&=-y-\cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.780 |
|
| 17368 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ \cos \left (t \right ) & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.781 |
|
| 17369 |
\begin{align*}
x^{\prime }&=4 x+2 y+{\mathrm e}^{t} \\
y^{\prime }&=-x+3 y-{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.782 |
|
| 17370 |
\begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.782 |
|
| 17371 |
\begin{align*}
y^{\prime }+3 x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.783 |
|
| 17372 |
\begin{align*}
-y+\left (x +a \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.783 |
|
| 17373 |
\begin{align*}
x y^{\prime }+a +x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.783 |
|
| 17374 |
\begin{align*}
y^{\prime }-a y&=f \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.783 |
|
| 17375 |
\begin{align*}
y^{\prime }&=\left (1-y\right ) \cos \left (x \right ) \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.785 |
|
| 17376 |
\begin{align*}
x -2 y x +{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.786 |
|
| 17377 |
\begin{align*}
y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.786 |
|
| 17378 |
\begin{align*}
y^{\prime \prime }&=4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.786 |
|
| 17379 |
\begin{align*}
y^{\prime \prime }&=2 x +\left (x^{2}-y^{\prime }\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.786 |
|
| 17380 |
\begin{align*}
y^{\prime }&=\frac {x}{-y+x^{4}+2 x^{2} y^{2}+y^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.786 |
|
| 17381 |
\begin{align*}
{y^{\prime }}^{2} x +y y^{\prime }&=3 y^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.786 |
|
| 17382 |
\begin{align*}
y^{\prime }&=-y x +1 \\
y \left (2\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.786 |
|
| 17383 |
\begin{align*}
x y^{\prime }&=a \,x^{2}+y+b y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.787 |
|
| 17384 |
\begin{align*}
\left (-a \,x^{2}+2\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.787 |
|
| 17385 |
\begin{align*}
y^{\prime \prime }-9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.787 |
|
| 17386 |
\begin{align*}
h^{2}+\frac {2 a h}{\sqrt {1+{h^{\prime }}^{2}}}&=b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.788 |
|
| 17387 |
\begin{align*}
3 {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.788 |
|
| 17388 |
\begin{align*}
2+2 x^{2}-2 y x +\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.788 |
|
| 17389 |
\begin{align*}
y^{\prime }+y^{2}+\left (y x -1\right ) f \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.789 |
|
| 17390 |
\begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.789 |
|
| 17391 |
\begin{align*}
x^{\prime \prime }+x&=0 \\
x \left (\frac {\pi }{4}\right ) &= \sqrt {2} \\
x^{\prime }\left (\frac {\pi }{4}\right ) &= 2 \sqrt {2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.789 |
|
| 17392 |
\begin{align*}
x^{\prime }&=-x+t^{2} \\
x \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.790 |
|
| 17393 |
\begin{align*}
x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.793 |
|
| 17394 |
\begin{align*}
x^{2} y^{\prime }+x \left (x +2\right ) y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.793 |
|
| 17395 |
\begin{align*}
y^{\prime }&=y^{2}-y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.793 |
|
| 17396 |
\begin{align*}
y^{\prime }-2 y x&={\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.795 |
|
| 17397 |
\begin{align*}
y {y^{\prime }}^{2}-x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.795 |
|
| 17398 |
\begin{align*}
x y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.796 |
|
| 17399 |
\begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.796 |
|
| 17400 |
\begin{align*}
f \left (x \right )^{2} y^{\prime \prime }&=-24 f \left (x \right )^{4}+\left (3 f \left (x \right )^{3}-f \left (x \right )^{2} y+3 f \left (x \right ) f^{\prime }\left (x \right )\right ) y^{\prime } \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.796 |
|