| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 16301 |
\begin{align*}
2 x^{2} y^{\prime \prime }-7 y^{\prime } x +7 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.548 |
|
| 16302 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=2 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.548 |
|
| 16303 |
\begin{align*}
i^{\prime }+3 i&={\mathrm e}^{-2 t} \\
i \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.548 |
|
| 16304 |
\begin{align*}
2 y a^{2} b^{2}+2 \left (a^{2}+b^{2}\right ) y^{\prime \prime }+2 y^{\prime \prime \prime \prime }&=\cos \left (a x \right )+\cos \left (b x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.549 |
|
| 16305 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= y_{0} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.549 |
|
| 16306 |
\begin{align*}
x^{2} y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| 16307 |
\begin{align*}
4 y+y^{\prime \prime }&=\sec \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| 16308 |
\begin{align*}
x +\frac {y^{\prime }}{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| 16309 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=-2 x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| 16310 |
\begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=\ln \left (x \right ) \left (\frac {1}{x^{3}}+\frac {1}{x^{5}}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| 16311 |
\begin{align*}
y^{\prime }&=\tan \left (x \right ) \\
y \left (\frac {\pi }{4}\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.551 |
|
| 16312 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+\sqrt {3}\, x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=\sqrt {3}\, x_{1}-x_{2}+\sqrt {3}\, {\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.551 |
|
| 16313 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\frac {a^{2} y}{-x^{2}+1}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.551 |
|
| 16314 |
\begin{align*}
\left (\cos \left (2 t \right )+1\right ) y^{\prime \prime }-4 y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.551 |
|
| 16315 |
\begin{align*}
y^{\prime \prime }+9 y&=\left (1+\sin \left (3 x \right )\right ) \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.552 |
|
| 16316 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=y x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.552 |
|
| 16317 |
\begin{align*}
\left (x y^{2}+1+x \right ) y^{\prime }+y+y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.552 |
|
| 16318 | \begin{align*}
y^{\prime } x -3 y&=x^{3} \\
y \left (1\right ) &= 10 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.553 |
|
| 16319 |
\begin{align*}
y^{2} y^{\prime }&=x \left (1+y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.553 |
|
| 16320 |
\begin{align*}
x -y^{\prime } y&=a {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.553 |
|
| 16321 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }&=2 t^{4}+t^{2} {\mathrm e}^{-3 t}+\sin \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.553 |
|
| 16322 |
\begin{align*}
\frac {x+y \,{\mathrm e}^{y}}{x^{\prime }}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.554 |
|
| 16323 |
\begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.554 |
|
| 16324 |
\begin{align*}
y^{\prime }+\tan \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.554 |
|
| 16325 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=10 x^{4}+2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.554 |
|
| 16326 |
\begin{align*}
3 x^{2} y-x^{2}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.554 |
|
| 16327 |
\begin{align*}
\cot \left (x \right ) y^{\prime }+y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.555 |
|
| 16328 |
\begin{align*}
y^{\prime }&=6 \sqrt {y}+5 x^{3} \\
y \left (-1\right ) &= 4 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.555 |
|
| 16329 |
\begin{align*}
x^{2} y^{\prime \prime }-6 y^{\prime } x +10 y&=3 x^{4}+6 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.555 |
|
| 16330 |
\begin{align*}
y^{\prime }+\frac {y}{x}&={\mathrm e}^{x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.555 |
|
| 16331 |
\begin{align*}
y&=y^{\prime } x +\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.555 |
|
| 16332 |
\begin{align*}
y^{\prime }&=3 \left (y+7\right ) x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.556 |
|
| 16333 |
\begin{align*}
y^{\prime }+2 a \,x^{3} y^{3}+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.556 |
|
| 16334 |
\begin{align*}
3 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.556 |
|
| 16335 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{n +2}+b \,x^{2}+c \right ) y^{\prime }+\left (a n \,x^{n +1}+x^{n} a c +b c \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.556 |
|
| 16336 |
\begin{align*}
1+\left (x -y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.557 |
|
| 16337 |
\begin{align*}
x^{\prime }-x&=\frac {t}{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.557 |
|
| 16338 | \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=x^{{3}/{2}} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.558 |
|
| 16339 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.558 |
|
| 16340 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{\left (x^{3}+1\right ) y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.559 |
|
| 16341 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (2\right ) &= 0 \\
y^{\prime }\left (2\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.559 |
|
| 16342 |
\begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=t^{7} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.559 |
|
| 16343 |
\begin{align*}
y^{\prime } x +2 y-\cos \left (x \right ) x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.559 |
|
| 16344 |
\begin{align*}
y^{4} y^{\prime }&=t +2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.559 |
|
| 16345 |
\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*} |
✗ |
✗ |
✗ |
✗ |
1.560 |
|
| 16346 |
\begin{align*}
9 {y^{\prime }}^{4}+8 y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.560 |
|
| 16347 |
\begin{align*}
x^{\prime \prime }+x&=0 \\
x \left (0\right ) &= 3 \\
x^{\prime }\left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.560 |
|
| 16348 |
\begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=6 \left (x^{2}+1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.560 |
|
| 16349 |
\begin{align*}
y^{\prime }-3 y&=25 \cos \left (4 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.560 |
|
| 16350 |
\begin{align*}
t y+y^{\prime }&=t +1 \\
y \left (\frac {3}{2}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.561 |
|
| 16351 |
\begin{align*}
y&=-y^{\prime } x +x^{4} {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.561 |
|
| 16352 |
\begin{align*}
x^{\prime }-2 x&=2 t \\
x \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.561 |
|
| 16353 |
\begin{align*}
y^{\prime }-2 y&=y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.561 |
|
| 16354 |
\begin{align*}
y^{\prime }&=\frac {4 x^{3}+1}{y \left (2+3 y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.562 |
|
| 16355 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{3} y^{\prime }-\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.562 |
|
| 16356 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x -n y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.562 |
|
| 16357 |
\begin{align*}
y^{\prime \prime }-\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.562 |
|
| 16358 | \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }-y&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.562 |
|
| 16359 |
\begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }-4 \left (x -1\right ) y^{\prime }-14 y&=x^{3}-3 x^{2}+3 x -8 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.562 |
|
| 16360 |
\begin{align*}
y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.562 |
|
| 16361 |
\begin{align*}
y^{\prime \prime }&=\left (a -x \right ) {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.563 |
|
| 16362 |
\begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=x^{2}+16 \ln \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.564 |
|
| 16363 |
\begin{align*}
4 y y^{\prime \prime }-5 {y^{\prime }}^{2}+a y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.565 |
|
| 16364 |
\begin{align*}
y^{\prime }+\cot \left (x \right ) y&=2 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.566 |
|
| 16365 |
\begin{align*}
2 y^{\prime } y+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.566 |
|
| 16366 |
\begin{align*}
y+\left (x y^{2}+x -y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.566 |
|
| 16367 |
\begin{align*}
y^{\prime }-2 y x&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.566 |
|
| 16368 |
\begin{align*}
u v-2 v+\left (-u^{2}+u \right ) v^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.566 |
|
| 16369 |
\begin{align*}
3 y^{2} x^{2}+2 y+2 y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.567 |
|
| 16370 |
\begin{align*}
y^{\prime \prime }+a x y^{\prime }+\left (b x +c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.567 |
|
| 16371 |
\begin{align*}
{\mathrm e}^{x}+x^{3} y^{\prime }+4 x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.568 |
|
| 16372 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-y x&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.568 |
|
| 16373 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -\left (-x^{2}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.569 |
|
| 16374 |
\begin{align*}
-9 y-3 \left (1-3 x \right ) y^{\prime }+\left (1-3 x \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.569 |
|
| 16375 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-1+t \right )+\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= -{\frac {2}{3}} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.569 |
|
| 16376 |
\begin{align*}
y^{\prime }+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.570 |
|
| 16377 | \begin{align*}
y^{\prime } x&=x^{m}+y \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.570 |
|
| 16378 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +\left (n -1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.571 |
|
| 16379 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.571 |
|
| 16380 |
\begin{align*}
2 y+y^{\prime }&=1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.571 |
|
| 16381 |
\begin{align*}
y^{\prime }&=\frac {3 x^{2}}{-4+3 y^{2}} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.572 |
|
| 16382 |
\begin{align*}
y^{\prime }-7 y&=\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.572 |
|
| 16383 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}+4&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.573 |
|
| 16384 |
\begin{align*}
y^{\prime }&=x^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.573 |
|
| 16385 |
\begin{align*}
y^{\prime }+\frac {2 y}{x}&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.573 |
|
| 16386 |
\begin{align*}
1+{y^{\prime }}^{2}+2 y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.573 |
|
| 16387 |
\begin{align*}
x^{2}-a y&=\left (a x -y^{2}\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.574 |
|
| 16388 |
\begin{align*}
t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.575 |
|
| 16389 |
\begin{align*}
f^{\prime \prime }+8 f^{\prime }+12 f&=12 \,{\mathrm e}^{-4 t} \\
f \left (0\right ) &= 0 \\
f^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.575 |
|
| 16390 |
\begin{align*}
x \left (-x^{3}+1\right ) y^{\prime }&=2 x -\left (-4 x^{3}+1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.575 |
|
| 16391 |
\begin{align*}
y^{\prime \prime }+16 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.575 |
|
| 16392 |
\begin{align*}
y^{\prime }&=-\frac {y}{t}+\cos \left (t^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.575 |
|
| 16393 |
\begin{align*}
y^{\prime }+\frac {y}{x \ln \left (x \right )}&=9 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.576 |
|
| 16394 |
\begin{align*}
y^{2} y^{\prime }+x \left (2-y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.576 |
|
| 16395 |
\begin{align*}
y^{\prime }&=1+\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.576 |
|
| 16396 | \begin{align*}
x^{3} y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✗ | 1.577 |
|
| 16397 |
\begin{align*}
y^{\prime \prime }&=9 x^{2}+2 x -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.577 |
|
| 16398 |
\begin{align*}
y^{\prime }-4 y&=\left \{\begin {array}{cc} 12 \,{\mathrm e}^{t} & 0\le t <1 \\ 12 \,{\mathrm e} & 1\le t \end {array}\right . \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.577 |
|
| 16399 |
\begin{align*}
a^{2} y^{\prime \prime }+a \left (a^{2}-2 b \,{\mathrm e}^{-a x}\right ) y^{\prime }+b^{2} {\mathrm e}^{-2 a x} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.578 |
|
| 16400 |
\begin{align*}
y+\left (2 x -{\mathrm e}^{y} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.578 |
|