| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 18401 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+l x y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.270 |
|
| 18402 |
\begin{align*}
y^{\prime }&=\frac {\sin \left (x \right ) \sin \left (y\right )}{\cos \left (x \right ) \cos \left (y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.270 |
|
| 18403 |
\begin{align*}
y^{\prime }&=x^{3}-2 y x \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.271 |
|
| 18404 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a^{2} x^{2}-6\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.272 |
|
| 18405 |
\begin{align*}
y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.273 |
|
| 18406 |
\begin{align*}
x \left (-2 x^{3}+1\right ) y^{\prime }&=2 \left (-x^{3}+1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.273 |
|
| 18407 |
\begin{align*}
y^{\prime }&=\frac {x -y^{2}}{2 y \left (x +y^{2}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.273 |
|
| 18408 |
\begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}-a y^{3} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.274 |
|
| 18409 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.274 |
|
| 18410 |
\begin{align*}
y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.275 |
|
| 18411 |
\begin{align*}
y^{\prime }&=\frac {1-2 x}{y} \\
y \left (1\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.275 |
|
| 18412 |
\begin{align*}
{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.275 |
|
| 18413 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.275 |
|
| 18414 |
\begin{align*}
y^{\prime } x +x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.275 |
|
| 18415 |
\begin{align*}
\frac {1}{x}-\frac {y^{2}}{\left (x -y\right )^{2}}+\left (\frac {x^{2}}{\left (x -y\right )^{2}}-\frac {1}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.275 |
|
| 18416 |
\begin{align*}
\left (x +y^{2}\right ) y^{\prime }+y-x^{2}&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.277 |
|
| 18417 |
\begin{align*}
x^{2} y^{\prime }+2 y x -x +1&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.277 |
|
| 18418 | \begin{align*}
x^{\prime }&=x+2 y+{\mathrm e}^{t} \\
y^{\prime }&=x-2 y-{\mathrm e}^{t} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.277 |
|
| 18419 |
\begin{align*}
x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.278 |
|
| 18420 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (1\right ) &= 0 \\
y \left (2\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.278 |
|
| 18421 |
\begin{align*}
x -2 y x +{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.280 |
|
| 18422 |
\begin{align*}
x^{\prime }&=k \left (A -x\right )^{2} \\
x \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.280 |
|
| 18423 |
\begin{align*}
y^{\prime }&=y^{2}-t \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.280 |
|
| 18424 |
\begin{align*}
y+y^{\prime }&=1+t \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.281 |
|
| 18425 |
\begin{align*}
y^{\prime }-\frac {3 y}{x -1}&=\left (x -1\right )^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.281 |
|
| 18426 |
\begin{align*}
y^{\prime }+\frac {2 y}{x}&=2 y^{2} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.283 |
|
| 18427 |
\begin{align*}
\csc \left (y\right )+\sec \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.283 |
|
| 18428 |
\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*} |
✓ |
✓ |
✓ |
✓ |
2.284 |
|
| 18429 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+3 x +2}{y-2} \\
y \left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.284 |
|
| 18430 |
\begin{align*}
\left (x^{2}-5 x +6\right ) y^{\prime }+3 y x -8 y+x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.284 |
|
| 18431 |
\begin{align*}
y+y^{\prime }&=t^{3}+\sin \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.284 |
|
| 18432 |
\begin{align*}
y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.286 |
|
| 18433 |
\begin{align*}
x {y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.286 |
|
| 18434 |
\begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=\ln \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.287 |
|
| 18435 |
\begin{align*}
y^{\prime }-3 y-2 z&=0 \\
z^{\prime }+y-2 z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.287 |
|
| 18436 |
\begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.287 |
|
| 18437 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.288 |
|
| 18438 | \begin{align*}
{\mathrm e}^{2 x +3 y}+{\mathrm e}^{4 x -5 y} y^{\prime }&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.288 |
|
| 18439 |
\begin{align*}
\frac {2 x}{y}-\frac {y}{y^{2}+x^{2}}+\left (-\frac {x^{2}}{y^{2}}+\frac {x}{y^{2}+x^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.289 |
|
| 18440 |
\begin{align*}
y^{\prime }+f \left (x \right ) y-g \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.289 |
|
| 18441 |
\begin{align*}
y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 a x +y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.289 |
|
| 18442 |
\begin{align*}
x^{\prime }&=1+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.289 |
|
| 18443 |
\begin{align*}
4 t y+\left (t^{2}+1\right ) y^{\prime }&=t \\
y \left (1\right ) &= {\frac {1}{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.290 |
|
| 18444 |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }+6 y&={\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.290 |
|
| 18445 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}-4 x_{2}+5 x_{3}+9 x_{4} \\
x_{2}^{\prime }&=-2 x_{1}-5 x_{2}+4 x_{3}+12 x_{4} \\
x_{3}^{\prime }&=-2 x_{1}-x_{3}+2 x_{4} \\
x_{4}^{\prime }&=-2 x_{2}+2 x_{3}+3 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.290 |
|
| 18446 |
\begin{align*}
x^{\prime }-t x&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.290 |
|
| 18447 |
\begin{align*}
\cosh \left (y\right ) y^{\prime }+\sinh \left (y\right )-{\mathrm e}^{-x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.291 |
|
| 18448 |
\begin{align*}
y \ln \left (y\right )-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.291 |
|
| 18449 |
\begin{align*}
x^{2} y^{\prime \prime }+a y^{\prime }-\left (b^{2} x^{2}+a b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.291 |
|
| 18450 |
\begin{align*}
y^{\prime }&=2 y^{2}+x y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.292 |
|
| 18451 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{3} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.292 |
|
| 18452 |
\begin{align*}
y^{\prime } x +3 y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.293 |
|
| 18453 |
\begin{align*}
2 x^{3}-y^{3}-3 x +3 y^{2} y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.294 |
|
| 18454 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\frac {\alpha \left (\alpha +1\right ) \mu ^{2} y}{-x^{2}+1}&=0 \\
y \left (0\right ) &= y_{0} \\
y^{\prime }\left (0\right ) &= y_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.294 |
|
| 18455 |
\begin{align*}
y^{\prime }&=\frac {\cot \left (t \right ) y}{1+y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.295 |
|
| 18456 |
\begin{align*}
3 x^{2}+2 y x +4 y^{2}+\left (x^{2}+8 y x +18 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.295 |
|
| 18457 | \begin{align*}
y^{\prime }&=\frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.295 |
|
| 18458 |
\begin{align*}
x^{2} y^{\prime }&=\left (y-1\right ) x +\left (y-1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.295 |
|
| 18459 |
\begin{align*}
\left ({\mathrm e}^{x}+x \,{\mathrm e}^{y}\right ) y^{\prime }+{\mathrm e}^{x} y+{\mathrm e}^{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.296 |
|
| 18460 |
\begin{align*}
y^{\prime }-y&=\sin \left (x \right )+\cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.296 |
|
| 18461 |
\begin{align*}
y^{\prime }&=2 x y^{2}+3 y^{2} x^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.297 |
|
| 18462 |
\begin{align*}
n^{\prime }+n&=n t \,{\mathrm e}^{t +2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.297 |
|
| 18463 |
\begin{align*}
y^{\prime }&=y^{2}-4 y-12 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.297 |
|
| 18464 |
\begin{align*}
x^{2}+\frac {y}{x}+\left (\ln \left (x \right )+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.298 |
|
| 18465 |
\begin{align*}
\tan \left (x \right ) y^{\prime }&=y-\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.299 |
|
| 18466 |
\begin{align*}
x \left (3-2 x^{2} y\right ) y^{\prime }&=4 x -3 y+3 y^{2} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.299 |
|
| 18467 |
\begin{align*}
x \left (1-2 x y^{3}\right ) y^{\prime }+\left (1-2 x^{3} y\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.300 |
|
| 18468 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}-3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.300 |
|
| 18469 |
\begin{align*}
y^{\prime } x +y&=3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.300 |
|
| 18470 |
\begin{align*}
y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.301 |
|
| 18471 |
\begin{align*}
y+\left (x^{2}-4 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.301 |
|
| 18472 |
\begin{align*}
\left (\operatorname {a2} x +\operatorname {c2} \right ) {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {a0} x +\operatorname {b0} y+\operatorname {c0}&=0 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
2.301 |
|
| 18473 |
\begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=4 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.301 |
|
| 18474 |
\begin{align*}
y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.301 |
|
| 18475 |
\begin{align*}
\sin \left (x \right )+y^{\prime } y&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.302 |
|
| 18476 | \begin{align*}
y^{\prime }+2 y&=3 t^{2}+2 t -1 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.302 |
|
| 18477 |
\begin{align*}
y^{\prime }&=3-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.302 |
|
| 18478 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=\frac {1}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.302 |
|
| 18479 |
\begin{align*}
\left (6+3 y x -4 y^{3}\right ) x +\left (x^{3}-6 y^{2} x^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.302 |
|
| 18480 |
\begin{align*}
g \left (x \right ) y^{\prime }&=f_{1} \left (x \right ) y+f_{0} \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.303 |
|
| 18481 |
\begin{align*}
8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.303 |
|
| 18482 |
\begin{align*}
y^{\prime }&=y+4 \cos \left (t^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.303 |
|
| 18483 |
\begin{align*}
2 x y^{\prime } y+\ln \left (x \right )&=-1-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.303 |
|
| 18484 |
\begin{align*}
y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.304 |
|
| 18485 |
\begin{align*}
x +y y^{\prime } {\mathrm e}^{-x}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.305 |
|
| 18486 |
\begin{align*}
\cos \left (\theta \right ) r^{\prime }&=2+2 r \sin \left (\theta \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.306 |
|
| 18487 |
\begin{align*}
y^{\prime }&=\left (y-1\right ) \left (x +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.306 |
|
| 18488 |
\begin{align*}
\left (x^{n}+a \right )^{2} y^{\prime \prime }-b \,x^{-2+n} \left (\left (b -1\right ) x^{n}+a \left (n -1\right )\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
2.306 |
|
| 18489 |
\begin{align*}
{x^{\prime }}^{2}-t x+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.306 |
|
| 18490 |
\begin{align*}
3-2 y x -\left (x^{2}+\frac {1}{y^{2}}+\frac {1}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.306 |
|
| 18491 |
\begin{align*}
y^{\prime } x +y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.307 |
|
| 18492 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +5 y&=8 x \ln \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.308 |
|
| 18493 |
\begin{align*}
{y^{\prime }}^{4}+4 y {y^{\prime }}^{3}+6 y^{2} {y^{\prime }}^{2}-\left (1-4 y^{3}\right ) y^{\prime }-\left (3-y^{3}\right ) y&=0 \\
\end{align*} |
✓ |
✗ |
✓ |
✓ |
2.308 |
|
| 18494 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
y \left (2\right ) &= 0 \\
y^{\prime }\left (2\right ) &= {\mathrm e}^{-2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.308 |
|
| 18495 | \begin{align*}
2 x^{3}-y+y^{\prime } x&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.308 |
|
| 18496 |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }-4 y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.309 |
|
| 18497 |
\begin{align*}
y \left (2 x^{2} y+{\mathrm e}^{x}\right )-\left ({\mathrm e}^{x}+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.309 |
|
| 18498 |
\begin{align*}
y^{\prime }+2 y&=t \,{\mathrm e}^{-2 t} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.310 |
|
| 18499 |
\begin{align*}
-y+y^{\prime } x&=x^{2} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.310 |
|
| 18500 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{t}}{1+y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.310 |
|