| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 25401 |
\begin{align*}
y^{2}-3 y x -2 x^{2}+\left (y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.565 |
|
| 25402 |
\begin{align*}
y^{\prime }&=\frac {-x^{2}+x +2+2 x^{3} \sqrt {x^{2}-4 x +4 y}}{2 x +2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
18.568 |
|
| 25403 |
\begin{align*}
1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.586 |
|
| 25404 |
\begin{align*}
y \left (x +y^{2}\right )+x^{2} \left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
18.607 |
|
| 25405 |
\begin{align*}
x -y+\left (3 x +y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.622 |
|
| 25406 |
\begin{align*}
y^{\prime }&=\frac {\left (27 y^{3}+27 \,{\mathrm e}^{3 x^{2}} y+18 \,{\mathrm e}^{3 x^{2}} y^{2}+3 y^{3} {\mathrm e}^{3 x^{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y+9 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y^{2}+{\mathrm e}^{\frac {9 x^{2}}{2}} y^{3}\right ) {\mathrm e}^{3 x^{2}} x \,{\mathrm e}^{-\frac {9 x^{2}}{2}}}{243 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.623 |
|
| 25407 |
\begin{align*}
x y^{2} \left (y^{\prime } x +3 y\right )-2 y+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.644 |
|
| 25408 |
\begin{align*}
x y^{\prime } \sqrt {-a^{2}+x^{2}}&=y \sqrt {y^{2}-b^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.648 |
|
| 25409 |
\begin{align*}
b y+a \tanh \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
18.668 |
|
| 25410 |
\begin{align*}
{y^{\prime }}^{2}-a x y y^{\prime }+2 a y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.673 |
|
| 25411 |
\begin{align*}
\left (-y+y^{\prime } x \right ) \cos \left (\frac {y}{x}\right )^{2}+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.687 |
|
| 25412 |
\begin{align*}
x^{2} y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+a y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
18.691 |
|
| 25413 |
\begin{align*}
x^{{3}/{2}} y^{\prime \prime }&=f \left (\frac {y}{\sqrt {x}}\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
18.711 |
|
| 25414 |
\begin{align*}
y^{\prime }+\sqrt {y}&=3 x \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
18.724 |
|
| 25415 |
\begin{align*}
x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.725 |
|
| 25416 |
\begin{align*}
y^{\prime }&=\frac {x}{2}+\frac {1}{2}+\sqrt {x^{2}+2 x +1-4 y}+x^{2} \sqrt {x^{2}+2 x +1-4 y}+x^{3} \sqrt {x^{2}+2 x +1-4 y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
18.743 |
|
| 25417 |
\begin{align*}
y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.751 |
|
| 25418 |
\begin{align*}
{\mathrm e}^{\frac {y}{x}} x +y&=y^{\prime } x \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.760 |
|
| 25419 |
\begin{align*}
x -y \ln \left (y\right )+y \ln \left (x \right )+x \left (\ln \left (y\right )-\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.762 |
|
| 25420 |
\begin{align*}
-y+y^{\prime } x&=x^{2} y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.766 |
|
| 25421 |
\begin{align*}
\left (3 x +2\right ) \left (y-2 x -1\right ) y^{\prime }-y^{2}+y x -7 x^{2}-9 x -3&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.796 |
|
| 25422 |
\begin{align*}
y x +\left (x^{2}-3 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.815 |
|
| 25423 |
\begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=4 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.816 |
|
| 25424 |
\begin{align*}
x {y^{\prime }}^{2}+a y y^{\prime }+b x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.842 |
|
| 25425 |
\begin{align*}
2 y^{2}-4 x +5&=\left (4-2 y+4 y x \right ) y^{\prime } \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
18.845 |
|
| 25426 |
\begin{align*}
y+\left (2 x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.846 |
|
| 25427 |
\begin{align*}
x \left (x^{2}+a x y+2 y^{2}\right ) y^{\prime }&=\left (a x +2 y\right ) y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.851 |
|
| 25428 |
\begin{align*}
x \left (x -y\right ) y^{\prime }+2 x^{2}+3 y x -y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.858 |
|
| 25429 |
\begin{align*}
y^{\prime }&=\frac {y+x \sqrt {x^{2}+y^{2}}+x^{3} \sqrt {x^{2}+y^{2}}+x^{4} \sqrt {x^{2}+y^{2}}}{x} \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
18.885 |
|
| 25430 |
\begin{align*}
-y+2 y^{\prime } x +x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
18.924 |
|
| 25431 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=3 x -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.937 |
|
| 25432 |
\begin{align*}
y^{\prime }-2 y x +y^{2}&=-x^{2}+5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.963 |
|
| 25433 |
\begin{align*}
y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+\sqrt {x^{2}-2 x +1+8 y}+x^{2} \sqrt {x^{2}-2 x +1+8 y}+x^{3} \sqrt {x^{2}-2 x +1+8 y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
18.979 |
|
| 25434 |
\begin{align*}
y^{\prime }&=2 x +\frac {x y}{x^{2}-1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.987 |
|
| 25435 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
19.006 |
|
| 25436 |
\begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.028 |
|
| 25437 |
\begin{align*}
y^{\prime }&=\frac {\left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}\right )^{3} {\mathrm e}^{x}}{4 \left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}+2\right ) \sqrt {y}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
19.032 |
|
| 25438 |
\begin{align*}
y^{\prime }&=\frac {t -y}{y+t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.075 |
|
| 25439 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda \arccos \left (x \right )^{n} y-a^{2}+a \lambda \arccos \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.083 |
|
| 25440 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=24 x +24 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.093 |
|
| 25441 |
\begin{align*}
2 t \sin \left (\frac {y}{t}\right )-y \cos \left (\frac {y}{t}\right )+t \cos \left (\frac {y}{t}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.095 |
|
| 25442 |
\begin{align*}
y-t +\left (t +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.102 |
|
| 25443 |
\begin{align*}
x^{2}+y^{2}+3 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.108 |
|
| 25444 |
\begin{align*}
2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.125 |
|
| 25445 |
\begin{align*}
3 x -y-\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.132 |
|
| 25446 |
\begin{align*}
y^{\prime }&=\frac {y-\sqrt {x^{2}+y^{2}}}{x} \\
y \left (3\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.191 |
|
| 25447 |
\begin{align*}
y^{\prime }&=\frac {-y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +2 \sin \left (\frac {y}{x}\right ) x^{3} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{4} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.201 |
|
| 25448 |
\begin{align*}
y^{\prime }&=\frac {\left (x -y\right )^{3} \left (x +y\right )^{3} x}{\left (x^{2}-y^{2}-1\right ) y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.231 |
|
| 25449 |
\begin{align*}
y+2 \left (1-x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
19.234 |
|
| 25450 |
\begin{align*}
y^{\prime }&=\frac {-150 x^{3} y+60 x^{6}+350 x^{{7}/{2}}-150 x^{3}-125 \sqrt {x}\, y+250 x -125 \sqrt {x}-125 y^{3}+150 x^{3} y^{2}+750 y^{2} \sqrt {x}-60 x^{6} y-600 y x^{{7}/{2}}-1500 y x +8 x^{9}+120 x^{{13}/{2}}+600 x^{4}+1000 x^{{3}/{2}}}{25 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.244 |
|
| 25451 |
\begin{align*}
y^{\prime }&=\frac {y \left (x \ln \left (x \right )+\ln \left (x \right )+\ln \left (y\right ) x +\ln \left (y\right )-x -1+x \ln \left (x \right )^{2}+2 x \ln \left (y\right ) \ln \left (x \right )+x \ln \left (y\right )^{2}\right )}{x \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
19.261 |
|
| 25452 |
\begin{align*}
y^{\prime }-\frac {\sqrt {-1+y^{2}}}{\sqrt {x^{2}-1}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.283 |
|
| 25453 |
\begin{align*}
x +2 y-4-\left (-5+2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.296 |
|
| 25454 |
\begin{align*}
6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime }&=0 \\
y \left (\frac {1}{2}\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.306 |
|
| 25455 |
\begin{align*}
x^{2}+2 y x -4 y^{2}-\left (x^{2}-8 y x -4 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.317 |
|
| 25456 |
\begin{align*}
\frac {y \cos \left (\frac {y}{x}\right )}{x}-\left (\frac {x \sin \left (\frac {y}{x}\right )}{y}+\cos \left (\frac {y}{x}\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.318 |
|
| 25457 |
\begin{align*}
2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y&=\ln \left (x^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.322 |
|
| 25458 |
\begin{align*}
2 x -y+1+\left (2 y-x -1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.362 |
|
| 25459 |
\begin{align*}
x^{3} {y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.375 |
|
| 25460 |
\begin{align*}
y^{\prime }-\frac {3 y}{x}&=\frac {y^{2}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.399 |
|
| 25461 |
\begin{align*}
y^{\prime }&=t y^{{1}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.419 |
|
| 25462 |
\begin{align*}
x^{2} y^{\prime }&=x^{4} f \left (x \right ) y^{2}+1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
19.427 |
|
| 25463 |
\begin{align*}
y^{\prime } \sin \left (2 x \right )&=2 y+2 \cos \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
19.437 |
|
| 25464 |
\begin{align*}
y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.444 |
|
| 25465 |
\begin{align*}
2 x^{3} y+y^{3}-\left (x^{4}+2 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.445 |
|
| 25466 |
\begin{align*}
4 y&={y^{\prime }}^{2}+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.451 |
|
| 25467 |
\begin{align*}
2 \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) y^{\prime \prime }-\left (\left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )+\left (y-b \right ) \left (y-c \right )\right ) {y^{\prime }}^{2}+\left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} \left (A_{0} +\frac {B_{0}}{\left (y-a \right )^{2}}+\frac {C_{1}}{\left (y-b \right )^{2}}+\frac {D_{0}}{\left (y-c \right )^{2}}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.464 |
|
| 25468 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+g \left (x \right ) y+a \lambda \,{\mathrm e}^{\lambda x}-a \,{\mathrm e}^{\lambda x} g \left (x \right )-a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right ) \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
19.492 |
|
| 25469 |
\begin{align*}
\left (4 x -y\right ) y^{\prime }+2 x -5 y&=0 \\
y \left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.514 |
|
| 25470 |
\begin{align*}
a^{3} y^{\prime \prime \prime } y^{\prime \prime }&=\sqrt {1+c^{2} {y^{\prime \prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.519 |
|
| 25471 |
\begin{align*}
y^{\prime }&=\frac {y^{3} x \,{\mathrm e}^{2 x^{2}}}{y \,{\mathrm e}^{x^{2}}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.528 |
|
| 25472 |
\begin{align*}
y^{\prime }&=\frac {x +\frac {y}{2}}{\frac {x}{2}-y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.530 |
|
| 25473 |
\begin{align*}
y^{m} x^{n} \left (a x y^{\prime }+b y\right )+\alpha x y^{\prime }+\beta y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.533 |
|
| 25474 |
\begin{align*}
\left (2 y+x +7\right ) y^{\prime }-y+2 x +4&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.539 |
|
| 25475 |
\begin{align*}
x^{2}-y x +y^{2}-y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.542 |
|
| 25476 |
\begin{align*}
y^{\prime } y^{\prime \prime }&=x y^{2}+x^{2} y y^{\prime } \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
19.552 |
|
| 25477 |
\begin{align*}
y&=x \left (x^{2} y-1\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.554 |
|
| 25478 |
\begin{align*}
y^{\prime }&=\left (y x \right )^{{1}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.556 |
|
| 25479 |
\begin{align*}
y+\left (y^{n} a \,x^{2}-2 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.566 |
|
| 25480 |
\begin{align*}
x^{2} y^{\prime \prime }+6 y^{\prime } x +6 y&=4 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.580 |
|
| 25481 |
\begin{align*}
3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.582 |
|
| 25482 |
\begin{align*}
x^{3}+y^{3}&=3 y^{2} y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.606 |
|
| 25483 |
\begin{align*}
2 x \left (5 x^{2}+y^{2}\right ) y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.612 |
|
| 25484 |
\begin{align*}
2 y^{2}+4 x^{2}-y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.628 |
|
| 25485 |
\begin{align*}
x^{2} y^{\prime \prime }+2 \left (a +x \right ) y^{\prime }-b \left (b -1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
19.634 |
|
| 25486 |
\begin{align*}
x \left (x -a y\right ) y^{\prime }&=y \left (y-a x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.641 |
|
| 25487 |
\begin{align*}
x^{4} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (a \,x^{n -1}+a b \,x^{-2+n}+b^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
19.677 |
|
| 25488 |
\begin{align*}
3 x^{2} y+y^{2}-\left (-x^{3}-2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.686 |
|
| 25489 |
\begin{align*}
2 x^{2} y+2 \sqrt {1+y^{2} x^{4}}+x^{3} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.690 |
|
| 25490 |
\begin{align*}
y y^{\prime } x +x^{2}+y^{2}&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.704 |
|
| 25491 |
\begin{align*}
y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+3 y \ln \left (t \right )&=0 \\
y \left (2\right ) &= 3 \\
y^{\prime }\left (2\right ) &= 1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
19.705 |
|
| 25492 |
\begin{align*}
x \left (x +y\right ) y^{\prime }-y \left (x +y\right )+x \sqrt {x^{2}-y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.709 |
|
| 25493 |
\begin{align*}
2 x +4 y+\left (2 x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.714 |
|
| 25494 |
\begin{align*}
x^{3}+y^{3}+3 y^{2} y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.717 |
|
| 25495 |
\begin{align*}
y^{\prime }&=-\sin \left (y\right )^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.719 |
|
| 25496 |
\begin{align*}
\frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.727 |
|
| 25497 |
\begin{align*}
y^{2}-x^{2}+y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.738 |
|
| 25498 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
19.753 |
|
| 25499 |
\begin{align*}
\left (1+{y^{\prime }}^{2}\right )^{2}&=y^{2} y^{\prime \prime } \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= \sqrt {2} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
19.761 |
|
| 25500 |
\begin{align*}
y^{\prime \prime } x -2 \left (x^{2}-a \right ) y^{\prime }+2 n x y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
19.780 |
|