| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 25501 |
\begin{align*}
x^{\prime }&=4 x^{2}+4 \\
x \left (\frac {\pi }{4}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
49.737 |
|
| 25502 |
\begin{align*}
y^{\prime }&=3 x y^{{1}/{3}} \\
y \left (-1\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.748 |
|
| 25503 |
\begin{align*}
2 x +3 y-1+\left (2 x -3 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.819 |
|
| 25504 |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{-y x +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.886 |
|
| 25505 |
\begin{align*}
x^{n} y^{\prime \prime }+\left (x^{n} a -x^{n -1}+a b x +b \right ) y^{\prime }+a^{2} b x y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
49.899 |
|
| 25506 |
\begin{align*}
x^{\prime }&=7 x+5 y-9 z-8 \,{\mathrm e}^{-2 t} \\
y^{\prime }&=4 x+y+z+2 \,{\mathrm e}^{5 t} \\
z^{\prime }&=-2 y+3 z+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.906 |
|
| 25507 |
\begin{align*}
\left (a \,x^{2}+b x +c \right ) y^{\prime }&=y^{2}+\left (a x +\mu \right ) y-\lambda ^{2} x^{2}+\lambda \left (b -\mu \right ) x +\lambda c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.936 |
|
| 25508 |
\begin{align*}
y+2 \left (1-x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
49.964 |
|
| 25509 |
\begin{align*}
y^{\prime }&=\frac {x^{2}-y^{2}}{3 x y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.984 |
|
| 25510 |
\begin{align*}
z^{\prime }+4 z&={\mathrm e}^{8 i t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.995 |
|
| 25511 |
\begin{align*}
y^{\prime }&=\frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.125 |
|
| 25512 |
\begin{align*}
\frac {x^{2}-y^{2}}{x \left (2 x^{2}+y^{2}\right )}+\frac {\left (x^{2}+2 y^{2}\right ) y^{\prime }}{y \left (2 x^{2}+y^{2}\right )}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.180 |
|
| 25513 |
\begin{align*}
y y^{\prime \prime }&=y^{2}-3 y y^{\prime }+3 {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.253 |
|
| 25514 |
\begin{align*}
x \left (-x^{2}+1\right ) {y^{\prime }}^{2}-2 \left (-x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
50.306 |
|
| 25515 |
\begin{align*}
y^{\prime \prime }+x^{n} \left (a \,x^{2}+\left (a c +b \right ) x +b c \right ) y^{\prime }-x^{n} \left (a x +b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
50.324 |
|
| 25516 |
\begin{align*}
3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.335 |
|
| 25517 |
\begin{align*}
s^{2}+s^{\prime }&=\frac {s+1}{s t} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
50.335 |
|
| 25518 |
\begin{align*}
\frac {2 y}{x}+\left (4 x^{2} y-3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.513 |
|
| 25519 |
\begin{align*}
y^{\prime }&=y^{2}-\frac {\lambda ^{2}}{2}-\frac {3 \lambda ^{2} \tan \left (\lambda x \right )^{2}}{4}+a \cos \left (\lambda x \right )^{2} \sin \left (\lambda x \right )^{n} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
50.523 |
|
| 25520 |
\begin{align*}
y^{\prime }&=-\frac {\left (-8-8 y^{3}+24 y^{{3}/{2}} {\mathrm e}^{x}-18 \,{\mathrm e}^{2 x}-8 y^{{9}/{2}}+36 y^{3} {\mathrm e}^{x}-54 \,{\mathrm e}^{2 x} y^{{3}/{2}}+27 \,{\mathrm e}^{3 x}\right ) {\mathrm e}^{x}}{8 \sqrt {y}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
50.639 |
|
| 25521 |
\begin{align*}
z^{\prime }+4 i z&={\mathrm e}^{8 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.648 |
|
| 25522 |
\begin{align*}
\left (5-x +6 y\right ) y^{\prime }&=3-x +4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.653 |
|
| 25523 |
\begin{align*}
x^{\prime }&=x^{3}+a x^{2}-b x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.878 |
|
| 25524 |
\begin{align*}
\left (t -1\right ) y^{\prime \prime }-3 y^{\prime } t +4 y&=\sin \left (t \right ) \\
y \left (-2\right ) &= 2 \\
y^{\prime }\left (-2\right ) &= 1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
50.931 |
|
| 25525 |
\begin{align*}
y^{\prime }&=\frac {-b^{3}+6 b^{2} x -12 b \,x^{2}+8 x^{3}-4 b y^{2}+8 x y^{2}+8 y^{3}}{\left (2 x -b \right )^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.935 |
|
| 25526 |
\begin{align*}
\left (x -3 y+4\right ) y^{\prime }&=5 x -7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.976 |
|
| 25527 |
\begin{align*}
y&=y^{\prime } x +x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.026 |
|
| 25528 |
\begin{align*}
x^{2} {y^{\prime }}^{3}+\left (2 x +y\right ) y y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
51.049 |
|
| 25529 |
\begin{align*}
y^{\prime }&=\frac {y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right ) x +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 ) x +y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )-y \sin \left (\frac {y}{x}\right ) x -y \sin \left (\frac {y}{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 \cos \left (\frac {y}{x}\right ) \sin \left (\frac {y}{2 x}\right ) x \cos \left (\frac {y}{2 x}\right ) \left (x +1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
51.109 |
|
| 25530 |
\begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=-4 x+4 y-2 z \\
z^{\prime }&=-4 y+4 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.181 |
|
| 25531 |
\begin{align*}
2 x^{3} y^{\prime }&=\left (3 x^{2}+a y^{2}\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.223 |
|
| 25532 |
\begin{align*}
y y^{\prime }+a x +b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
51.227 |
|
| 25533 |
\begin{align*}
y^{\prime }&=y^{2}+a \tan \left (\beta x \right ) y+a b \tan \left (\beta x \right )-b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
51.262 |
|
| 25534 |
\begin{align*}
a_{2} x^{2} y^{\prime \prime }+\left (a_{1} x^{2}+b_{1} x \right ) y^{\prime }+\left (a_{0} x^{2}+b_{0} x +c_{0} \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
51.316 |
|
| 25535 |
\begin{align*}
y^{\prime }&=y^{{1}/{5}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
51.344 |
|
| 25536 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+\left (k \left (a -k \right ) x^{2}+\left (a n +b k -2 k n \right ) x +n \left (b -n -1\right )\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
51.357 |
|
| 25537 |
\begin{align*}
4 x +3 y+2+\left (5 x +4 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.507 |
|
| 25538 |
\begin{align*}
\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.634 |
|
| 25539 |
\begin{align*}
x +3 y-4+\left (x +4 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.690 |
|
| 25540 |
\begin{align*}
x y^{2}+\left (3-2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.753 |
|
| 25541 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{2}+b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
51.779 |
|
| 25542 |
\begin{align*}
y^{\prime }&=\left (a \cosh \left (\lambda x \right )^{2}-\lambda \right ) y^{2}+a +\lambda -a \cosh \left (\lambda x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
51.826 |
|
| 25543 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x \left (x^{2}-a \right ) y^{\prime }+\left (2 n \,x^{2}+\left (\left (-1\right )^{n}-1\right ) a \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
51.864 |
|
| 25544 |
\begin{align*}
y^{\prime }&=3 x y^{{1}/{3}} \\
y \left (-1\right ) &= {\frac {3}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
51.934 |
|
| 25545 |
\begin{align*}
z^{\prime \prime }+z+z^{5}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
51.956 |
|
| 25546 |
\begin{align*}
y y^{\prime }&=\frac {y}{\left (a x +b \right )^{2}}+1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
51.981 |
|
| 25547 |
\begin{align*}
x {y^{\prime }}^{2}-a y y^{\prime }+b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
51.995 |
|
| 25548 |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
52.019 |
|
| 25549 |
\begin{align*}
y^{\prime }&=\frac {y \ln \left (x \right )+\cosh \left (x \right ) x a y^{2}+\cosh \left (x \right ) x^{3} b}{x \ln \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.035 |
|
| 25550 |
\begin{align*}
\left (a \,x^{3}+\left (a x +b y\right )^{3}\right ) y y^{\prime }+x \left (\left (a x +b y\right )^{3}+y^{3} b \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.038 |
|
| 25551 |
\begin{align*}
y^{\prime \prime }&=\frac {1}{y}-\frac {x y^{\prime }}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.106 |
|
| 25552 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (x^{2}+1\right ) y^{\prime }}{x^{3}}-\frac {y}{x^{4}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
52.123 |
|
| 25553 |
\begin{align*}
\left (x^{2}+1\right ) \ln \left (x^{2}+1\right ) y^{\prime }-2 y x&=\ln \left (x^{2}+1\right )-2 x \arctan \left (x \right ) \\
y \left (-\infty \right ) &= -\frac {\pi }{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
52.217 |
|
| 25554 |
\begin{align*}
y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.342 |
|
| 25555 |
\begin{align*}
y \left (2 x^{2}-y x +y^{2}\right )-x^{2} \left (2 x -y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.345 |
|
| 25556 |
\begin{align*}
-y+y^{\prime } x&=x^{2} \sqrt {x^{2}-y^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
52.347 |
|
| 25557 |
\begin{align*}
\left (x^{n}+a \right )^{2} y^{\prime \prime }+b \,x^{m} \left (x^{n}+a \right ) y^{\prime }-x^{-2+n} \left (b \,x^{m +1}+a n -a \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
52.357 |
|
| 25558 |
\begin{align*}
2 y y^{\prime } x&=y^{2}-x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.372 |
|
| 25559 |
\begin{align*}
y^{\prime }&=\left (a \sinh \left (\lambda x \right )^{2}-\lambda \right ) y^{2}-a \sinh \left (\lambda x \right )^{2}+\lambda -a \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.373 |
|
| 25560 |
\begin{align*}
y^{\prime }&=\frac {2 a +\sqrt {-y^{2}+4 a x}+x^{2} \sqrt {-y^{2}+4 a x}+x^{3} \sqrt {-y^{2}+4 a x}}{y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
52.446 |
|
| 25561 |
\begin{align*}
\left (a x +b \right ) y^{\prime \prime }+s \left (c x +d \right ) y^{\prime }-s^{2} \left (\left (a +c \right ) x +b +d \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
52.504 |
|
| 25562 |
\begin{align*}
x -y y^{\prime }&=a {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.505 |
|
| 25563 |
\begin{align*}
y^{\prime }&=\frac {1}{y+2+\sqrt {1+3 x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.557 |
|
| 25564 |
\begin{align*}
2 y^{2}+4 x^{2} y+\left (4 y x +3 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.636 |
|
| 25565 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (x -1\right )}+\frac {v \left (v +1\right ) y}{4 x^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
52.664 |
|
| 25566 |
\begin{align*}
y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.673 |
|
| 25567 |
\begin{align*}
y x +y^{2}+\left (x^{2}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.712 |
|
| 25568 |
\begin{align*}
\left (x +y\right )^{2} y^{\prime }&=\left (x +y+2\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.717 |
|
| 25569 |
\begin{align*}
\left (1+a \cos \left (2 x \right )\right ) y^{\prime \prime }+\lambda y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
52.802 |
|
| 25570 |
\begin{align*}
y^{\prime \prime }-\frac {a^{2}}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.882 |
|
| 25571 |
\begin{align*}
y y^{\prime }-y&=\frac {\left (2 m +1\right ) x}{4 m^{2}}+\frac {A}{x}-\frac {A^{2}}{x^{3}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
52.898 |
|
| 25572 |
\begin{align*}
2 y&=3 y^{\prime } x +4+2 \ln \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.917 |
|
| 25573 |
\begin{align*}
\left (a_{2} x +b_{2} \right ) y^{\prime \prime }+\left (a_{1} x +b_{1} \right ) y^{\prime }+\left (a_{0} x +b_{0} \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
52.931 |
|
| 25574 |
\begin{align*}
y^{\prime }&=\frac {2 y^{2}-y x +2 x^{2}}{y x +2 x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
53.018 |
|
| 25575 |
\begin{align*}
y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}-1}+\frac {v \left (v +1\right ) y}{x^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
53.083 |
|
| 25576 |
\begin{align*}
y^{\prime }&=y \left (\mu -y\right ) \left (\mu -2 y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
53.084 |
|
| 25577 |
\begin{align*}
\left (11-11 x -4 y\right ) y^{\prime }&=62-8 x -25 y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
53.137 |
|
| 25578 |
\begin{align*}
y^{2} y^{\prime \prime }-a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
53.158 |
|
| 25579 |
\begin{align*}
\left (5 x -2 y+7\right ) y^{\prime }&=x -3 y+2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
53.171 |
|
| 25580 |
\begin{align*}
x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
53.254 |
|
| 25581 |
\begin{align*}
y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}}&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
53.283 |
|
| 25582 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{2}+\sqrt {x^{3}-6 y}+x^{2} \sqrt {x^{3}-6 y}+x^{3} \sqrt {x^{3}-6 y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
53.389 |
|
| 25583 |
\begin{align*}
2 y^{\prime \prime }&=1+12 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
53.504 |
|
| 25584 |
\begin{align*}
y y^{\prime }-y&=12 x +\frac {A}{x^{{5}/{2}}} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
53.536 |
|
| 25585 |
\begin{align*}
y^{\prime }&=\frac {\cos \left (y\right ) \left (\cos \left (y\right ) x^{3}-x -1\right )}{\left (x \sin \left (y\right )-1\right ) \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
53.580 |
|
| 25586 |
\begin{align*}
\left (t^{4}+t^{2}\right ) x^{\prime \prime }+2 t^{3} x^{\prime }+3 x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
53.603 |
|
| 25587 |
\begin{align*}
y^{\prime }&=y^{2}+x^{n -1} a n -a^{2} x^{2 n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
53.609 |
|
| 25588 |
\begin{align*}
x \left (2 x +3 y\right ) y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
53.683 |
|
| 25589 |
\begin{align*}
y+\sqrt {x^{2}-y^{2}}&=y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
53.722 |
|
| 25590 |
\begin{align*}
\left (x^{2}-y\right ) y^{\prime }-4 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
53.956 |
|
| 25591 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -v \left (v -1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
53.957 |
|
| 25592 |
\begin{align*}
x -2 y+1+\left (4 x -3 y-6\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
53.974 |
|
| 25593 |
\begin{align*}
\left (-\left (1-y\right ) \left (-y+a \right )+y \left (1-y\right )+\left (-y+a \right ) y\right ) {y^{\prime }}^{2}+2 \left (1-y\right ) \left (-y+a \right ) y y^{\prime \prime }&=\operatorname {a3} \left (1-y\right )^{2} \left (-y+a \right )^{2}+\operatorname {a1} \left (1-y\right )^{2} y^{2}+\operatorname {a2} \left (-y+a \right )^{2} y^{2}+\operatorname {a0} \left (-y+a \right )^{2} y^{2} \left (1-y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
54.072 |
|
| 25594 |
\begin{align*}
\left (a_{2} x^{2}+b_{2} x +c_{2} \right ) y^{\prime }&=y^{2}+\left (a_{1} x +b_{1} \right ) y-\lambda \left (\lambda +a_{1} -a_{2} \right ) x^{2}+\lambda \left (b_{2} -b_{1} \right ) x +\lambda c_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
54.072 |
|
| 25595 |
\begin{align*}
y^{\prime }&=t^{m} y^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
54.098 |
|
| 25596 |
\begin{align*}
x^{2}-y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
54.124 |
|
| 25597 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\lambda x} y^{2}+a \,x^{n} y+a \lambda \,x^{n} {\mathrm e}^{-\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
54.161 |
|
| 25598 |
\begin{align*}
\left (x +2 y+1\right ) y^{\prime }+7+x -4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
54.332 |
|
| 25599 |
\begin{align*}
y^{\prime }&=\frac {4 x^{3} y^{2}}{x^{4} y+2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
54.369 |
|
| 25600 |
\begin{align*}
y^{\prime }&=\frac {2 x +y-1}{x -y-2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
54.516 |
|