| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 25501 |
\begin{align*}
2 \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (3 a \,x^{2}+2 b x +c \right ) y^{\prime }+\lambda y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
88.898 |
|
| 25502 |
\begin{align*}
y^{\prime } x&=a \sin \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \sin \left (\lambda x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
89.113 |
|
| 25503 |
\begin{align*}
\operatorname {a2} y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x \left (\operatorname {a0} +x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
89.646 |
|
| 25504 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}+\left (-1+a y\right ) y^{\prime }-y \left (1+y\right ) \left (b^{2} y^{2}-a^{2}\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
89.889 |
|
| 25505 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -v \left (v +1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
89.920 |
|
| 25506 |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}&=a \left (1+{y^{\prime }}^{2}\right ) \left (y^{2}+x^{2}\right )^{{3}/{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
89.935 |
|
| 25507 |
\begin{align*}
x^{\prime }&=\frac {9 x}{10}+\frac {21 y}{10}+\frac {16 z}{5} \\
y^{\prime }&=\frac {7 x}{10}+\frac {13 y}{2}+\frac {21 z}{5} \\
z^{\prime }&=\frac {11 x}{10}+\frac {17 y}{10}+\frac {17 z}{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
89.959 |
|
| 25508 |
\begin{align*}
y^{\prime }&=b \,{\mathrm e}^{\mu x} y^{2}+a \lambda \,{\mathrm e}^{\lambda x}-a^{2} b \,{\mathrm e}^{\left (2 \lambda +\mu \right ) x} \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
90.135 |
|
| 25509 |
\begin{align*}
x^{2} \left (a^{2} x^{2 n}-1\right ) y^{\prime \prime }+x \left (a^{2} \left (n +1\right ) x^{2 n}+n -1\right ) y^{\prime }-\nu \left (\nu +1\right ) a^{2} n^{2} x^{2 n} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
90.798 |
|
| 25510 |
\begin{align*}
y^{\prime }&=x \left (y-4\right )^{2}-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
90.978 |
|
| 25511 |
\begin{align*}
\left (-x^{2}+1\right ) \eta ^{\prime \prime }-\left (x +1\right ) \eta ^{\prime }+\left (1+k \right ) \eta &=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
91.349 |
|
| 25512 |
\begin{align*}
{y^{\prime }}^{2}-\left (y^{4}+x y^{2}+x^{2}\right ) {y^{\prime }}^{2}+\left (x y^{6}+x^{2} y^{4}+x^{3} y^{2}\right ) y^{\prime }-x^{3} y^{6}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
91.522 |
|
| 25513 |
\begin{align*}
y^{\prime } y-y&=2 x +2 A \left (10 \sqrt {x}+31 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
91.533 |
|
| 25514 |
\begin{align*}
3 y+2 y^{\prime } x +4 x y^{2}+3 x^{2} y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
91.640 |
|
| 25515 |
\begin{align*}
\left (3 x +4 y\right ) y^{\prime }+y-2 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
91.762 |
|
| 25516 |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{3}+a b x -x^{2}+b \right ) y^{\prime }+a^{2} b x y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
91.907 |
|
| 25517 |
\begin{align*}
y^{\prime }&=\frac {2 x y \,{\mathrm e}^{\frac {x^{2}}{y^{2}}}}{y^{2}+y^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}+2 x^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
92.088 |
|
| 25518 | \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+\left (2 a +1\right ) y^{\prime }-b \left (2 a +b \right ) y&=0 \\
\end{align*} | ✗ | ✓ | ✓ | ✗ | 92.341 |
|
| 25519 |
\begin{align*}
y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+\lambda \operatorname {arccot}\left (x \right )^{n} \left (x^{1+k} y-1\right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
92.391 |
|
| 25520 |
\begin{align*}
y^{\prime } y-y&=-\frac {30 x}{121}+\frac {3 A \left (21 \sqrt {x}+35 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{242} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
92.425 |
|
| 25521 |
\begin{align*}
y^{\prime } y+\frac {a \left (39 x -4\right ) y}{42 x^{{9}/{7}}}&=-\frac {a^{2} \left (x -1\right ) \left (9 x -1\right )}{42 x^{{11}/{7}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
92.563 |
|
| 25522 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}+b y+c \,{\mathrm e}^{-\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
92.642 |
|
| 25523 |
\begin{align*}
\left (a y^{2}+2 b x y+c \,x^{2}\right ) y^{\prime }+b y^{2}+2 c x y+d \,x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
93.020 |
|
| 25524 |
\begin{align*}
\left (x -3 y+4\right ) y^{\prime }&=5 x -7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
93.069 |
|
| 25525 |
\begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
93.940 |
|
| 25526 |
\begin{align*}
\left (1+{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
94.017 |
|
| 25527 |
\begin{align*}
\left (y \sqrt {y^{2}+x^{2}}+\left (y^{2}-x^{2}\right ) \sin \left (\alpha \right )-2 x y \cos \left (\alpha \right )\right ) y^{\prime }+x \sqrt {y^{2}+x^{2}}+2 x y \sin \left (\alpha \right )+\left (y^{2}-x^{2}\right ) \cos \left (\alpha \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
94.152 |
|
| 25528 |
\begin{align*}
\left (\cos \left (\lambda x \right ) a +b \right ) \left (y^{\prime }-y^{2}\right )-a \,\lambda ^{2} \cos \left (\lambda x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
94.211 |
|
| 25529 |
\begin{align*}
{\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
94.399 |
|
| 25530 |
\begin{align*}
y^{\prime } x&=a \,x^{n} y^{2}+b -a \,b^{2} x^{n} \ln \left (x \right )^{2} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
94.418 |
|
| 25531 |
\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*} |
✓ |
✓ |
✓ |
✗ |
94.498 |
|
| 25532 |
\begin{align*}
\left (a \tan \left (\lambda x \right )+b \right ) y^{\prime }&=y^{2}+k \tan \left (\mu x \right ) y-d^{2}+k d \tan \left (\mu x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
94.793 |
|
| 25533 |
\begin{align*}
y^{\prime } y-y&=\frac {2 a^{2}}{\sqrt {8 a^{2}+x^{2}}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
94.857 |
|
| 25534 |
\begin{align*}
y^{\prime } y+a y+\frac {\left (a^{2}-1\right ) x}{4}+b \,x^{n}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
94.935 |
|
| 25535 |
\begin{align*}
y^{\prime } y-y&=-\frac {4 x}{25}+\frac {A \left (7 \sqrt {x}+49 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{50} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
94.966 |
|
| 25536 |
\begin{align*}
y^{\prime } y&={\mathrm e}^{a x} \left (2 a \,x^{2}+b +2 x \right ) y+{\mathrm e}^{2 a x} \left (-a \,x^{4}-b \,x^{2}+c \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
95.198 |
|
| 25537 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=x \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
95.683 |
|
| 25538 | \begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 95.737 |
|
| 25539 |
\begin{align*}
f \left (x \right )^{2} y^{\prime }-f^{\prime }\left (x \right ) y^{2}+g \left (x \right ) \left (y-f \left (x \right )\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
95.931 |
|
| 25540 |
\begin{align*}
y^{\prime } y-y&=-\frac {10 x}{49}+\frac {2 A \left (4 \sqrt {x}+61 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
96.036 |
|
| 25541 |
\begin{align*}
y^{\prime }&=\lambda \sin \left (\lambda x \right ) y^{2}+f \left (x \right ) \cos \left (\lambda x \right ) y-f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
96.381 |
|
| 25542 |
\begin{align*}
y^{\prime } y-y&=2 x +2 A \left (-10 \sqrt {x}+19 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
96.424 |
|
| 25543 |
\begin{align*}
{y^{\prime }}^{3}+y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
96.434 |
|
| 25544 |
\begin{align*}
x -y \arctan \left (\frac {y}{x}\right )+x \arctan \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
96.438 |
|
| 25545 |
\begin{align*}
\operatorname {A2} \left (a x +b \right )^{2} y^{\prime \prime }+\operatorname {A1} \left (a x +b \right ) y^{\prime }+\operatorname {A0} \left (a x +b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
96.482 |
|
| 25546 |
\begin{align*}
y^{3} \left (y^{\prime } y+x \right )&=\left (y^{2}+x^{2}\right )^{3} y^{\prime } \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
96.524 |
|
| 25547 |
\begin{align*}
t \left (t -4\right ) y^{\prime \prime }+3 t y^{\prime }+4 y&=2 \\
y \left (3\right ) &= 0 \\
y^{\prime }\left (3\right ) &= -1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
96.614 |
|
| 25548 |
\begin{align*}
y {y^{\prime \prime }}^{3}+y^{3} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
96.657 |
|
| 25549 |
\begin{align*}
y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (-a^{2} \left (x^{2}-1\right )^{2}-n \left (n +1\right ) \left (x^{2}-1\right )-m^{2}\right ) y}{\left (x^{2}-1\right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
97.168 |
|
| 25550 |
\begin{align*}
y^{\prime } y&=-n y^{2}+a \left (2 n +1\right ) {\mathrm e}^{x} y+b y-a^{2} n \,{\mathrm e}^{2 x}-a b \,{\mathrm e}^{x}+c \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
97.182 |
|
| 25551 |
\begin{align*}
{y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
97.200 |
|
| 25552 |
\begin{align*}
\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }&=a \,x^{-2+n} y^{2}+b \,x^{m -1} y+c \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
97.312 |
|
| 25553 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x \left (x^{2}+1\right )}-\frac {\left (-v \left (v +1\right ) x^{2}-n^{2}\right ) y}{x^{2} \left (x^{2}+1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
97.404 |
|
| 25554 |
\begin{align*}
y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}+1}-\frac {\left (a^{2} \left (x^{2}+1\right )^{2}-n \left (n +1\right ) \left (x^{2}+1\right )+m^{2}\right ) y}{\left (x^{2}+1\right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
97.415 |
|
| 25555 |
\begin{align*}
\left (-x^{2}+1\right ) z^{\prime \prime }+\left (1-3 x \right ) z^{\prime }+k z&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
97.579 |
|
| 25556 |
\begin{align*}
y&=\frac {k \left (y^{\prime } y+x \right )}{\sqrt {1+{y^{\prime }}^{2}}} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
97.827 |
|
| 25557 |
\begin{align*}
y^{\prime } x&=a \cos \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \cos \left (\lambda x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
97.864 |
|
| 25558 | \begin{align*}
x^{2} \left (a^{2} x^{2 n}-1\right ) y^{\prime \prime }+x \left (a p \,x^{n}+q \right ) y^{\prime }+\left (a r \,x^{n}+s \right ) y&=0 \\
\end{align*} | ✗ | ✓ | ✗ | ✗ | 98.126 |
|
| 25559 |
\begin{align*}
p \left (1+p \right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
99.261 |
|
| 25560 |
\begin{align*}
\left (x^{3}+3\right ) y^{\prime }+2 y x +5 x^{2}&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
99.512 |
|
| 25561 |
\begin{align*}
\frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
99.708 |
|
| 25562 |
\begin{align*}
2 x^{2} y^{\prime }&=2 y x +\left (-x \cot \left (x \right )+1\right ) \left (x^{2}-y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
99.829 |
|
| 25563 |
\begin{align*}
\left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
101.105 |
|
| 25564 |
\begin{align*}
y^{\prime } y-y&=A \sqrt {x}+2 A^{2}+\frac {B}{\sqrt {x}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
101.280 |
|
| 25565 |
\begin{align*}
\left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 y x +x^{2}+2\right ) y^{\prime }+2 y^{2}+1&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
101.599 |
|
| 25566 |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }-y^{{3}/{2}}+12 y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
102.039 |
|
| 25567 |
\begin{align*}
2 x \sin \left (y\right )+2 x +3 y \cos \left (x \right )+\left (\cos \left (y\right ) x^{2}+3 \sin \left (x \right )\right ) y^{\prime }&=0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
102.067 |
|
| 25568 |
\begin{align*}
\left (-k +p \right ) \left (1+k +p \right ) y+\left (1+k \right ) \left (1-2 x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
102.152 |
|
| 25569 |
\begin{align*}
b y+a x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
102.343 |
|
| 25570 |
\begin{align*}
-\left (k -p \right ) \left (1+k +p \right ) y+2 \left (1-\left (3-2 k \right ) x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
102.491 |
|
| 25571 |
\begin{align*}
x^{\prime \prime }&=x^{2}-4 x+\lambda \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
102.660 |
|
| 25572 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+\left (\left (a +1\right ) x +b \right ) y^{\prime }-l y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
102.675 |
|
| 25573 |
\begin{align*}
y^{\prime } x&=a \,x^{n} \left (y+b \ln \left (x \right )\right )^{2}-b \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
102.704 |
|
| 25574 |
\begin{align*}
y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (\left (x^{2}-1\right ) \left (a \,x^{2}+b x +c \right )-k^{2}\right ) y}{\left (x^{2}-1\right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
102.747 |
|
| 25575 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}+b \lambda \,{\mathrm e}^{\lambda x}-a \,b^{2} x^{n} {\mathrm e}^{2 \lambda x} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
102.967 |
|
| 25576 |
\begin{align*}
y^{\prime } y-\frac {a \left (x +1\right ) y}{2 x^{{7}/{4}}}&=\frac {a^{2} \left (x -1\right ) \left (3 x +5\right )}{4 x^{{5}/{2}}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
103.300 |
|
| 25577 |
\begin{align*}
\left (A x y+B \,x^{2}+k x \right ) y^{\prime }&=A y^{2}+c x y+d \,x^{2}+\left (-A \beta +k \right ) y-c \beta x -k \beta \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
103.514 |
|
| 25578 | \begin{align*}
y^{\prime }&=\frac {y^{2}}{y x +\left (x y^{2}\right )^{{1}/{3}}} \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 104.149 |
|
| 25579 |
\begin{align*}
x +\sin \left (y\right )-\cos \left (y\right )-x \cos \left (y\right ) \left (2 x \sin \left (y\right )+1\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
105.339 |
|
| 25580 |
\begin{align*}
f \left (y^{2}+x^{2}\right ) \sqrt {1+{y^{\prime }}^{2}}-y^{\prime } x +y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
105.477 |
|
| 25581 |
\begin{align*}
y \,{\mathrm e}^{2 x}-3 x \,{\mathrm e}^{2 y}+\left (\frac {{\mathrm e}^{2 x}}{2}-3 x^{2} {\mathrm e}^{2 y}-{\mathrm e}^{y}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
106.050 |
|
| 25582 |
\begin{align*}
y^{\prime }&=\lambda \operatorname {arccot}\left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
106.079 |
|
| 25583 |
\begin{align*}
x^{n +1} y^{\prime }&=x^{2 n} a y^{2}+c \,x^{m}+d \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
106.598 |
|
| 25584 |
\begin{align*}
\left (\sinh \left (\lambda x \right ) a +b \right ) y^{\prime }&=y^{2}+c \sinh \left (\mu x \right ) y-d^{2}+c d \sinh \left (\mu x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
107.322 |
|
| 25585 |
\begin{align*}
x^{2}+y \,{\mathrm e}^{2 y}+\left (2 y x +x \right ) {\mathrm e}^{2 y} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
107.351 |
|
| 25586 |
\begin{align*}
4 x +3 y+2+\left (5 x +4 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
107.516 |
|
| 25587 |
\begin{align*}
\left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y-2 x \left (a^{2}-x^{2}\right ) y^{\prime }+\left (a^{2}-x^{2}\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
107.534 |
|
| 25588 |
\begin{align*}
\left (y^{2}+2 x^{2} y^{\prime }\right ) y^{\prime \prime }+2 \left (x +y\right ) {y^{\prime }}^{2}+y^{\prime } x +y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
107.994 |
|
| 25589 |
\begin{align*}
{y^{\prime }}^{2}&=\left (y-a \right ) \left (y-b \right ) \left (y-c \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
108.305 |
|
| 25590 |
\begin{align*}
a \left (x^{2}-1\right )^{2} y^{\prime \prime }+b x \left (x^{2}-1\right ) y^{\prime }+\left (c \,x^{2}+d x +e \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
108.353 |
|
| 25591 |
\begin{align*}
y^{\prime }&=\frac {-x \sin \left (2 y\right )-\sin \left (2 y\right )+x \cos \left (2 y\right )+x}{2 x \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
108.608 |
|
| 25592 |
\begin{align*}
y^{\prime }&=\frac {x +y+1}{x +2 y+3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
108.659 |
|
| 25593 |
\begin{align*}
y^{\prime }&=\frac {x +y-1}{x +4 y+2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
108.712 |
|
| 25594 |
\begin{align*}
{\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
109.216 |
|
| 25595 |
\begin{align*}
y^{\prime \prime }&=-\frac {b x y^{\prime }}{\left (x^{2}-1\right ) a}-\frac {\left (c \,x^{2}+d x +e \right ) y}{a \left (x^{2}-1\right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
109.396 |
|
| 25596 |
\begin{align*}
\left (x^{2}+y x +a y^{2}\right ) y^{\prime }&=a \,x^{2}+y x +y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
109.470 |
|
| 25597 |
\begin{align*}
y {y^{\prime \prime }}^{4}+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
109.688 |
|
| 25598 | \begin{align*}
\left ({y^{\prime }}^{2}+y^{2}\right ) \cos \left (x \right )^{4}-a^{2}&=0 \\
\end{align*} | ✗ | ✗ | ✗ | ✗ | 109.708 |
|
| 25599 |
\begin{align*}
\left (x -{y^{\prime }}^{2}\right ) y^{\prime \prime }&=x^{2}-y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
110.177 |
|
| 25600 |
\begin{align*}
\left (a \cosh \left (\lambda x \right )+b \right ) y^{\prime }&=y^{2}+c \cosh \left (\mu x \right ) y-d^{2}+c d \cosh \left (\mu x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
110.319 |
|