| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 27601 |
\begin{align*}
\left (A x y+A k y+B \,x^{2}+B k x \right ) y^{\prime }&=c y^{2}+d x y+k \left (d -B \right ) y \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
186.410 |
|
| 27602 |
\begin{align*}
y y^{\prime \prime }&=\operatorname {a0} +\operatorname {a1} y+y^{3} \left (\operatorname {a2} +\operatorname {a3} y\right )+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
186.436 |
|
| 27603 |
\begin{align*}
y y^{\prime }+\frac {a \left (x -2\right ) y}{x}&=\frac {2 a^{2} \left (x -1\right )}{x} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
187.403 |
|
| 27604 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (\alpha -\beta +\left (\alpha +\beta -2\right ) x \right ) y^{\prime }+\left (n +1\right ) \left (n +\alpha +\beta \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
187.523 |
|
| 27605 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
187.730 |
|
| 27606 |
\begin{align*}
y y^{\prime }-y&=a x +b \,x^{m} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
188.477 |
|
| 27607 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (\beta -\alpha -\left (\alpha +\beta +2\right ) x \right ) y^{\prime }+n \left (n +\alpha +\beta +1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
188.690 |
|
| 27608 |
\begin{align*}
y y^{\prime }+\frac {a \left (6 x -1\right ) y}{2 x}&=-\frac {a^{2} \left (x -1\right ) \left (4 x -1\right )}{2 x} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
188.853 |
|
| 27609 |
\begin{align*}
y y^{\prime }-a \left (1-\frac {b}{x}\right ) y&=a^{2} b \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
189.984 |
|
| 27610 |
\begin{align*}
-4 x -y-1+\left (x +y+3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
191.014 |
|
| 27611 |
\begin{align*}
y y^{\prime }+\frac {a \left (x -6\right ) y}{5 x^{{7}/{5}}}&=\frac {2 a^{2} \left (x -1\right ) \left (x +4\right )}{5 x^{{9}/{5}}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
191.431 |
|
| 27612 |
\begin{align*}
y y^{\prime }-y&=2 A \left (\sqrt {x}+4 A +\frac {3 A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
193.079 |
|
| 27613 |
\begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
195.343 |
|
| 27614 |
\begin{align*}
y y^{\prime }+\frac {a \left (13 x -3\right ) y}{6 x^{{2}/{3}}}&=-\frac {a^{2} \left (x -1\right ) \left (5 x -1\right )}{6 x^{{1}/{3}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
195.554 |
|
| 27615 |
\begin{align*}
y y^{\prime }+\frac {3 a \left (13 x -8\right ) y}{20 x^{{7}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (27 x -32\right )}{20 x^{{9}/{5}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
196.868 |
|
| 27616 |
\begin{align*}
x \left (x^{2}+a \right ) y^{\prime \prime }+\left (b \,x^{2}+c \right ) y^{\prime }+s x y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
197.030 |
|
| 27617 |
\begin{align*}
y y^{\prime }+\frac {a \left (7 x -12\right ) y}{10 x^{{7}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (x -16\right )}{10 x^{{9}/{5}}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
197.543 |
|
| 27618 |
\begin{align*}
x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
198.194 |
|
| 27619 |
\begin{align*}
y y^{\prime }+\frac {a \left (13 x -18\right ) y}{15 x^{{7}/{5}}}&=-\frac {4 a^{2} \left (x -1\right ) \left (x -6\right )}{15 x^{{9}/{5}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
198.205 |
|
| 27620 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (a \left (b +2\right ) x^{2}+\left (c -d +1\right ) x \right ) y^{\prime }}{\left (a x +1\right ) x^{2}}-\frac {\left (a b x -c d \right ) y}{\left (a x +1\right ) x^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
199.913 |
|
| 27621 |
\begin{align*}
y y^{\prime }-y&=-\frac {2 x}{9}+6 A^{2} \left (1+\frac {2 A}{\sqrt {x}}\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
201.399 |
|
| 27622 |
\begin{align*}
y y^{\prime }-\frac {2 a \left (3 x +2\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (8 x +1\right )}{5 x^{{11}/{5}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
202.412 |
|
| 27623 |
\begin{align*}
y y^{\prime }+\frac {a \left (33 x +2\right ) y}{30 x^{{6}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (9 x -4\right )}{30 x^{{7}/{5}}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
202.630 |
|
| 27624 |
\begin{align*}
y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (3 x +7\right )}{5 x^{{11}/{5}}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
203.314 |
|
| 27625 |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}&=a \left (1+{y^{\prime }}^{2}\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
204.188 |
|
| 27626 |
\begin{align*}
x^{\prime }&=x-y+2 z+{\mathrm e}^{-t}-3 t \\
y^{\prime }&=3 x-4 y+z+2 \,{\mathrm e}^{-t}+t \\
z^{\prime }&=-2 x+5 y+6 z+2 \,{\mathrm e}^{-t}-t \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
204.309 |
|
| 27627 |
\begin{align*}
y y^{\prime }-\frac {6 a \left (4 x +1\right ) y}{5 x^{{7}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (27 x +8\right )}{5 x^{{9}/{5}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
204.379 |
|
| 27628 |
\begin{align*}
y^{\prime \prime }+d +b y^{2}+c y+a y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
205.554 |
|
| 27629 |
\begin{align*}
y y^{\prime }-\frac {a \left (3 x -4\right ) y}{4 x^{{5}/{2}}}&=\frac {a^{2} \left (x -1\right ) \left (2+x \right )}{4 x^{4}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
206.335 |
|
| 27630 |
\begin{align*}
y^{\prime \prime }&=-\frac {2 x \left (n +1-2 a \right ) y^{\prime }}{x^{2}-1}-\frac {\left (4 a \,x^{2} \left (a -n \right )-\left (x^{2}-1\right ) \left (2 a +\left (v -n \right ) \left (v +n +1\right )\right )\right ) y}{\left (x^{2}-1\right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
207.154 |
|
| 27631 |
\begin{align*}
x^{2} \left (x +a_{2} \right ) y^{\prime \prime }+x \left (b_{1} x +a_{1} \right ) y^{\prime }+\left (b_{0} x +a_{0} \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
207.662 |
|
| 27632 |
\begin{align*}
y^{\prime }&=\sqrt {25-y^{2}} \\
y \left (-4\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
207.766 |
|
| 27633 |
\begin{align*}
y y^{\prime }-\frac {a \left (x -8\right ) y}{8 x^{{5}/{2}}}&=-\frac {a^{2} \left (x -1\right ) \left (3 x -4\right )}{8 x^{4}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
208.275 |
|
| 27634 |
\begin{align*}
y y^{\prime }-\frac {a \left (2 x -1\right ) y}{x^{{5}/{2}}}&=\frac {a^{2} \left (x -1\right ) \left (1+3 x \right )}{2 x^{4}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
208.615 |
|
| 27635 |
\begin{align*}
y y^{\prime }&=\frac {3 y}{\sqrt {a \,x^{{3}/{2}}+8 x}}+1 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
209.129 |
|
| 27636 |
\begin{align*}
\left (A x y+B \,x^{2}+x k \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*} |
✗ |
✓ |
✗ |
✗ |
209.319 |
|
| 27637 |
\begin{align*}
y y^{\prime }-\frac {a \left (6 x -13\right ) y}{13 x^{{5}/{2}}}&=-\frac {a^{2} \left (x -1\right ) \left (x -13\right )}{26 x^{4}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
209.642 |
|
| 27638 |
\begin{align*}
y^{\prime } x +y&=3 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✗ |
✗ |
✗ |
✓ |
211.237 |
|
| 27639 |
\begin{align*}
{y^{\prime \prime }}^{3}+y^{\prime \prime }+1&=x \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
212.178 |
|
| 27640 |
\begin{align*}
y^{\prime }&=\frac {-3 x^{2} y-y^{2}}{2 x^{3}+3 y x} \\
y \left (1\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
212.855 |
|
| 27641 |
\begin{align*}
y y^{\prime }-y&=\frac {9 x}{32}+\frac {15 \sqrt {b^{2}+x^{2}}}{32}+\frac {3 b^{2}}{64 \sqrt {b^{2}+x^{2}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
213.281 |
|
| 27642 |
\begin{align*}
y y^{\prime \prime }+a {y^{\prime }}^{2}+b y^{2} y^{\prime }+c y^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
213.378 |
|
| 27643 |
\begin{align*}
y y^{\prime }-y&=\frac {k}{\sqrt {A \,x^{2}+B x +c}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
214.457 |
|
| 27644 |
\begin{align*}
y y^{\prime }&=a x \cos \left (\lambda \,x^{2}\right ) y+x \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
215.227 |
|
| 27645 |
\begin{align*}
-\left (a \left (1+a \right ) \left (1-x \right )+b^{2} x \right ) y+2 \left (1-3 x \right ) \left (1-x \right ) x y^{\prime }+4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
216.529 |
|
| 27646 |
\begin{align*}
\left (a_{2} x^{2}+b_{2} x +c_{2} \right ) y^{\prime \prime }+\left (b_{1} x +c_{1} \right ) y^{\prime }+c_{0} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
216.964 |
|
| 27647 |
\begin{align*}
y y^{\prime }+\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*} |
✗ |
✗ |
✗ |
✗ |
217.768 |
|
| 27648 |
\begin{align*}
y y^{\prime }-\frac {a \left (4 x +3\right ) y}{14 x^{{8}/{7}}}&=-\frac {a^{2} \left (x -1\right ) \left (16 x +5\right )}{14 x^{{9}/{7}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
219.094 |
|
| 27649 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+\left (\left (\alpha +\beta +1\right ) x -\gamma \right ) y^{\prime }+\alpha \beta y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
219.729 |
|
| 27650 |
\begin{align*}
{y^{\prime }}^{4}-4 y \left (y^{\prime } x -2 y\right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
220.323 |
|
| 27651 |
\begin{align*}
y^{\prime }&=\frac {x +y-1}{x +4 y+2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
220.730 |
|
| 27652 |
\begin{align*}
y y^{\prime }-y&=\frac {3 x}{8}+\frac {3 \sqrt {a^{2}+x^{2}}}{8}-\frac {a^{2}}{16 \sqrt {a^{2}+x^{2}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
220.780 |
|
| 27653 |
\begin{align*}
x y^{2} {y^{\prime }}^{2}-\left (y^{3}+x^{3}-a \right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
220.952 |
|
| 27654 |
\begin{align*}
{y^{\prime }}^{3}+\left (2+x \right ) {\mathrm e}^{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
221.424 |
|
| 27655 |
\begin{align*}
\left (A y+B x +a \right ) y^{\prime }+B y+x k +b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
222.365 |
|
| 27656 |
\begin{align*}
\left (a \,x^{2}+b x +c \right ) y^{\prime \prime }-\left (-k^{2}+x^{2}\right ) y^{\prime }+\left (k +x \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
222.427 |
|
| 27657 |
\begin{align*}
y^{\prime }&=\frac {x^{3} \left (3 x +3+\sqrt {9 x^{4}-4 y^{3}}\right )}{\left (x +1\right ) y^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
223.348 |
|
| 27658 |
\begin{align*}
y y^{\prime } x&=a y^{2}+b y+c \,x^{n}+s \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
223.547 |
|
| 27659 |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime \prime }+\left (\lambda \left (a +c \right ) x^{2}+\left (c -a \right ) x +2 b \lambda \right ) y^{\prime }+\lambda ^{2} \left (c \,x^{2}+b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
223.711 |
|
| 27660 |
\begin{align*}
y y^{\prime }-a \left (1-\frac {b}{\sqrt {x}}\right ) y&=\frac {a^{2} b}{\sqrt {x}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
223.882 |
|
| 27661 |
\begin{align*}
y^{\prime }&=\frac {x^{2} \left (3 x +\sqrt {-9 x^{4}+4 y^{3}}\right )}{y^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
226.897 |
|
| 27662 |
\begin{align*}
y y^{\prime }+\frac {a \left (5 x +1\right ) y}{2 \sqrt {x}}&=a^{2} \left (-x^{2}+1\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
227.189 |
|
| 27663 |
\begin{align*}
{y^{\prime \prime }}^{2}+{y^{\prime }}^{2}&=a^{2} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
227.237 |
|
| 27664 |
\begin{align*}
x \left (x^{2}-1\right ) y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }-y x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
228.743 |
|
| 27665 |
\begin{align*}
y y^{\prime }&={\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*} |
✗ |
✗ |
✗ |
✗ |
228.951 |
|
| 27666 |
\begin{align*}
{y^{\prime }}^{4}&=4 y \left (y^{\prime } x -2 y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
230.046 |
|
| 27667 |
\begin{align*}
x y^{2} {y^{\prime }}^{2}+\left (a -x^{3}-y^{3}\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
230.535 |
|
| 27668 |
\begin{align*}
y^{\prime }&=\frac {x +y-1}{x +4 y+2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
231.377 |
|
| 27669 |
\begin{align*}
y^{\prime } x&=3 x^{2 n +1} y^{3}+\left (b x -n \right ) y+c \,x^{1-n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
232.461 |
|
| 27670 |
\begin{align*}
\left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (k^{3}+x^{3}\right ) y^{\prime }-\left (k^{2}-x k +x^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
233.139 |
|
| 27671 |
\begin{align*}
y y^{\prime }-y&=A \sqrt {x}+2 A^{2}+\frac {B}{\sqrt {x}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
233.346 |
|
| 27672 |
\begin{align*}
{y^{\prime }}^{4}&=4 y \left (y^{\prime } x -2 y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
233.684 |
|
| 27673 |
\begin{align*}
y^{\prime }&=3 x +\sqrt {-x^{2}+y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
233.819 |
|
| 27674 |
\begin{align*}
y y^{\prime }-\frac {3 a y}{x^{{7}/{4}}}&=\frac {a^{2} \left (x -1\right ) \left (x -9\right )}{4 x^{{5}/{2}}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
234.491 |
|
| 27675 |
\begin{align*}
y^{\prime } x&=y \cos \left (\ln \left (\frac {y}{x}\right )\right ) \\
\end{align*} |
✓ |
✗ |
✓ |
✓ |
235.951 |
|
| 27676 |
\begin{align*}
x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
236.425 |
|
| 27677 |
\begin{align*}
y^{3}+\left ({y^{\prime }}^{2}+y^{2}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
237.418 |
|
| 27678 |
\begin{align*}
\left (a \,x^{3}+x^{2}+b \right ) y^{\prime \prime }+a^{2} x \left (x^{2}-b \right ) y^{\prime }-a^{3} b x y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
238.479 |
|
| 27679 |
\begin{align*}
y y^{\prime }-y&=-\frac {x}{4}+\frac {6 A \left (\sqrt {x}+8 A +\frac {5 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
238.542 |
|
| 27680 |
\begin{align*}
y^{\prime }&=y \sqrt {-1+y^{2}} \\
y \left (a \right ) &= b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
240.378 |
|
| 27681 |
\begin{align*}
y^{\prime \prime }+a y y^{\prime }+y^{3} b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
240.819 |
|
| 27682 |
\begin{align*}
\left (y+a x +b \right ) y^{\prime }&=\alpha y+\beta x +\gamma \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
241.664 |
|
| 27683 |
\begin{align*}
y y^{\prime \prime }&=\operatorname {a2} y^{2}+\operatorname {a3} y^{1+a}+\operatorname {a1} y y^{\prime }+a {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
243.527 |
|
| 27684 |
\begin{align*}
\left (x -1\right ) \left (x -2\right ) y^{\prime \prime }-\left (2 x -3\right ) y^{\prime }+y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
245.188 |
|
| 27685 |
\begin{align*}
y y^{\prime }-y&=2 x +2 A \left (-10 \sqrt {x}+19 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
247.770 |
|
| 27686 |
\begin{align*}
\left (\operatorname {b1} \,x^{2}+\operatorname {b0} \right ) y+\left (\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0} \right ) y^{\prime }+4 \left (1-x \right ) x \left (-a x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
247.796 |
|
| 27687 |
\begin{align*}
y y^{\prime }+x \left (a \,x^{2}+b \right ) y+x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
248.257 |
|
| 27688 |
\begin{align*}
y y^{\prime }-y&=-\frac {x}{4}+\frac {A \left (\sqrt {x}+5 A +\frac {3 A^{2}}{\sqrt {x}}\right )}{4} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
249.146 |
|
| 27689 |
\begin{align*}
y y^{\prime }&=\left (a \,{\mathrm e}^{\lambda x}+b \right ) y+c \left (a^{2} {\mathrm e}^{2 \lambda x}+a b \left (\lambda x +1\right ) {\mathrm e}^{\lambda x}+b^{2} \lambda x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
249.945 |
|
| 27690 |
\begin{align*}
y y^{\prime }-y&=2 x +2 A \left (10 \sqrt {x}+31 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
252.598 |
|
| 27691 |
\begin{align*}
y y^{\prime }-y&=-\frac {6 x}{25}+\frac {6 A \left (2 \sqrt {x}+7 A +\frac {4 A^{2}}{\sqrt {x}}\right )}{25} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
253.493 |
|
| 27692 |
\begin{align*}
3 y {y^{\prime }}^{2}-2 y y^{\prime } x +4 y^{2}-x^{2}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
255.404 |
|
| 27693 |
\begin{align*}
x^{2} \left (a x +b \right ) y^{\prime \prime }+\left (c \,x^{2}+\left (a \lambda +2 b \right ) x +b \lambda \right ) y^{\prime }+\lambda \left (c -2 a \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
255.741 |
|
| 27694 |
\begin{align*}
y y^{\prime }-\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*} |
✗ |
✓ |
✗ |
✗ |
255.870 |
|
| 27695 |
\begin{align*}
y y^{\prime }&=\left (\left (3-m \right ) x -1\right ) y-\left (m -1\right ) a x \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
256.361 |
|
| 27696 |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {4 A \left (-10 \sqrt {x}+27 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
258.152 |
|
| 27697 |
\begin{align*}
y y^{\prime }&=x^{n -1} \left (\left (2 n +1\right ) x +a n \right ) y-n \,x^{2 n} \left (a +x \right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
258.522 |
|
| 27698 |
\begin{align*}
\left (2 x +y+5\right ) y^{\prime }&=3 x +6 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
259.418 |
|
| 27699 |
\begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+3 x^{3} y^{\prime }+\frac {4 y}{x -1}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
260.213 |
|
| 27700 |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {2 A \left (5 \sqrt {x}+34 A +\frac {15 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
261.745 |
|