| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 27601 |
\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*} |
✓ |
✓ |
✓ |
✗ |
170.814 |
|
| 27602 |
\begin{align*}
x \left (x^{2 n}+a \right ) y^{\prime \prime }+\left (x^{2 n}+a -a n \right ) y^{\prime }-b^{2} x^{2 n -1} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
172.263 |
|
| 27603 |
\begin{align*}
y y^{\prime }-y&=-\frac {30 x}{121}+\frac {3 A \left (21 \sqrt {x}+35 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{242} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
173.875 |
|
| 27604 |
\begin{align*}
y^{\prime \prime }&=\frac {2 x \left (2 a -1\right ) y^{\prime }}{x^{2}-1}-\frac {\left (x^{2} \left (2 a \left (2 a -1\right )-v \left (v +1\right )\right )+2 a +v \left (v +1\right )\right ) y}{\left (x^{2}-1\right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
174.214 |
|
| 27605 |
\begin{align*}
x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-2 x^{3} y^{\prime }-\left (\left (a -n \right ) \left (a +n +1\right ) x^{2} \left (x^{2}-1\right )+2 a \,x^{2}+n \left (n +1\right ) \left (x^{2}-1\right )\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
174.345 |
|
| 27606 |
\begin{align*}
x y {y^{\prime }}^{2}-\left (a -b \,x^{2}+y^{2}\right ) y^{\prime }-b x y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
174.573 |
|
| 27607 |
\begin{align*}
-a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
174.786 |
|
| 27608 |
\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*} |
✓ |
✗ |
✓ |
✗ |
175.447 |
|
| 27609 |
\begin{align*}
y^{\prime }&=a \cos \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
175.640 |
|
| 27610 |
\begin{align*}
\left (1-3 x +y\right ) y^{\prime }&=2 x -2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
176.494 |
|
| 27611 |
\begin{align*}
-\left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y+2 x \left (a^{2}+2 x^{2}\right ) y^{\prime }+\left (a^{2}+x^{2}\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
176.671 |
|
| 27612 |
\begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
176.794 |
|
| 27613 |
\begin{align*}
2 \operatorname {a2} y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (\operatorname {c0} \,x^{2}+\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
177.108 |
|
| 27614 |
\begin{align*}
{y^{\prime }}^{4}&=4 y \left (x y^{\prime }-2 y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
178.191 |
|
| 27615 |
\begin{align*}
y y^{\prime }-y&=-\frac {2 x}{9}+A +\frac {B}{\sqrt {x}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
178.790 |
|
| 27616 |
\begin{align*}
\left (\left (a -y\right ) \left (b -y\right )+\left (a -y\right ) \left (-y+c \right )+\left (b -y\right ) \left (-y+c \right )\right ) {y^{\prime }}^{2}+2 \left (a -y\right ) \left (b -y\right ) \left (-y+c \right ) y^{\prime \prime }&=\operatorname {a3} \left (a -y\right )^{2} \left (b -y\right )^{2}+2 \operatorname {a2} \left (a -y\right )^{2} \left (-y+c \right )^{2}+\operatorname {a1} \left (b -y\right )^{2} \left (-y+c \right )^{2}+\operatorname {a0} \left (a -y\right )^{2} \left (b -y\right )^{2} \left (-y+c \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
179.759 |
|
| 27617 |
\begin{align*}
{\mathrm e}^{-x} y^{\prime }+y^{2}-2 y \,{\mathrm e}^{x}&=1-{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
179.796 |
|
| 27618 |
\begin{align*}
x&=y^{\prime } \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
181.111 |
|
| 27619 |
\begin{align*}
y+2 t +2 t y y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
181.960 |
|
| 27620 |
\begin{align*}
x y^{2} {y^{\prime }}^{2}-\left (y^{3}+x^{3}-a \right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
182.073 |
|
| 27621 |
\begin{align*}
x y^{\prime }+y&=4 \sqrt {y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
182.532 |
|
| 27622 |
\begin{align*}
x +\sin \left (y\right )-\cos \left (y\right )-x \cos \left (y\right ) \left (2 \sin \left (y\right ) x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
183.086 |
|
| 27623 |
\begin{align*}
x^{\prime }&=-x \left (k^{2}+x^{2}\right ) \\
x \left (0\right ) &= x_{0} \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
183.655 |
|
| 27624 |
\begin{align*}
2 y^{2}+4 x^{2} y+\left (4 y x +3 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
183.906 |
|
| 27625 |
\begin{align*}
y y^{\prime }-y&=-\frac {10 x}{49}+\frac {2 A \left (4 \sqrt {x}+61 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
184.507 |
|
| 27626 |
\begin{align*}
\sqrt {a {y^{\prime \prime }}^{2}+b {y^{\prime }}^{2}}+c y y^{\prime \prime }+d {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
185.464 |
|
| 27627 |
\begin{align*}
x^{4} y \left (3 y+2 x y^{\prime }\right )+x^{2} \left (4 y+3 x y^{\prime }\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
185.912 |
|
| 27628 |
\begin{align*}
y^{2}+\left (x \sqrt {y^{2}-x^{2}}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
186.047 |
|
| 27629 |
\begin{align*}
y y^{\prime }&=\left (\left (3-m \right ) x -1\right ) y-\left (m -1\right ) a x \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
187.392 |
|
| 27630 |
\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 |
|
| 27631 |
\begin{align*}
{y^{\prime }}^{2} x +y y^{\prime }+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
187.598 |
|
| 27632 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
187.730 |
|
| 27633 |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {2 A \left (\sqrt {x}+166 A +\frac {55 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
188.651 |
|
| 27634 |
\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 |
|
| 27635 |
\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*} |
✗ |
✗ |
✗ |
✗ |
189.659 |
|
| 27636 |
\begin{align*}
x^{\prime }&=-3 x+4 y+{\mathrm e}^{-t} \sin \left (2 t \right ) \\
y^{\prime }&=5 x+9 z+4 \,{\mathrm e}^{-t} \cos \left (2 t \right ) \\
z^{\prime }&=y+6 z-{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
189.839 |
|
| 27637 |
\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*} |
✗ |
✓ |
✓ |
✗ |
189.935 |
|
| 27638 |
\begin{align*}
y^{\prime \prime }+d +b y^{2}+c y+a y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
191.736 |
|
| 27639 |
\begin{align*}
y^{\prime \prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
192.496 |
|
| 27640 |
\begin{align*}
{y^{\prime \prime }}^{3}+y^{\prime \prime }+1&=x \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
192.915 |
|
| 27641 |
\begin{align*}
x^{4} {y^{\prime }}^{3}-x^{3} y {y^{\prime }}^{2}-x^{2} y^{2} y^{\prime }+x y^{3}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
193.980 |
|
| 27642 |
\begin{align*}
y^{\prime \prime }+y y^{\prime }-y^{3}+a y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
194.312 |
|
| 27643 |
\begin{align*}
{y^{\prime }}^{2}-2 \left (1-3 y\right ) y^{\prime }-\left (4-9 y\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
194.513 |
|
| 27644 |
\begin{align*}
\left (5 x -7 y+1\right ) y^{\prime }+x +y-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
194.849 |
|
| 27645 |
\begin{align*}
n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
195.343 |
|
| 27646 |
\begin{align*}
x y {y^{\prime }}^{2}+\left (a +x^{2}-y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
195.393 |
|
| 27647 |
\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 |
|
| 27648 |
\begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {A}{x^{{1}/{3}}}+\frac {B}{x^{{5}/{3}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
197.048 |
|
| 27649 |
\begin{align*}
x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
198.194 |
|
| 27650 |
\begin{align*}
y^{\prime }&=\frac {x^{2} \left (3 x +\sqrt {-9 x^{4}+4 y^{3}}\right )}{y^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
198.205 |
|
| 27651 |
\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*} |
✗ |
✓ |
✓ |
✗ |
198.299 |
|
| 27652 |
\begin{align*}
8 x^{2} y^{3}-2 y^{4}+\left (5 x^{3} y^{2}-8 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
198.453 |
|
| 27653 |
\begin{align*}
\left (6+3 x +5 y\right ) y^{\prime }&=2+x +7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
198.494 |
|
| 27654 |
\begin{align*}
y b^{2}+x \left (a^{2}+2 x^{2}\right ) y^{\prime }+x^{2} \left (a^{2}+x^{2}\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
200.159 |
|
| 27655 |
\begin{align*}
y^{\prime }&=\sqrt {\frac {y+1}{y^{2}}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
200.454 |
|
| 27656 |
\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*} |
✗ |
✓ |
✓ |
✗ |
201.472 |
|
| 27657 |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {A \left (5 \sqrt {x}+262 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
202.002 |
|
| 27658 |
\begin{align*}
\left (x y^{\prime }-y\right )^{2}&=a \left (1+{y^{\prime }}^{2}\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
204.188 |
|
| 27659 |
\begin{align*}
y x +x^{2} y^{\prime }&=\frac {y^{3}}{x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
204.229 |
|
| 27660 |
\begin{align*}
y y^{\prime }-\frac {a \left (x +1\right ) y}{2 x^{{7}/{4}}}&=\frac {a^{2} \left (x -1\right ) \left (5+3 x \right )}{4 x^{{5}/{2}}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
205.729 |
|
| 27661 |
\begin{align*}
y^{\prime \prime }&=a +b y+2 y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
205.765 |
|
| 27662 |
\begin{align*}
\left (\frac {y^{2}}{b}+\frac {x^{2}}{a}\right ) \left (y y^{\prime }+x \right )+\frac {\left (a -b \right ) \left (y y^{\prime }-x \right )}{a +b}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
206.154 |
|
| 27663 |
\begin{align*}
y y^{\prime }+y^{\prime \prime }&=y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
206.774 |
|
| 27664 |
\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 |
|
| 27665 |
\begin{align*}
x y^{\prime }+y&=3 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✗ |
✗ |
✗ |
✓ |
211.237 |
|
| 27666 |
\begin{align*}
\left (x^{3}+3 x y^{2}\right ) y^{\prime }&=y^{3}+3 x^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
211.522 |
|
| 27667 |
\begin{align*}
y y^{\prime }-\left (\left (2 n -1\right ) x -a n \right ) x^{-1-n} y&=n \left (x -a \right ) x^{-2 n} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
212.486 |
|
| 27668 |
\begin{align*}
\left (3 x -y-9\right ) y^{\prime }&=10-2 x +2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
215.521 |
|
| 27669 |
\begin{align*}
y&=\frac {k \left (y y^{\prime }+x \right )}{\sqrt {1+{y^{\prime }}^{2}}} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
216.297 |
|
| 27670 |
\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 |
|
| 27671 |
\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*} |
✓ |
✓ |
✓ |
✗ |
218.064 |
|
| 27672 |
\begin{align*}
{y^{\prime }}^{3}&=y \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
218.561 |
|
| 27673 |
\begin{align*}
y y^{\prime }-a \left (\frac {n +2}{n}+b \,x^{n}\right ) y&=-\frac {a^{2} x \left (\frac {n +1}{n}+b \,x^{n}\right )}{n} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
219.167 |
|
| 27674 |
\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 |
|
| 27675 |
\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 |
|
| 27676 |
\begin{align*}
x y^{2}+2 y+\left (3 x^{2} y-4 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
222.692 |
|
| 27677 |
\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*} |
✗ |
✓ |
✓ |
✗ |
223.079 |
|
| 27678 |
\begin{align*}
y^{\prime }&=\frac {x +y-1}{x +4 y+2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
223.433 |
|
| 27679 |
\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 |
|
| 27680 |
\begin{align*}
{y^{\prime }}^{3}+\left (x +2\right ) {\mathrm e}^{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
223.964 |
|
| 27681 |
\begin{align*}
{y^{\prime }}^{3}+\left (x +2\right ) {\mathrm e}^{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
229.930 |
|
| 27682 |
\begin{align*}
\left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (k^{3}+x^{3}\right ) y^{\prime }-\left (k^{2}-k x +x^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
233.139 |
|
| 27683 |
\begin{align*}
y y^{\prime }-\frac {a \left (\left (1+k \right ) x -1\right ) y}{x^{2}}&=\frac {a^{2} \left (1+k \right ) \left (x -1\right )}{x^{2}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
234.345 |
|
| 27684 |
\begin{align*}
\left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (1-x \right ) x \left (\operatorname {b2} x +\operatorname {a1} \right ) y^{\prime }+x^{2} \left (1-x \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
234.563 |
|
| 27685 |
\begin{align*}
y y^{\prime }-y&=A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (2 n +3\right ) A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
234.694 |
|
| 27686 |
\begin{align*}
x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
236.425 |
|
| 27687 |
\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 |
|
| 27688 |
\begin{align*}
{y^{\prime }}^{3}+y^{2}&=x y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
238.708 |
|
| 27689 |
\begin{align*}
y^{\prime \prime }&=a \left (1+2 y y^{\prime }\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
239.062 |
|
| 27690 |
\begin{align*}
x \left (3+2 x^{2} y\right ) y^{\prime }+\left (4+3 x^{2} y\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
243.663 |
|
| 27691 |
\begin{align*}
x \left (x^{2}-1\right ) y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }-y x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
248.449 |
|
| 27692 |
\begin{align*}
3 y {y^{\prime }}^{2}-2 x y y^{\prime }+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 (\lambda a +2 b \right ) x +b \lambda \right ) y^{\prime }+\lambda \left (c -2 a \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
255.741 |
|
| 27694 |
\begin{align*}
\left (1+{y^{\prime }}^{2}+y y^{\prime \prime }\right )^{2}&=\left (1+{y^{\prime }}^{2}\right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
258.079 |
|
| 27695 |
\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 |
|
| 27696 |
\begin{align*}
r^{\prime \prime }&=-\frac {k}{r^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
263.880 |
|
| 27697 |
\begin{align*}
y^{\prime }&=\frac {x +y-1}{x +4 y+2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
267.683 |
|
| 27698 |
\begin{align*}
y y^{\prime }&=a \left (-n b +x \right ) x^{n -1} y+c \left (x^{2}-\left (1+2 n \right ) b x +n \left (n +1\right ) b^{2}\right ) x^{2 n -1} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
268.816 |
|
| 27699 |
\begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
269.159 |
|
| 27700 |
\begin{align*}
y y^{\prime }-y&=A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (n +1\right ) \left (n +3\right ) A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
272.079 |
|