| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 27701 |
\begin{align*}
{y^{\prime }}^{2}-y y^{\prime \prime }&=n \sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
414.626 |
|
| 27702 |
\begin{align*}
x \left (2 x^{3}+y^{3}\right ) y^{\prime }&=\left (2 x^{3}-x^{2} y+y^{3}\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
414.749 |
|
| 27703 |
\begin{align*}
y^{\prime }&=a \tan \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
415.996 |
|
| 27704 |
\begin{align*}
y^{\prime \prime }&=\frac {\left (2 b c \,x^{c} \left (x^{2}-1\right )+2 \left (a -1\right ) x^{2}-2 a \right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (b^{2} c^{2} x^{2 c} \left (x^{2}-1\right )+b c \,x^{c +2} \left (2 a -c -1\right )-b c \,x^{c} \left (2 a -c +1\right )+x^{2} \left (a \left (a -1\right )-v \left (v +1\right )\right )-a \left (1+a \right )\right ) y}{x^{2} \left (x^{2}-1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
419.687 |
|
| 27705 |
\begin{align*}
\ln \left (y^{x}\right ) y^{\prime }&=3 x^{2} y \\
y \left (2\right ) &= {\mathrm e}^{3} \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
420.029 |
|
| 27706 |
\begin{align*}
2 y^{2}-9 y x +\left (3 y x -6 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
420.175 |
|
| 27707 |
\begin{align*}
\left (y x +1\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
421.050 |
|
| 27708 |
\begin{align*}
y^{\prime \prime }&=\frac {1}{\sqrt {a y}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
421.883 |
|
| 27709 |
\begin{align*}
y^{\prime }&=\frac {x^{3}+x^{2} y-y^{3}}{x^{3}-x y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
427.782 |
|
| 27710 |
\begin{align*}
x \left (-y x +1\right ) y^{\prime }+\left (y x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
429.247 |
|
| 27711 |
\begin{align*}
x \left (-1+x \right ) \left (x -a \right ) y^{\prime \prime }+\left (\left (\alpha +\beta +1\right ) x^{2}-\left (\alpha +\beta +1+a \left (\gamma +d \right )-a \right ) x +a \gamma \right ) y^{\prime }+\left (\alpha \beta x -q \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
430.402 |
|
| 27712 |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime }+\alpha y^{2}+\beta x y+\frac {b \left (a +\beta \right )}{\alpha }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
433.767 |
|
| 27713 |
\begin{align*}
y {y^{\prime \prime }}^{4}+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
434.559 |
|
| 27714 |
\begin{align*}
x^{2}+2 y^{2}+\left (4 y x -y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
437.006 |
|
| 27715 |
\begin{align*}
\sqrt {x}\, y^{\prime }&=\sqrt {-x +y}+\sqrt {x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
440.903 |
|
| 27716 |
\begin{align*}
y y^{\prime }-y&=-\frac {6 x}{25}+\frac {4 B^{2} \left (\left (2-A \right ) x^{{1}/{3}}-\frac {3 B \left (2 A +1\right )}{2}+\frac {B^{2} \left (1-3 A \right )}{x^{{1}/{3}}}-\frac {A \,B^{3}}{x^{{2}/{3}}}\right )}{75} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
441.402 |
|
| 27717 |
\begin{align*}
\left (x^{2} y^{\prime }+y^{2}\right ) \left (y^{\prime } x +y\right )&=\left (1+y^{\prime }\right )^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
451.090 |
|
| 27718 |
\begin{align*}
y+x \left (3 y x -2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
454.818 |
|
| 27719 |
\begin{align*}
4 x y^{2}+\left (3 x^{2} y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
455.817 |
|
| 27720 |
\begin{align*}
x^{\prime \prime }-2 {x^{\prime }}^{2}+x^{\prime }-2 x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
464.071 |
|
| 27721 |
\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*} |
✗ |
✗ |
✓ |
✗ |
465.243 |
|
| 27722 |
\begin{align*}
x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
466.247 |
|
| 27723 |
\begin{align*}
x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
467.554 |
|
| 27724 |
\begin{align*}
\left (y x +1\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
469.667 |
|
| 27725 |
\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*} |
✗ |
✗ |
✗ |
✗ |
479.194 |
|
| 27726 |
\begin{align*}
\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
483.683 |
|
| 27727 |
\begin{align*}
y+x y^{2}-\left (x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
485.473 |
|
| 27728 |
\begin{align*}
y^{\prime }&=-\frac {3 t^{2}+2 y^{2}}{4 t y+6 y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
487.855 |
|
| 27729 |
\begin{align*}
y^{\prime }&=\frac {x +y-1}{x +4 y+2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
488.808 |
|
| 27730 |
\begin{align*}
x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}-h^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
498.173 |
|
| 27731 |
\begin{align*}
\left (y x +a \,x^{n}+b \,x^{2}\right ) y^{\prime }&=y^{2}+c \,x^{n}+b x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
498.445 |
|
| 27732 |
\begin{align*}
-x^{\prime \prime }&=\arctan \left (x\right ) \\
x \left (0\right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
498.662 |
|
| 27733 |
\begin{align*}
3 x^{2}-8 y x +2 y^{2}-\left (4 x^{2}-4 y x +3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
508.468 |
|
| 27734 |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}&={y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
509.422 |
|
| 27735 |
\begin{align*}
y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}}&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
514.570 |
|
| 27736 |
\begin{align*}
y^{\prime }&=\frac {-3 t^{2}-2 y^{2}}{4 t y+6 y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
517.423 |
|
| 27737 |
\begin{align*}
y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}}&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
517.874 |
|
| 27738 |
\begin{align*}
y y^{\prime }+y^{\prime \prime }&=1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
519.237 |
|
| 27739 |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}&={y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
521.882 |
|
| 27740 |
\begin{align*}
{y^{\prime \prime }}^{2}+{y^{\prime }}^{2}&={y^{\prime }}^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
523.152 |
|
| 27741 |
\begin{align*}
c y+b x y^{\prime }+\left (a \,x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
524.683 |
|
| 27742 |
\begin{align*}
x^{\prime }&=t +x^{2} \\
x \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
528.707 |
|
| 27743 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }-\left (-\lambda ^{2}+x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
533.427 |
|
| 27744 |
\begin{align*}
{y^{\prime }}^{3}&=\frac {y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
534.105 |
|
| 27745 |
\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*} |
✗ |
✗ |
✗ |
✗ |
550.113 |
|
| 27746 |
\begin{align*}
\left (1+{y^{\prime }}^{2}+y y^{\prime \prime }\right )^{2}&=\left (1+{y^{\prime }}^{2}\right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
550.113 |
|
| 27747 |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime }+\alpha y^{2}+\beta x y+\gamma &=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
552.357 |
|
| 27748 |
\begin{align*}
y^{\prime \prime }&=a \sqrt {b y^{2}+{y^{\prime }}^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
560.101 |
|
| 27749 |
\begin{align*}
2 y x +\left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
569.703 |
|
| 27750 |
\begin{align*}
x -\frac {y}{y^{\prime }}&=\frac {2}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
579.215 |
|
| 27751 |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime \prime }+\left (2 n +1\right ) a x y^{\prime }+c y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
586.213 |
|
| 27752 |
\begin{align*}
y^{\prime }&=x +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
606.068 |
|
| 27753 |
\begin{align*}
y y^{\prime }+y x&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
617.938 |
|
| 27754 |
\begin{align*}
y+x \left (2 y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
620.671 |
|
| 27755 |
\begin{align*}
y^{\prime \prime }+\sin \left (y\right )&=0 \\
y \left (\infty \right ) &= \pi \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
636.684 |
|
| 27756 |
\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*} |
✗ |
✓ |
✓ |
✗ |
682.009 |
|
| 27757 |
\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*} |
✗ |
✓ |
✓ |
✗ |
684.507 |
|
| 27758 |
\begin{align*}
\left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}}&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
716.943 |
|
| 27759 |
\begin{align*}
\left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}}&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
731.178 |
|
| 27760 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x -\left (v +2\right ) \left (v -1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
734.075 |
|
| 27761 |
\begin{align*}
y^{\prime \prime }-y y^{\prime }&=6 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
790.796 |
|
| 27762 |
\begin{align*}
{y^{\prime }}^{4} x -2 y {y^{\prime }}^{3}+12 x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
823.299 |
|
| 27763 |
\begin{align*}
y^{\prime \prime }&=a \sqrt {b y^{2}+{y^{\prime }}^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
835.448 |
|
| 27764 |
\begin{align*}
{y^{\prime \prime }}^{2}+{y^{\prime }}^{2}&=a^{2} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
855.779 |
|
| 27765 |
\begin{align*}
-x^{\prime \prime }&=1-x-x^{2} \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
876.397 |
|
| 27766 |
\begin{align*}
-x^{\prime \prime }&=2 x-x^{2} \\
x \left (0\right ) &= 0 \\
x \left (\pi \right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
879.198 |
|
| 27767 |
\begin{align*}
a x y {y^{\prime }}^{2}+\left (x^{2}-a y^{2}-b \right ) y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
904.268 |
|
| 27768 |
\begin{align*}
3 y {y^{\prime }}^{2}-2 y y^{\prime } x +4 y^{2}-x^{2}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
916.148 |
|
| 27769 |
\begin{align*}
{y^{\prime }}^{2}+4 x^{4} y^{\prime }-12 x^{4} y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
928.867 |
|
| 27770 |
\begin{align*}
{y^{\prime }}^{3}+\left (2+x \right ) {\mathrm e}^{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
933.712 |
|
| 27771 |
\begin{align*}
x \left (\left (m -1\right ) \left (A x +B \right ) y+m \left (d \,x^{2}+e x +F \right )\right ) y^{\prime }&=\left (A \left (1-n \right ) x -B n \right ) y^{2}+\left (d \left (2-n \right ) x^{2}+e \left (1-n \right ) x -F n \right ) y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
968.244 |
|
| 27772 |
\begin{align*}
{y^{\prime }}^{3}+\left (2+x \right ) {\mathrm e}^{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
970.081 |
|
| 27773 |
\begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{2+2 y^{4}-4 y^{2} x^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 y^{2} x^{4}-2 x^{6}}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{2+2 y^{4}-4 y^{2} x^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 y^{2} x^{4}-2 x^{6}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
977.704 |
|
| 27774 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (\lambda ^{3}+x^{3}\right ) y^{\prime }-\left (\lambda ^{2}-\lambda x +x^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1014.590 |
|
| 27775 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\left (\alpha \gamma +\beta \right ) x +\beta \lambda \right ) y^{\prime }-\left (x \alpha +\beta \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1027.932 |
|
| 27776 |
\begin{align*}
y^{\prime \prime }&=-\left (\frac {1-\operatorname {a1} -\operatorname {b1}}{x -\operatorname {c1}}+\frac {1-\operatorname {a2} -\operatorname {b2}}{x -\operatorname {c2}}+\frac {1-\operatorname {a3} -\operatorname {b3}}{x -\operatorname {c3}}\right ) y^{\prime }-\frac {\left (\frac {\operatorname {a1} \operatorname {b1} \left (\operatorname {c1} -\operatorname {c3} \right ) \left (\operatorname {c1} -\operatorname {c2} \right )}{x -\operatorname {c1}}+\frac {\operatorname {a2} \operatorname {b2} \left (\operatorname {c2} -\operatorname {c1} \right ) \left (\operatorname {c2} -\operatorname {c3} \right )}{x -\operatorname {c2}}+\frac {\operatorname {a3} \operatorname {b3} \left (\operatorname {c3} -\operatorname {c2} \right ) \left (\operatorname {c3} -\operatorname {c1} \right )}{x -\operatorname {c3}}\right ) y}{\left (x -\operatorname {c1} \right ) \left (x -\operatorname {c2} \right ) \left (x -\operatorname {c3} \right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1117.693 |
|
| 27777 |
\begin{align*}
y^{\prime \prime }&=-\left (\frac {\left (1-\operatorname {al1} -\operatorname {bl1} \right ) \operatorname {b1}}{\operatorname {b1} x -\operatorname {a1}}+\frac {\left (1-\operatorname {al2} -\operatorname {bl2} \right ) \operatorname {b2}}{\operatorname {b2} x -\operatorname {a2}}+\frac {\left (1-\operatorname {al3} -\operatorname {bl3} \right ) \operatorname {b3}}{\operatorname {b3} x -\operatorname {a3}}\right ) y^{\prime }-\frac {\left (\frac {\operatorname {al1} \operatorname {bl1} \left (\operatorname {a1} \operatorname {b2} -\operatorname {a2} \operatorname {b1} \right ) \left (-\operatorname {a1} \operatorname {b3} +\operatorname {a3} \operatorname {b1} \right )}{\operatorname {b1} x -\operatorname {a1}}+\frac {\operatorname {al2} \operatorname {bl2} \left (\operatorname {a2} \operatorname {b3} -\operatorname {a3} \operatorname {b2} \right ) \left (\operatorname {a1} \operatorname {b2} -\operatorname {a2} \operatorname {b1} \right )}{\operatorname {b2} x -\operatorname {a2}}+\frac {\operatorname {al3} \operatorname {bl3} \left (-\operatorname {a1} \operatorname {b3} +\operatorname {a3} \operatorname {b1} \right ) \left (\operatorname {a2} \operatorname {b3} -\operatorname {a3} \operatorname {b2} \right )}{\operatorname {b3} x -\operatorname {a3}}\right ) y}{\left (\operatorname {b1} x -\operatorname {a1} \right ) \left (\operatorname {b2} x -\operatorname {a2} \right ) \left (\operatorname {b3} x -\operatorname {a3} \right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1248.425 |
|
| 27778 |
\begin{align*}
y^{\prime }&=\frac {-2 x +4 y}{x +y} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1304.962 |
|
| 27779 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (x^{2} \left (\left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right )+\left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )+\left (x^{2}-\operatorname {a3} \right ) \left (x^{2}-\operatorname {a1} \right )\right )-\left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )\right ) y^{\prime }}{x \left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )}-\frac {\left (A \,x^{2}+B \right ) y}{x \left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1347.449 |
|
| 27780 |
\begin{align*}
{y^{\prime }}^{4}&=4 y \left (y^{\prime } x -2 y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1371.358 |
|
| 27781 |
\begin{align*}
\left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (a -x \right ) \left (b -x \right ) \left (c -x \right ) \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (a -x \right )^{2} \left (b -x \right )^{2} \left (c -x \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1379.480 |
|
| 27782 |
\begin{align*}
9 y^{4} \left (x^{2}-1\right ) {y^{\prime }}^{2}-6 x y^{5} y^{\prime }-4 x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1398.160 |
|
| 27783 |
\begin{align*}
{y^{\prime }}^{4} x -2 y {y^{\prime }}^{3}+12 x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1405.746 |
|
| 27784 |
\begin{align*}
9 \left (-x^{2}+1\right ) y^{4} {y^{\prime }}^{2}+6 x y^{5} y^{\prime }+4 x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1444.556 |
|
| 27785 |
\begin{align*}
y {y^{\prime \prime }}^{2}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1538.779 |
|
| 27786 |
\begin{align*}
y^{\prime }&=t +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2296.239 |
|
| 27787 |
\begin{align*}
y^{\prime }-y y^{\prime \prime }&=n \sqrt {{y^{\prime }}^{2}+a^{2} y^{\prime \prime }} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
3241.424 |
|