| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 27701 |
\begin{align*}
y^{\prime }&=t +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
274.027 |
|
| 27702 |
\begin{align*}
y^{\prime }&=x +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
280.695 |
|
| 27703 |
\begin{align*}
x y^{2} {y^{\prime }}^{2}+\left (a -x^{3}-y^{3}\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
289.033 |
|
| 27704 |
\begin{align*}
-\left (a \left (a +1\right ) \left (1-x \right )+b^{2} x \right ) y+2 \left (-3 x +1\right ) \left (1-x \right ) x y^{\prime }+4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
292.661 |
|
| 27705 |
\begin{align*}
{y^{\prime }}^{2}+4 x^{4} y^{\prime }-12 x^{4} y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
293.428 |
|
| 27706 |
\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*} |
✗ |
✓ |
✗ |
✗ |
293.472 |
|
| 27707 |
\begin{align*}
\left (\left (a x +c \right ) y+\left (1-n \right ) x^{2}+\left (2 n -1\right ) x -n \right ) y^{\prime }&=2 a y^{2}+2 y x \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
297.907 |
|
| 27708 |
\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*} |
✗ |
✓ |
✗ |
✗ |
299.332 |
|
| 27709 |
\begin{align*}
2 x^{3} {y^{\prime }}^{3}+6 x^{2} y {y^{\prime }}^{2}-\left (1-6 y x \right ) y y^{\prime }+2 y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
305.499 |
|
| 27710 |
\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*} |
✗ |
✗ |
✗ |
✗ |
306.392 |
|
| 27711 |
\begin{align*}
\ln \left (x^{2}+1\right ) y^{\prime \prime }+\frac {4 x y^{\prime }}{x^{2}+1}+\frac {\left (-x^{2}+1\right ) y}{\left (x^{2}+1\right )^{2}}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
308.815 |
|
| 27712 |
\begin{align*}
\operatorname {a0} \operatorname {a1} \left (-k +x \right ) y+\left (1-\operatorname {a0} +\operatorname {a1} +\operatorname {a0} \operatorname {a2} -\operatorname {a3} +\left (\operatorname {a2} +\operatorname {a3} \right ) x +\left (1+\operatorname {a0} +\operatorname {a1} \right ) x^{2}\right ) y^{\prime }+\left (1-x \right ) \left (-x +a \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
311.214 |
|
| 27713 |
\begin{align*}
y^{\prime }&=x -y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
313.578 |
|
| 27714 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (-2 a \,x^{2}-\left (b +1\right ) x +k \right ) y^{\prime }+2 \left (a x +1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
320.237 |
|
| 27715 |
\begin{align*}
2 \left (x y^{\prime }+y\right )^{3}-y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
321.520 |
|
| 27716 |
\begin{align*}
y^{\prime }&=a \cot \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
321.929 |
|
| 27717 |
\begin{align*}
{y^{\prime }}^{4}-4 x^{2} y {y^{\prime }}^{2}+16 x y^{2} y^{\prime }-16 y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
323.892 |
|
| 27718 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\beta x +2 c \right ) y^{\prime }-\left (\alpha x +2 b -\beta \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
324.352 |
|
| 27719 |
\begin{align*}
y y^{\prime \prime }&=c y^{2}+b y y^{\prime }+a {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
328.318 |
|
| 27720 |
\begin{align*}
\left (y x +a \,x^{n}+b \,x^{2}\right ) y^{\prime }&=y^{2}+c \,x^{n}+b x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
330.362 |
|
| 27721 |
\begin{align*}
y^{3} y^{\prime }+y^{\prime \prime }&=y y^{\prime } \sqrt {y^{4}+4 y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
330.502 |
|
| 27722 |
\begin{align*}
y y^{\prime }&={\mathrm e}^{\lambda x} \left (2 a \lambda x +a +b \right ) y-{\mathrm e}^{2 \lambda x} \left (a^{2} \lambda \,x^{2}+a b x +c \right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
332.758 |
|
| 27723 |
\begin{align*}
\left (a \,x^{n +1}+b \,x^{n}+c \right )^{2} y^{\prime \prime }+\left (\alpha \,x^{n}+\beta \,x^{n -1}+\gamma \right ) y^{\prime }+\left (n \left (-a n -a +\alpha \right ) x^{n -1}+\left (n -1\right ) \left (-n b +\beta \right ) x^{-2+n}\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
336.962 |
|
| 27724 |
\begin{align*}
y^{\prime \prime \prime } {y^{\prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
337.752 |
|
| 27725 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\beta x +2 c \right ) y^{\prime }+\left (\beta -2 b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
339.320 |
|
| 27726 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (\left (1-4 a \right ) x^{2}-1\right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (\left (-v^{2}+x^{2}\right ) \left (x^{2}-1\right )^{2}+4 a \left (a +1\right ) x^{4}-2 a \,x^{2} \left (x^{2}-1\right )\right ) y}{x^{2} \left (x^{2}-1\right )^{2}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
341.467 |
|
| 27727 |
\begin{align*}
\operatorname {f5} y^{2}+\operatorname {f4} y y^{\prime }+\operatorname {f3} {y^{\prime }}^{2}+\operatorname {f2} y y^{\prime \prime }+\operatorname {f1} y^{\prime } y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
342.536 |
|
| 27728 |
\begin{align*}
y^{\prime \prime }-y y^{\prime }&=6 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
353.107 |
|
| 27729 |
\begin{align*}
y^{\prime }&=\sqrt {25-y^{2}} \\
y \left (-4\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
355.482 |
|
| 27730 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (\left (\alpha +\beta +1\right ) x^{2}-\left (\alpha +\beta +1+a \left (\gamma +\delta \right )-\delta \right ) x +a \gamma \right ) y^{\prime }}{x \left (x -1\right ) \left (x -a \right )}-\frac {\left (\alpha \beta x -q \right ) y}{x \left (x -1\right ) \left (x -a \right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
363.013 |
|
| 27731 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (n \,x^{2}+m x +k \right ) y^{\prime }+\left (-1+k \right ) \left (\left (-a k +n \right ) x +m -b k \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
367.449 |
|
| 27732 |
\begin{align*}
2 \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+3 \left (3 a \,x^{2}+2 b x +c \right ) y^{\prime }+\left (6 a x +2 b +\lambda \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
367.931 |
|
| 27733 |
\begin{align*}
y y^{\prime \prime }+a {y^{\prime }}^{2}+b y y^{\prime }+c y^{2}+d y^{1-a}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
368.750 |
|
| 27734 |
\begin{align*}
y^{\prime \prime }&=a \sqrt {b y^{2}+{y^{\prime }}^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
372.311 |
|
| 27735 |
\begin{align*}
\left (x -1\right ) \left (x -2\right ) y^{\prime \prime }-\left (2 x -3\right ) y^{\prime }+y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
376.827 |
|
| 27736 |
\begin{align*}
x \left (a \,x^{2}+b x +1\right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y^{\prime }+\left (n x +m \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
390.722 |
|
| 27737 |
\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*} |
✓ |
✓ |
✓ |
✗ |
391.796 |
|
| 27738 |
\begin{align*}
a y+y y^{\prime }+y^{\prime \prime }&=y^{3} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
395.638 |
|
| 27739 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (A \,x^{2}+B x +C \right ) y^{\prime }}{\left (x -a \right ) \left (x -b \right ) \left (x -c \right )}-\frac {\left (\operatorname {DD} x +E \right ) y}{\left (x -a \right ) \left (x -b \right ) \left (x -c \right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
396.663 |
|
| 27740 |
\begin{align*}
\left (2 x^{3}-x^{2} y+y^{3}\right ) y-x \left (2 x^{3}+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
405.438 |
|
| 27741 |
\begin{align*}
y^{3}+\left ({y^{\prime }}^{2}+y^{2}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
407.533 |
|
| 27742 |
\begin{align*}
y y^{\prime \prime }&=\operatorname {a2} y^{2}+\operatorname {a3} y^{a +1}+\operatorname {a1} y y^{\prime }+a {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
416.876 |
|
| 27743 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (n \,x^{2}+m x +k \right ) y^{\prime }+\left (-2 \left (a +n \right ) x +1\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
417.223 |
|
| 27744 |
\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*} |
✓ |
✓ |
✓ |
✗ |
418.898 |
|
| 27745 |
\begin{align*}
{y^{\prime }}^{3}+\left (x +2\right ) {\mathrm e}^{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
428.332 |
|
| 27746 |
\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 (\left (a -1\right ) a -v \left (v +1\right )\right )-a \left (a +1\right )\right ) y}{x^{2} \left (x^{2}-1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
433.976 |
|
| 27747 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2}+\sin \left (t \right ) \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+\tan \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -1 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
440.890 |
|
| 27748 |
\begin{align*}
y^{\prime \prime }&=a \sqrt {b y^{2}+{y^{\prime }}^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
447.299 |
|
| 27749 |
\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*} |
✓ |
✓ |
✓ |
✗ |
459.419 |
|
| 27750 |
\begin{align*}
\left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+x \left (\operatorname {b0} \,x^{2}+\operatorname {a0} \right ) y^{\prime }+\left (a^{2}+x^{2}\right )^{2} \left (b^{2}+x^{2}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
461.256 |
|
| 27751 |
\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*} |
✗ |
✓ |
✗ |
✗ |
462.855 |
|
| 27752 |
\begin{align*}
x \left (x -1\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*} |
✗ |
✓ |
✓ |
✗ |
477.614 |
|
| 27753 |
\begin{align*}
x^{\prime \prime }-x+3 x^{2}&=0 \\
x \left (0\right ) &= {\frac {1}{4}} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
478.628 |
|
| 27754 |
\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*} |
✗ |
✓ |
✓ |
✗ |
481.081 |
|
| 27755 |
\begin{align*}
x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
494.707 |
|
| 27756 |
\begin{align*}
\left (\operatorname {c1} x +\operatorname {c0} \right ) y+\left (\operatorname {b2} \,x^{2}+\operatorname {b1} x +\operatorname {b0} \right ) y^{\prime }+\left (\operatorname {a1} -x \right ) \left (\operatorname {a2} -x \right ) \left (\operatorname {a3} -x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
497.457 |
|
| 27757 |
\begin{align*}
y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
498.497 |
|
| 27758 |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime }+\alpha y^{2}+\beta x y+\gamma &=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
506.861 |
|
| 27759 |
\begin{align*}
4 x y^{\prime \prime }+2 y^{\prime }+y&=\frac {6+x}{x^{2}} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
509.012 |
|
| 27760 |
\begin{align*}
x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
525.321 |
|
| 27761 |
\begin{align*}
{y^{\prime }}^{4}&=2 y y^{\prime }+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
562.776 |
|
| 27762 |
\begin{align*}
3 {y^{\prime }}^{4}&=y^{\prime }+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
573.396 |
|
| 27763 |
\begin{align*}
\left (\operatorname {c1} \,x^{4}+\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+x \left (\operatorname {b0} \,x^{2}+\operatorname {a0} \right ) y^{\prime }+\left (a^{2}-x^{2}\right )^{2} \left (b^{2}-x^{2}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
577.877 |
|
| 27764 |
\begin{align*}
c y+b x y^{\prime }+\left (a \,x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
579.307 |
|
| 27765 |
\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*} |
✗ |
✓ |
✗ |
✗ |
583.089 |
|
| 27766 |
\begin{align*}
{y^{\prime }}^{4}-{y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
597.000 |
|
| 27767 |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime \prime }+\left (1+2 n \right ) a x y^{\prime }+c y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
602.134 |
|
| 27768 |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }-y^{{3}/{2}}+12 y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
606.358 |
|
| 27769 |
\begin{align*}
-x^{\prime \prime }&=\arctan \left (x\right ) \\
x \left (0\right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
616.861 |
|
| 27770 |
\begin{align*}
\left (2 x +y+5\right ) y^{\prime }&=3 x +6 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
625.926 |
|
| 27771 |
\begin{align*}
x y^{\prime }&=2 y+\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
676.727 |
|
| 27772 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }-\left (v +2\right ) \left (v -1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
761.251 |
|
| 27773 |
\begin{align*}
x y^{\prime }+y&=y^{\prime } \sqrt {y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
857.964 |
|
| 27774 |
\begin{align*}
x y^{\prime }&=y \cos \left (\ln \left (\frac {y}{x}\right )\right ) \\
\end{align*} |
✓ |
✗ |
✓ |
✓ |
863.770 |
|
| 27775 |
\begin{align*}
{y^{\prime }}^{4} x -2 y {y^{\prime }}^{3}+12 x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
913.014 |
|
| 27776 |
\begin{align*}
x&=y^{\prime } \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1072.464 |
|
| 27777 |
\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 (\alpha x +\beta \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1113.779 |
|
| 27778 |
\begin{align*}
y^{\prime }-y y^{\prime \prime }&=n \sqrt {{y^{\prime }}^{2}+a^{2} y^{\prime \prime }} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1118.642 |
|
| 27779 |
\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*} |
✗ |
✓ |
✓ |
✗ |
1133.063 |
|
| 27780 |
\begin{align*}
y {y^{\prime \prime }}^{2}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1139.300 |
|
| 27781 |
\begin{align*}
y^{\prime } y^{\prime \prime }&=a x {y^{\prime }}^{5}+3 {y^{\prime \prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1194.938 |
|
| 27782 |
\begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{2+2 y^{4}-4 x^{2} y^{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 x^{2} y^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 y^{2} x^{4}-2 x^{6}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1446.041 |
|
| 27783 |
\begin{align*}
{y^{\prime }}^{4} x -2 y {y^{\prime }}^{3}+12 x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1458.479 |
|
| 27784 |
\begin{align*}
\left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (-x +a \right ) \left (-x +b \right ) \left (c -x \right ) \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (-x +a \right )^{2} \left (-x +b \right )^{2} \left (c -x \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1646.184 |
|
| 27785 |
\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*} |
✗ |
✓ |
✓ |
✗ |
1747.858 |
|
| 27786 |
\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*} |
✗ |
✗ |
✗ |
✗ |
1818.500 |
|
| 27787 |
\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*} |
✗ |
✓ |
✓ |
✗ |
2121.220 |
|