| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime } = \frac {-150 x^{3} y+60 x^{6}+350 x^{{7}/{2}}-150 x^{3}-125 y \sqrt {x}+250 x -125 \sqrt {x}-125 y^{3}+150 y^{2} x^{3}+750 y^{2} \sqrt {x}-60 x^{6} y-600 y x^{{7}/{2}}-1500 x y+8 x^{9}+120 x^{{13}/{2}}+600 x^{4}+1000 x^{{3}/{2}}}{25 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {y \left (-1-x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} x^{2}-x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} x^{2} \ln \left (x \right )+x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} x^{2} y+2 x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} x^{2} y \ln \left (x \right )+x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} x^{2} y \ln \left (x \right )^{2}\right )}{\left (\ln \left (x \right )+1\right ) x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = \frac {y \left (-1-x^{3} x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}}-x^{3} x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} \ln \left (x \right )+x^{3} x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} y+2 x^{3} x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} y \ln \left (x \right )+x^{3} x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} y \ln \left (x \right )^{2}\right )}{\left (\ln \left (x \right )+1\right ) x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = \frac {2 x +4 y \ln \left (2 x +1\right ) x +6 y^{2} \ln \left (2 x +1\right ) x +6 y \ln \left (2 x +1\right )^{2} x +2 \ln \left (2 x +1\right )^{3} x +2 x y^{3}+2 \ln \left (2 x +1\right )^{2} x +2 x y^{2}-1+3 y^{2} \ln \left (2 x +1\right )+3 y \ln \left (2 x +1\right )^{2}+y^{2}+y^{3}+2 y \ln \left (2 x +1\right )+\ln \left (2 x +1\right )^{2}+\ln \left (2 x +1\right )^{3}}{2 x +1}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {-y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{3} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {-y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{2} \sin \left (\frac {y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{2+2 y^{4}-4 x^{2} y^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 x^{4} y^{2}-2 x^{6}}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{2+2 y^{4}-4 x^{2} y^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 x^{4} y^{2}-2 x^{6}}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {4 x \left (a -1\right ) \left (a +1\right ) \left (-y^{2}+a^{2} x^{2}-x^{2}-2\right )}{-4 y^{3}+4 a^{2} x^{2} y-4 x^{2} y-8 y-a^{2} y^{6}+3 a^{4} y^{4} x^{2}-6 y^{4} a^{2} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-9 y^{2} a^{2} x^{4}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}-4 a^{2} x^{6}+y^{6}+3 x^{2} y^{4}+3 x^{4} y^{2}+x^{6}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {-4 x \cos \left (x \right )+4 x^{2} \sin \left (x \right )+4 x +4+4 y^{2}+8 y \cos \left (x \right ) x -8 x y+2 x^{2} \cos \left (2 x \right )+6 x^{2}-8 x^{2} \cos \left (x \right )+4 y^{3}+12 y^{2} \cos \left (x \right ) x -12 x y^{2}+6 y x^{2} \cos \left (2 x \right )+18 x^{2} y-24 x^{2} \cos \left (x \right ) y+x^{3} \cos \left (3 x \right )+15 x^{3} \cos \left (x \right )-6 x^{3} \cos \left (2 x \right )-10 x^{3}}{4 x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -\frac {8 x \left (a -1\right ) \left (a +1\right )}{8+4 a^{4} y^{2} x^{2}-6 y^{4} a^{2} x^{2}-6 x^{4} a^{2}-2 a^{6} x^{4}+6 a^{4} x^{4}+3 a^{4} y^{4} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-9 y^{2} a^{2} x^{4}+3 x^{2} y^{4}+2 y^{4}+y^{6}-8 a^{2}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}-a^{2} y^{6}+3 x^{4} y^{2}-2 y^{4} a^{2}+4 x^{2} y^{2}-8 y^{2} a^{2} x^{2}-4 a^{2} x^{6}-8 y+2 x^{4}+x^{6}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {-y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +2 \sin \left (\frac {y}{x}\right ) x^{3} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{4} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -\frac {1296 y}{216+1080 x y^{5}+594 x y^{6}+72 y^{8} x +216 y^{7} x +1080 x y^{3}-324 x^{2} y^{3}-216 x^{2} y^{4}-1944 y^{4}-1728 y^{3}-648 x^{2} y-882 y^{6}+216 x y^{2}+1152 x y^{4}-432 x y-2376 y^{2}-612 y^{5}-126 y^{10}-8 y^{12}-36 y^{11}-846 y^{7}-570 y^{8}-315 y^{9}-648 x^{2} y^{2}+216 x^{2}+216 x^{3}-1296 y}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -\frac {x \left (-513+432 y^{2} x^{7}-288 y x^{8}+288 y x^{7}-216 x^{6} y^{3}+720 x^{3} y+1008 x^{5} y-216 y^{2} x^{6}+64 x^{9}-96 x^{8}-648 x^{2} y^{3}-288 x^{6} y+432 y^{2} x^{3}-216 y^{3}-594 x^{2} y+864 x^{5} y^{2}-972 x^{4} y^{2}-216 x^{4} y-540 y^{2}-1296 x^{2} y^{2}-648 y^{3} x^{4}-1134 x^{2}-576 x^{5}-756 x^{3}-378 y-864 x^{4}-144 x^{7}-432 x -456 x^{6}\right )}{216 \left (x^{2}+1\right )^{4}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {-\sin \left (\frac {y}{x}\right ) y x -y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right ) x +y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{4} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x \left (1+x \right )}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right ) x +y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )-\sin \left (\frac {y}{x}\right ) y x -y \sin \left (\frac {y}{x}\right )+2 \sin \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x}{2 \cos \left (\frac {y}{x}\right ) \sin \left (\frac {y}{2 x}\right ) x \cos \left (\frac {y}{2 x}\right ) \left (1+x \right )}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -\frac {216 y \left (-2 y^{4}-3 y^{3}-6 y^{2}-6 y+6 x +6\right )}{1080 x y^{5}+594 x y^{6}+72 y^{8} x +216 y^{7} x -648 x y^{3}-324 x^{2} y^{3}-216 x^{2} y^{4}+2808 y^{4}+1728 y^{3}-648 x^{2} y+2484 y^{6}-1944 x y^{2}-432 x y^{4}-1296 x y-1296 y^{2}+4428 y^{5}-126 y^{10}-8 y^{12}-36 y^{11}+594 y^{7}-18 y^{8}-315 y^{9}-648 x^{2} y^{2}+216 x^{3}-1296 y}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {\left (x y+1\right )^{3}}{x^{5}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = \frac {x \left (-x^{2}+2 x^{2} y-2 x^{4}+1\right )}{y-x^{2}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = y \left (y^{2}+y \,{\mathrm e}^{b x}+{\mathrm e}^{2 b x}\right ) {\mathrm e}^{-2 b x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = y^{3}-3 x^{2} y^{2}+3 x^{4} y-x^{6}+2 x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = y^{3}+x^{2} y^{2}+\frac {x^{4} y}{3}+\frac {x^{6}}{27}-\frac {2 x}{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = \frac {y \left (y^{2} x^{7}+x^{4} y+x -3\right )}{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = y \left (y^{2}+y \,{\mathrm e}^{-x^{2}}+{\mathrm e}^{-2 x^{2}}\right ) {\mathrm e}^{2 x^{2}} x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {y \left (y^{2}+x y+x^{2}+x \right )}{x^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x}{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = \frac {x^{3} y^{3}+6 x^{2} y^{2}+12 x y+8+2 x}{x^{3}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = \frac {a^{3} x^{3} y^{3}+3 y^{2} a^{2} x^{2}+3 a x y+1+a^{2} x}{x^{3} a^{3}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = \frac {y \,{\mathrm e}^{-\frac {x^{2}}{2}} \left (2 y^{2}+2 y \,{\mathrm e}^{\frac {x^{2}}{4}}+2 \,{\mathrm e}^{\frac {x^{2}}{2}}+x \,{\mathrm e}^{\frac {x^{2}}{2}}\right )}{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x^{2}}{\left (x -1\right ) \left (1+x \right )}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {y \left (x^{2} y^{2}+y x \,{\mathrm e}^{x}+{\mathrm e}^{2 x}\right ) {\mathrm e}^{-2 x} \left (x -1\right )}{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {\left (x y+1\right ) \left (x^{2} y^{2}+x^{2} y+2 x y+1+x +x^{2}\right )}{x^{5}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = \frac {y^{3}-3 x y^{2} \ln \left (x \right )+3 x^{2} \ln \left (x \right )^{2} y-x^{3} \ln \left (x \right )^{3}+x^{2}+x y}{x^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -F \left (x \right ) \left (-x^{2} a +y^{2}\right )+\frac {y}{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -F \left (x \right ) \left (-x^{2}-2 x y+y^{2}\right )+\frac {y}{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -F \left (x \right ) \left (-a y^{2}-b \,x^{2}\right )+\frac {y}{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -F \left (x \right ) \left (-y^{2}+2 x^{2} y+1-x^{4}\right )+2 x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -F \left (x \right ) \left (x^{2}+2 x y-y^{2}\right )+\frac {y}{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -F \left (x \right ) \left (-7 x y^{2}-x^{3}\right )+\frac {y}{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -F \left (x \right ) \left (-y^{2}-2 y \ln \left (x \right )-\ln \left (x \right )^{2}\right )+\frac {y}{x \ln \left (x \right )}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -x^{3} \left (-y^{2}-2 y \ln \left (x \right )-\ln \left (x \right )^{2}\right )+\frac {y}{x \ln \left (x \right )}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \left (y-{\mathrm e}^{x}\right )^{2}+{\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = \frac {\left (y-\operatorname {Si}\left (x \right )\right )^{2}+\sin \left (x \right )}{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = \left (y+\cos \left (x \right )\right )^{2}+\sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = \frac {\left (y-\ln \left (x \right )-\operatorname {Ci}\left (x \right )\right )^{2}+\cos \left (x \right )}{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = \frac {\left (y-x +\ln \left (1+x \right )\right )^{2}+x}{1+x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = \frac {2 x^{2} y+x^{3}+x y \ln \left (x \right )-y^{2}-x y}{x^{2} \left (x +\ln \left (x \right )\right )}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = f \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = f \left (y\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = f \left (x \right ) g \left (y\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} g \left (x \right ) y^{\prime } = f_{1} \left (x \right ) y+f_{0} \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} g \left (x \right ) y^{\prime } = f_{1} \left (x \right ) y+f_{n} \left (x \right ) y^{n}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = f \left (\frac {y}{x}\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = a y^{2}+b x +c
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}-a^{2} x^{2}+3 a
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+a^{2} x^{2}+b x +c
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a y^{2}+b \,x^{n}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+a n \,x^{n -1}-a^{2} x^{2 n}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a y^{2}+b \,x^{2 n}+c \,x^{n -1}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a \,x^{n} y^{2}+b \,x^{-n -2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a \,x^{n} y^{2}+b \,x^{m}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+k \left (a x +b \right )^{n} \left (c x +d \right )^{-n -4}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = a \,x^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{n +2 m}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \left (a \,x^{2 n}+b \,x^{n -1}\right ) y^{2}+c
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0} x +b_{0} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime } = a \,x^{2} y^{2}+b
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime } = x^{2} y^{2}-x^{4} a^{2}+a \left (1-2 b \right ) x^{2}-b \left (b +1\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime } = a \,x^{2} y^{2}+b \,x^{n}+c
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime } = x^{2} y^{2}+a \,x^{2 m} \left (b \,x^{m}+c \right )^{n}-\frac {n^{2}}{4}+\frac {1}{4}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (c_{2} x^{2}+b_{2} x +a_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{4} y^{\prime } = -x^{4} y^{2}-a^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} a \,x^{2} \left (x -1\right )^{2} \left (y^{\prime }+\lambda y^{2}\right )+b \,x^{2}+c x +s = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (x^{2} a +b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{n +1} y^{\prime } = a \,x^{2 n} y^{2}+c \,x^{m}+d
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a \,x^{n}+b \right ) y^{\prime } = b y^{2}+a \,x^{n -2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a \,x^{n}+b \,x^{m}+c \right ) \left (y^{\prime }-y^{2}\right )+a n \left (n -1\right ) x^{n -2}+b m \left (m -1\right ) x^{m -2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a y^{2}+b y+c x +k
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+a \,x^{n} y+a \,x^{n -1}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+a \,x^{n} y+b \,x^{n -1}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+\left (x \alpha +\beta \right ) y+x^{2} a +b x +c
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+a \,x^{n} y-a b \,x^{n}-b^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -\left (n +1\right ) x^{n} y^{2}+a \,x^{n +m +1}-a \,x^{m}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = a \,x^{n} y^{2}+b \,x^{m} y+b c \,x^{m}-a \,c^{2} x^{n}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a \,x^{n} y^{2}-a \,x^{n} \left (b \,x^{m}+c \right ) y+b m \,x^{m -1}
\]
|
✓ |
✗ |
✗ |
|
| \[
{} y^{\prime } = -a n \,x^{n -1} y^{2}+c \,x^{m} \left (a \,x^{n}+b \right ) y-c \,x^{m}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a \,x^{n} y^{2}+b \,x^{m} y+c k \,x^{k -1}-b c \,x^{m +k}-a \,c^{2} x^{n +2 k}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime } = a y^{2}+b y+c \,x^{2 b}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime } = a y^{2}+b y+c \,x^{n}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime } = a y^{2}+\left (n +b \,x^{n}\right ) y+c \,x^{2 n}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime } = x y^{2}+a y+b \,x^{n}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }+a_{3} x y^{2}+a_{2} y+a_{1} x +a_{0} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime } = a \,x^{n} y^{2}+b y+c \,x^{-n}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime } = a \,x^{n} y^{2}+m y-a \,b^{2} x^{n +2 m}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime } = x^{2 n} y^{2}+\left (m -n \right ) y+x^{2 m}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime } = a \,x^{n} y^{2}+b y+c \,x^{m}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime } = a \,x^{2 n} y^{2}+\left (b \,x^{n}-n \right ) y+c
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime } = a \,x^{2 n +m} y^{2}+\left (b \,x^{m +n}-n \right ) y+c \,x^{m}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (a_{1} x +b_{1} \right ) y+a_{0} x +b_{0} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a x +c \right ) y^{\prime } = \alpha \left (b x +a y\right )^{2}+\beta \left (b x +a y\right )-b x +\gamma
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 x^{2} y^{\prime } = 2 y^{2}+x y-2 a^{2} x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x^{2} y^{\prime } = 2 y^{2}+3 x y-2 a^{2} x
\]
|
✓ |
✓ |
✗ |
|