6.108 Problems 10701 to 10800

Table 6.215: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

10701

\[ {} y^{\prime } = \frac {y \left (1-x +y x^{2} \ln \left (x \right )+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (x -1\right ) x} \]

10702

\[ {} y^{\prime } = \frac {y \ln \left (x \right ) x -y+2 x^{5} b +2 x^{3} a y^{2}}{\left (x \ln \left (x \right )-1\right ) x} \]

10703

\[ {} y^{\prime } = \frac {\left (\ln \left (y\right )+x +x^{3}+x^{4}\right ) y}{x} \]

10704

\[ {} y^{\prime } = -\frac {\left (-\ln \left (-1+y\right )+\ln \left (y+1\right )+2 \ln \left (x \right )\right ) x \left (y+1\right )^{2}}{8} \]

10705

\[ {} y^{\prime } = \frac {\left (-\ln \left (-1+y\right )+\ln \left (y+1\right )+2 \ln \left (x \right )\right )^{2} x \left (y+1\right )^{2}}{16} \]

10706

\[ {} y^{\prime } = \frac {\left (-y^{2}+4 a x \right )^{3}}{\left (-y^{2}+4 a x -1\right ) y} \]

10707

\[ {} y^{\prime } = \frac {2 a x +2 a +x^{3} \sqrt {-y^{2}+4 a x}}{\left (1+x \right ) y} \]

10708

\[ {} y^{\prime } = \frac {-\ln \left (x \right )+{\mathrm e}^{\frac {1}{x}}+4 x^{2} y+2 x +2 x y^{2}+2 x^{3}}{\ln \left (x \right )-{\mathrm e}^{\frac {1}{x}}} \]

10709

\[ {} y^{\prime } = -\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-1\right ) y}{1+x} \]

10710

\[ {} y^{\prime } = \frac {x^{2}+2 x +1+2 x^{3} \sqrt {x^{2}+2 x +1-4 y}}{2+2 x} \]

10711

\[ {} y^{\prime } = \frac {-b y a +b^{2}+a b +b^{2} x -b a \sqrt {x}-a^{2}}{a \left (-a y+b +a +b x -a \sqrt {x}\right )} \]

10712

\[ {} y^{\prime } = -\frac {y \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}+y x^{2} \ln \left (x \right )+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right ) x} \]

10713

\[ {} y^{\prime } = \frac {-x^{2}+x +2+2 x^{3} \sqrt {x^{2}-4 x +4 y}}{2+2 x} \]

10714

\[ {} y^{\prime } = \frac {3 x^{4}+3 x^{3}+\sqrt {9 x^{4}-4 y^{3}}}{\left (1+x \right ) y^{2}} \]

10715

\[ {} y^{\prime } = -\frac {x^{2}+x +a x +a -2 \sqrt {x^{2}+2 a x +a^{2}+4 y}}{2 \left (1+x \right )} \]

10716

\[ {} y^{\prime } = \left (1+y^{2} {\mathrm e}^{2 x^{2}}+y^{3} {\mathrm e}^{3 x^{2}}\right ) {\mathrm e}^{-x^{2}} x \]

10717

\[ {} y^{\prime } = \frac {y \left (-{\mathrm e}^{x}+\ln \left (2 x \right ) x^{2} y-\ln \left (2 x \right ) x \right ) {\mathrm e}^{-x}}{x} \]

10718

\[ {} y^{\prime } = \frac {x^{3} \left (3 x +3+\sqrt {9 x^{4}-4 y^{3}}\right )}{\left (1+x \right ) y^{2}} \]

10719

\[ {} y^{\prime } = \frac {\left (18 x^{{3}/{2}}+36 y^{2}-12 x^{3} y+x^{6}\right ) \sqrt {x}}{36} \]

10720

\[ {} y^{\prime } = -\frac {y^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x} \]

10721

\[ {} y^{\prime } = \frac {2 a}{y+2 a y^{4}-16 a^{2} x y^{2}+32 a^{3} x^{2}} \]

10722

\[ {} y^{\prime } = -\frac {y^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x} \]

10723

\[ {} y^{\prime } = \frac {-\ln \left (x \right )+2 \ln \left (2 x \right ) x y+\ln \left (2 x \right )+\ln \left (2 x \right ) y^{2}+\ln \left (2 x \right ) x^{2}}{\ln \left (x \right )} \]

10724

\[ {} y^{\prime } = -\frac {b y a -b c +b^{2} x +b a \sqrt {x}-a^{2}}{a \left (a y-c +b x +a \sqrt {x}\right )} \]

10725

\[ {} y^{\prime } = \frac {\left (2 x +2+y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (1+x \right )} \]

10726

\[ {} y^{\prime } = \frac {\left (x^{3}+3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x} \]

10727

\[ {} y^{\prime } = \frac {y \left (x -y\right )}{x \left (x -y^{3}\right )} \]

10728

\[ {} y^{\prime } = \frac {\left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}\right )^{3} {\mathrm e}^{x}}{4 \left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}+2\right ) \sqrt {y}} \]

10729

\[ {} y^{\prime } = \frac {1+2 y}{x \left (-2+x y^{2}+2 x y^{3}\right )} \]

10730

\[ {} y^{\prime } = \frac {-x^{2}-x -a x -a +2 x^{3} \sqrt {x^{2}+2 a x +a^{2}+4 y}}{2+2 x} \]

10731

\[ {} y^{\prime } = \frac {2 x \sin \left (x \right )-\ln \left (2 x \right )+\ln \left (2 x \right ) x^{4}-2 \ln \left (2 x \right ) x^{2} y+\ln \left (2 x \right ) y^{2}}{\sin \left (x \right )} \]

10732

\[ {} y^{\prime } = \frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{3}\right ) y}{1+x} \]

10733

\[ {} y^{\prime } = \frac {\left (-1+2 y \ln \left (x \right )\right )^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x} \]

10734

\[ {} y^{\prime } = \frac {2 x^{2}+2 x +x^{4}-2 x^{2} y-1+y^{2}}{1+x} \]

10735

\[ {} y^{\prime } = \frac {x \left (-1+x -2 x y+2 x^{3}\right )}{x^{2}-y} \]

10736

\[ {} y^{\prime } = \frac {2 a}{-x^{2} y+2 a y^{4} x^{2}-16 a^{2} x y^{2}+32 a^{3}} \]

10737

\[ {} y^{\prime } = \frac {1+2 y}{x \left (-2+x y+2 x y^{2}\right )} \]

10738

\[ {} y^{\prime } = \frac {x +y^{4}-2 x^{2} y^{2}+x^{4}}{y} \]

10739

\[ {} y^{\prime } = \frac {\left (y^{2} a +b \,x^{2}\right )^{3} x}{a^{{5}/{2}} \left (y^{2} a +b \,x^{2}+a \right ) y} \]

10740

\[ {} y^{\prime } = -\frac {\cos \left (y\right ) \left (x -\cos \left (y\right )+1\right )}{\left (\sin \left (y\right ) x -1\right ) \left (1+x \right )} \]

10741

\[ {} y^{\prime } = -\frac {i \left (8 i x +16 y^{4}+8 x^{2} y^{2}+x^{4}\right )}{32 y} \]

10742

\[ {} y^{\prime } = \frac {x}{-y+x^{4}+2 x^{2} y^{2}+y^{4}} \]

10743

\[ {} y^{\prime } = \frac {\left (-1+y \ln \left (x \right )\right )^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x} \]

10744

\[ {} y^{\prime } = -\frac {i \left (i x +x^{4}+2 x^{2} y^{2}+y^{4}\right )}{y} \]

10745

\[ {} y^{\prime } = -\frac {y \left (\tan \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tan \left (x \right )} \]

10746

\[ {} y^{\prime } = \frac {y \left (x +y\right )}{x \left (x +y^{3}\right )} \]

10747

\[ {} y^{\prime } = \frac {\left (x -y\right )^{2} \left (x +y\right )^{2} x}{y} \]

10748

\[ {} y^{\prime } = \frac {\left (x^{2}+3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x} \]

10749

\[ {} y^{\prime } = \frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x^{4}\right ) y}{x \left (1+x \right )} \]

10750

\[ {} y^{\prime } = \frac {\cos \left (y\right ) \left (\cos \left (y\right ) x^{3}-x -1\right )}{\left (\sin \left (y\right ) x -1\right ) \left (1+x \right )} \]

10751

\[ {} y^{\prime } = \frac {\left (x +1+x^{4} \ln \left (y\right )\right ) y \ln \left (y\right )}{x \left (1+x \right )} \]

10752

\[ {} y^{\prime } = \frac {x y+x^{3}+x y^{2}+y^{3}}{x^{2}} \]

10753

\[ {} y^{\prime } = \frac {y^{{3}/{2}}}{y^{{3}/{2}}+x^{2}-2 x y+y^{2}} \]

10754

\[ {} y^{\prime } = \frac {2 x^{3} y+x^{6}+x^{2} y^{2}+y^{3}}{x^{4}} \]

10755

\[ {} y^{\prime } = \frac {-4 x y+x^{3}+2 x^{2}-4 x -8}{-8 y+2 x^{2}+4 x -8} \]

10756

\[ {} y^{\prime } = \frac {\left (2 x +2+x^{3} y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (1+x \right )} \]

10757

\[ {} y^{\prime } = -\frac {i \left (54 i x^{2}+81 y^{4}+18 x^{4} y^{2}+x^{8}\right ) x}{243 y} \]

10758

\[ {} y^{\prime } = \frac {\left (x y^{2}+1\right )^{3}}{x^{4} \left (x y^{2}+1+x \right ) y} \]

10759

\[ {} y^{\prime } = \frac {-4 x y-x^{3}+4 x^{2}-4 x +8}{8 y+2 x^{2}-8 x +8} \]

10760

\[ {} y^{\prime } = -\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-x \right ) y}{x \left (1+x \right )} \]

10761

\[ {} y^{\prime } = \frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x \right ) y}{x \left (1+x \right )} \]

10762

\[ {} y^{\prime } = \frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{4}\right ) y}{x \left (1+x \right )} \]

10763

\[ {} y^{\prime } = \frac {y \left (-1-\ln \left (\frac {\left (x -1\right ) \left (1+x \right )}{x}\right )+\ln \left (\frac {\left (x -1\right ) \left (1+x \right )}{x}\right ) x y\right )}{x} \]

10764

\[ {} y^{\prime } = \frac {y \left (-\ln \left (x \right )-x \ln \left (\frac {\left (x -1\right ) \left (1+x \right )}{x}\right )+\ln \left (\frac {\left (x -1\right ) \left (1+x \right )}{x}\right ) x^{2} y\right )}{x \ln \left (x \right )} \]

10765

\[ {} y^{\prime } = \frac {-8 x y-x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32} \]

10766

\[ {} y^{\prime } = \frac {y \left (y+1\right )}{x \left (-y-1+x y\right )} \]

10767

\[ {} y^{\prime } = -\frac {i \left (16 i x^{2}+16 y^{4}+8 x^{4} y^{2}+x^{8}\right ) x}{32 y} \]

10768

\[ {} y^{\prime } = \frac {2 y^{6}}{y^{3}+2+16 x y^{2}+32 x^{2} y^{4}} \]

10769

\[ {} y^{\prime } = \frac {-4 a x y-a^{2} x^{3}-2 a b \,x^{2}-4 a x +8}{8 y+2 a \,x^{2}+4 b x +8} \]

10770

\[ {} y^{\prime } = \frac {\left (x +1+\ln \left (y\right ) x \right ) \ln \left (y\right ) y}{x \left (1+x \right )} \]

10771

\[ {} y^{\prime } = \frac {x y+x +y^{2}}{\left (x -1\right ) \left (x +y\right )} \]

10772

\[ {} y^{\prime } = \frac {-4 x y-x^{3}-2 a \,x^{2}-4 x +8}{8 y+2 x^{2}+4 a x +8} \]

10773

\[ {} y^{\prime } = \frac {x -y+\sqrt {y}}{x -y+\sqrt {y}+1} \]

10774

\[ {} y^{\prime } = \frac {y \left (-\ln \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \ln \left (\frac {1}{x}\right )} \]

10775

\[ {} y^{\prime } = \frac {y \left (y+1\right )}{x \left (-y-1+y^{4} x \right )} \]

10776

\[ {} y^{\prime } = \frac {-3 x^{2} y+1+x^{6} y^{2}+y^{3} x^{9}}{x^{3}} \]

10777

\[ {} y^{\prime } = \frac {x^{3} y+x^{3}+x y^{2}+y^{3}}{\left (x -1\right ) x^{3}} \]

10778

\[ {} y^{\prime } = \frac {x y+y+x \sqrt {x^{2}+y^{2}}}{x \left (1+x \right )} \]

10779

\[ {} y^{\prime } = \frac {\left (x^{4}+x^{3}+x +3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x} \]

10780

\[ {} y^{\prime } = \frac {y \left (-\tanh \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \tanh \left (\frac {1}{x}\right )} \]

10781

\[ {} y^{\prime } = -\frac {y \left (\tanh \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tanh \left (x \right )} \]

10782

\[ {} y^{\prime } = \frac {-\sinh \left (x \right )+\ln \left (x \right ) x^{2}+2 y \ln \left (x \right ) x +\ln \left (x \right )+y^{2} \ln \left (x \right )}{\sinh \left (x \right )} \]

10783

\[ {} y^{\prime } = -\frac {\ln \left (x \right )-\sinh \left (x \right ) x^{2}-2 \sinh \left (x \right ) x y-\sinh \left (x \right )-\sinh \left (x \right ) y^{2}}{\ln \left (x \right )} \]

10784

\[ {} y^{\prime } = \frac {y \ln \left (x \right )+\cosh \left (x \right ) x a y^{2}+\cosh \left (x \right ) x^{3} b}{x \ln \left (x \right )} \]

10785

\[ {} y^{\prime } = \frac {x \left (-x -1+x^{2}-2 x^{2} y+2 x^{4}\right )}{\left (x^{2}-y\right ) \left (1+x \right )} \]

10786

\[ {} y^{\prime } = -\frac {y \left (\ln \left (x -1\right )+\coth \left (1+x \right ) x -\coth \left (1+x \right ) x^{2} y\right )}{x \ln \left (x -1\right )} \]

10787

\[ {} y^{\prime } = -\frac {\ln \left (x -1\right )-\coth \left (1+x \right ) x^{2}-2 \coth \left (1+x \right ) x y-\coth \left (1+x \right )-\coth \left (1+x \right ) y^{2}}{\ln \left (x -1\right )} \]

10788

\[ {} y^{\prime } = \frac {2 x \ln \left (\frac {1}{x -1}\right )-\coth \left (\frac {1+x}{x -1}\right )+\coth \left (\frac {1+x}{x -1}\right ) y^{2}-2 \coth \left (\frac {1+x}{x -1}\right ) x^{2} y+\coth \left (\frac {1+x}{x -1}\right ) x^{4}}{\ln \left (\frac {1}{x -1}\right )} \]

10789

\[ {} y^{\prime } = \frac {2 x^{2} \cosh \left (\frac {1}{x -1}\right )-2 x \cosh \left (\frac {1}{x -1}\right )-1+y^{2}-2 x^{2} y+x^{4}-x +x y^{2}-2 x^{3} y+x^{5}}{\left (x -1\right ) \cosh \left (\frac {1}{x -1}\right )} \]

10790

\[ {} y^{\prime } = \frac {y \left (-\cosh \left (\frac {1}{1+x}\right ) x +\cosh \left (\frac {1}{1+x}\right )-x +x^{2} y-x^{2}+x^{3} y\right )}{x \left (x -1\right ) \cosh \left (\frac {1}{1+x}\right )} \]

10791

\[ {} y^{\prime } = -\frac {y \left (1+x y\right )}{x \left (x y+1-y\right )} \]

10792

\[ {} y^{\prime } = \frac {y}{x \left (-1+y+x^{2} y^{3}+y^{4} x^{3}\right )} \]

10793

\[ {} y^{\prime } = \frac {x^{3}+3 a \,x^{2}+3 a^{2} x +a^{3}+x y^{2}+y^{2} a +y^{3}}{\left (x +a \right )^{3}} \]

10794

\[ {} y^{\prime } = \frac {y^{3} x \,{\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{9 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+3 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+9 y} \]

10795

\[ {} y^{\prime } = \frac {y \left (-1-\cosh \left (\frac {1+x}{x -1}\right ) x +\cosh \left (\frac {1+x}{x -1}\right ) x^{2} y-\cosh \left (\frac {1+x}{x -1}\right ) x^{2}+\cosh \left (\frac {1+x}{x -1}\right ) x^{3} y\right )}{x} \]

10796

\[ {} y^{\prime } = \frac {\left (x +y+1\right ) y}{\left (2 y^{3}+y+x \right ) \left (1+x \right )} \]

10797

\[ {} y^{\prime } = \frac {y \left (-1-x \,{\mathrm e}^{\frac {1+x}{x -1}}+x^{2} {\mathrm e}^{\frac {1+x}{x -1}} y-x^{2} {\mathrm e}^{\frac {1+x}{x -1}}+x^{3} {\mathrm e}^{\frac {1+x}{x -1}} y\right )}{x} \]

10798

\[ {} y^{\prime } = \frac {-b^{3}+6 b^{2} x -12 b \,x^{2}+8 x^{3}-4 b y^{2}+8 x y^{2}+8 y^{3}}{\left (2 x -b \right )^{3}} \]

10799

\[ {} y^{\prime } = \frac {\left (y \,{\mathrm e}^{-\frac {x^{2}}{4}} x +2+2 y^{2} {\mathrm e}^{-\frac {x^{2}}{2}}+2 y^{3} {\mathrm e}^{-\frac {3 x^{2}}{4}}\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2} \]

10800

\[ {} y^{\prime } = -\frac {-\frac {1}{x}-\textit {\_F1} \left (y+\frac {1}{x}\right )}{x} \]