6.168 Problems 16701 to 16800

Table 6.335: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

16701

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

16702

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

16703

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

16704

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

16705

\[ {} y^{\prime }-2 y \,{\mathrm e}^{x} = 2 \sqrt {y \,{\mathrm e}^{x}} \]

16706

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

16707

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

16708

\[ {} \left (x^{2}+y^{2}+1\right ) y^{\prime }+x y = 0 \]

16709

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

16710

\[ {} y^{\prime }-\tan \left (y\right ) = \frac {{\mathrm e}^{x}}{\cos \left (y\right )} \]

16711

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

16712

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

16713

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

16714

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

16715

\[ {} x \left (2 x^{2}+y^{2}\right )+y \left (x^{2}+2 y^{2}\right ) y^{\prime } = 0 \]

16716

\[ {} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime } = 0 \]

16717

\[ {} \frac {x}{\sqrt {x^{2}+y^{2}}}+\frac {1}{x}+\frac {1}{y}+\left (\frac {y}{\sqrt {x^{2}+y^{2}}}+\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime } = 0 \]

16718

\[ {} 3 x^{2} \tan \left (y\right )-\frac {2 y^{3}}{x^{3}}+\left (x^{3} \sec \left (y\right )^{2}+4 y^{3}+\frac {3 y^{2}}{x^{2}}\right ) y^{\prime } = 0 \]

16719

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

16720

\[ {} \frac {\sin \left (2 x \right )}{y}+x +\left (y-\frac {\sin \left (x \right )^{2}}{y^{2}}\right ) y^{\prime } = 0 \]

16721

\[ {} 3 x^{2}-2 x -y+\left (2 y-x +3 y^{2}\right ) y^{\prime } = 0 \]

16722

\[ {} \frac {x y}{\sqrt {x^{2}+1}}+2 x y-\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime } = 0 \]

16723

\[ {} \sin \left (y\right )+y \sin \left (x \right )+\frac {1}{x}+\left (x \cos \left (y\right )-\cos \left (x \right )+\frac {1}{y}\right ) y^{\prime } = 0 \]

16724

\[ {} \frac {y+\sin \left (x \right ) \cos \left (x y\right )^{2}}{\cos \left (x y\right )^{2}}+\left (\frac {x}{\cos \left (x y\right )^{2}}+\sin \left (y\right )\right ) y^{\prime } = 0 \]

16725

\[ {} \frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0 \]

16726

\[ {} y \left (x^{2}+y^{2}+a^{2}\right ) y^{\prime }+x \left (x^{2}+y^{2}-a^{2}\right ) = 0 \]

16727

\[ {} 3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime } = 0 \]

16728

\[ {} 1-x^{2} y+x^{2} \left (y-x \right ) y^{\prime } = 0 \]

16729

\[ {} x^{2}+y-x y^{\prime } = 0 \]

16730

\[ {} x +y^{2}-2 x y y^{\prime } = 0 \]

16731

\[ {} 2 x^{2} y+2 y+5+\left (2 x^{3}+2 x \right ) y^{\prime } = 0 \]

16732

\[ {} x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime } = 0 \]

16733

\[ {} x +\sin \left (x \right )+\sin \left (y\right )+y^{\prime } \cos \left (y\right ) = 0 \]

16734

\[ {} 2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime } = 0 \]

16735

\[ {} 3 y^{2}-x +\left (2 y^{3}-6 x y\right ) y^{\prime } = 0 \]

16736

\[ {} x^{2}+y^{2}+1-2 x y y^{\prime } = 0 \]

16737

\[ {} x -x y+\left (y+x^{2}\right ) y^{\prime } = 0 \]

16738

\[ {} 4 {y^{\prime }}^{2}-9 x = 0 \]

16739

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

16740

\[ {} {y^{\prime }}^{2}-2 x y^{\prime }-8 x^{2} = 0 \]

16741

\[ {} x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0 \]

16742

\[ {} {y^{\prime }}^{2}-\left (y+2 x \right ) y^{\prime }+x^{2}+x y = 0 \]

16743

\[ {} {y^{\prime }}^{3}+\left (x +2\right ) {\mathrm e}^{y} = 0 \]

16744

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

16745

\[ {} {y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0 \]

16746

\[ {} {y^{\prime }}^{2}-4 x y^{\prime }+2 y+2 x^{2} = 0 \]

16747

\[ {} y = {y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \]

16748

\[ {} y^{\prime } = {\mathrm e}^{\frac {y^{\prime }}{y}} \]

16749

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

16750

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

16751

\[ {} y = y^{\prime } \ln \left (y^{\prime }\right ) \]

16752

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

16753

\[ {} {y^{\prime }}^{2} x = {\mathrm e}^{\frac {1}{y^{\prime }}} \]

16754

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

16755

\[ {} y^{{2}/{5}}+{y^{\prime }}^{{2}/{5}} = a^{{2}/{5}} \]

16756

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

16757

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

16758

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

16759

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

16760

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

16761

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

16762

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

16763

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

16764

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

16765

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

16766

\[ {} {y^{\prime }}^{2} x -y y^{\prime }-y^{\prime }+1 = 0 \]

16767

\[ {} y = x y^{\prime }+a \sqrt {1+{y^{\prime }}^{2}} \]

16768

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

16769

\[ {} y^{\prime } {\mathrm e}^{-x}+y^{2}-2 y \,{\mathrm e}^{x} = 1-{\mathrm e}^{2 x} \]

16770

\[ {} y^{\prime }+y^{2}-2 y \sin \left (x \right )+\sin \left (x \right )^{2}-\cos \left (x \right ) = 0 \]

16771

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

16772

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

16773

\[ {} \left (1+{y^{\prime }}^{2}\right ) y^{2}-4 y y^{\prime }-4 x = 0 \]

16774

\[ {} {y^{\prime }}^{2}-4 y = 0 \]

16775

\[ {} {y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0 \]

16776

\[ {} {y^{\prime }}^{2}-y^{2} = 0 \]

16777

\[ {} y^{\prime } = y^{{2}/{3}}+a \]

16778

\[ {} \left (x y^{\prime }+y\right )^{2}+3 x^{5} \left (x y^{\prime }-2 y\right ) = 0 \]

16779

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

16780

\[ {} 8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2} = 27 y-27 x \]

16781

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

16782

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

16783

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

16784

\[ {} y^{2} {y^{\prime }}^{2}+y^{2} = 1 \]

16785

\[ {} {y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0 \]

16786

\[ {} 3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y = 0 \]

16787

\[ {} y = x y^{\prime }+\sqrt {a^{2} {y^{\prime }}^{2}+b^{2}} \]

16788

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

16789

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

16790

\[ {} y^{\prime }+\cos \left (x \right ) y = y^{n} \sin \left (2 x \right ) \]

16791

\[ {} x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime } = 0 \]

16792

\[ {} 5 x y-4 y^{2}-6 x^{2}+\left (y^{2}-8 x y+\frac {5 x^{2}}{2}\right ) y^{\prime } = 0 \]

16793

\[ {} 3 x y^{2}-x^{2}+\left (3 x^{2} y-6 y^{2}-1\right ) y^{\prime } = 0 \]

16794

\[ {} y-x y^{2} \ln \left (x \right )+x y^{\prime } = 0 \]

16795

\[ {} 2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime } = 0 \]

16796

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

16797

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

16798

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

16799

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

16800

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