6.167 Problems 16601 to 16700

Table 6.333: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

16601

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

16602

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

16603

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

16604

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

16605

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

16606

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

16607

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

16608

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

16609

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

16610

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

16611

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

16612

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

16613

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

16614

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

16615

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

16616

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

16617

\[ {} y^{\prime } = y \]

16618

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

16619

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

16620

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

16621

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

16622

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

16623

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

16624

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

16625

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

16626

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

16627

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

16628

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

16629

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

16630

\[ {} {\mathrm e}^{-y} y^{\prime } = 1 \]

16631

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

16632

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

16633

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

16634

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

16635

\[ {} {\mathrm e}^{x} \sin \left (y\right )^{3}+\left (1+{\mathrm e}^{2 x}\right ) \cos \left (y\right ) y^{\prime } = 0 \]

16636

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

16637

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

16638

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

16639

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

16640

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

16641

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

16642

\[ {} y^{\prime } = \frac {y}{x} \]

16643

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

16644

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

16645

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

16646

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

16647

\[ {} \tan \left (y^{\prime }\right ) = 0 \]

16648

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

16649

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

16650

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

16651

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

16652

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

16653

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

16654

\[ {} {\mathrm e}^{y} = {\mathrm e}^{4 y} y^{\prime }+1 \]

16655

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

16656

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

16657

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

16658

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

16659

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

16660

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

16661

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

16662

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

16663

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

16664

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

16665

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

16666

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

16667

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

16668

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

16669

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

16670

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

16671

\[ {} 8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime } = 0 \]

16672

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

16673

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

16674

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

16675

\[ {} 4 y^{6}+x^{3} = 6 x y^{5} y^{\prime } \]

16676

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

16677

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

16678

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

16679

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

16680

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

16681

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

16682

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

16683

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

16684

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

16685

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

16686

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

16687

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

16688

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

16689

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

16690

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

16691

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

16692

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

16693

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

16694

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

16695

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

16696

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

16697

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

16698

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

16699

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

16700

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