6.187 Problems 18601 to 18700

Table 6.373: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

18601

\[ {} e y^{\prime \prime } = -\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2} \]

18602

\[ {} e y^{\prime \prime } = -P \left (L -x \right ) \]

18603

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

18604

\[ {} e y^{\prime \prime } = P \left (-y+a \right ) \]

18605

\[ {} x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 x y^{\prime } = \ln \left (x \right )^{2} \]

18606

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

18607

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

18608

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

18609

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

18610

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

18611

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

18612

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

18613

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

18614

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

18615

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

18616

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

18617

\[ {} \left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y = x^{3} \]

18618

\[ {} x^{2} y^{\prime \prime \prime }+5 x y^{\prime \prime }+4 y^{\prime } = -\frac {1}{x^{2}} \]

18619

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

18620

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

18621

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

18622

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

18623

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

18624

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

18625

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

18626

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

18627

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

18628

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

18629

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

18630

\[ {} V^{\prime \prime }+\frac {2 V^{\prime }}{r} = 0 \]

18631

\[ {} V^{\prime \prime }+\frac {V^{\prime }}{r} = 0 \]

18632

\[ {} [z^{\prime }\left (x \right )+7 y \left (x \right )-3 z \left (x \right ) = 0, 7 y^{\prime }\left (x \right )+63 y \left (x \right )-36 z \left (x \right ) = 0] \]

18633

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

18634

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

18635

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

18636

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

18637

\[ {} [y^{\prime }\left (x \right )+z^{\prime }\left (x \right )+6 y \left (x \right ) = 0, z^{\prime }\left (x \right )+5 y \left (x \right )+z \left (x \right ) = 0] \]

18638

\[ {} [z^{\prime }\left (x \right )+y^{\prime }\left (x \right )+5 y \left (x \right )-3 z \left (x \right ) = x +{\mathrm e}^{x}, y^{\prime }\left (x \right )+2 y \left (x \right )-z \left (x \right ) = {\mathrm e}^{x}] \]

18639

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

18640

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

18641

\[ {} [z^{\prime }\left (x \right )+5 y \left (x \right )-2 z \left (x \right ) = x, y^{\prime }\left (x \right )+4 y \left (x \right )+z \left (x \right ) = x] \]

18642

\[ {} [z^{\prime }\left (x \right )+7 y \left (x \right )-9 z \left (x \right ) = {\mathrm e}^{x}, y^{\prime }\left (x \right )-y \left (x \right )-3 z \left (x \right ) = {\mathrm e}^{2 x}] \]

18643

\[ {} [y^{\prime }\left (x \right )-2 y \left (x \right )-2 z \left (x \right ) = {\mathrm e}^{3 x}, z^{\prime }\left (x \right )+5 y \left (x \right )-2 z \left (x \right ) = {\mathrm e}^{4 x}] \]

18644

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

18645

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

18646

\[ {} v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0 \]

18647

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

18648

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

18649

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

18650

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

18651

\[ {} 3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0 \]

18652

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

18653

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

18654

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

18655

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

18656

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

18657

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

18658

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

18659

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

18660

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

18661

\[ {} 2 a x +b y+g +\left (2 c y+b x +e \right ) y^{\prime } = 0 \]

18662

\[ {} \left (2 x^{2} y+4 x^{3}-12 x y^{2}+3 y^{2}-x \,{\mathrm e}^{y}+{\mathrm e}^{2 x}\right ) y^{\prime }+12 x^{2} y+2 x y^{2}+4 x^{3}-4 y^{3}+2 y \,{\mathrm e}^{2 x}-{\mathrm e}^{y} = 0 \]

18663

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

18664

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

18665

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

18666

\[ {} x^{4} {\mathrm e}^{x}-2 m x y^{2}+2 m \,x^{2} y y^{\prime } = 0 \]

18667

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

18668

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

18669

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

18670

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

18671

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

18672

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

18673

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

18674

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

18675

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

18676

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

18677

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

18678

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

18679

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

18680

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

18681

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

18682

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

18683

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

18684

\[ {} y^{\prime }+\frac {2 y}{x} = 3 x^{2} y^{{1}/{3}} \]

18685

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

18686

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

18687

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

18688

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

18689

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

18690

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

18691

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

18692

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

18693

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

18694

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

18695

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

18696

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

18697

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

18698

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

18699

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

18700

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