2.37 Problems 3601 to 3700

Table 2.73: Main lookup table

#

ODE

Mathematica result

Maple result

3601

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

3602

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

3603

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

3604

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

3605

\[ {}x^{3} y^{\prime }+20+x^{2} y \left (1-x^{2} y\right ) = 0 \]

3606

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

3607

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

3608

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

3609

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

3610

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

3611

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

3612

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

3613

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

3614

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

3615

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

3616

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

3617

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

3618

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

3619

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

3620

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

3621

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

3622

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

3623

\[ {}6 x^{3} y^{\prime } = 4 x^{2} y+\left (1-3 x \right ) y^{4} \]

3624

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

3625

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

3626

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

3627

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

3628

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

3629

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

3630

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

3631

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

3632

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

3633

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

3634

\[ {}x^{5} y^{\prime } = 1-3 x^{4} y \]

3635

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

3636

\[ {}x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3} = 0 \]

3637

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

3638

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

3639

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

3640

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

3641

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

3642

\[ {}x^{k} y^{\prime } = a \,x^{m}+b y^{n} \]

3643

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

3644

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

3645

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

3646

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

3647

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

3648

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

3649

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

3650

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

3651

\[ {}y^{\prime } \sqrt {X}+\sqrt {Y} = 0 \]

3652

\[ {}y^{\prime } \sqrt {X} = \sqrt {Y} \]

3653

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

3654

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

3655

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

3656

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

3657

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

3658

\[ {}y^{\prime } \sqrt {X} = 0 \]

3659

\[ {}y^{\prime } \sqrt {X}+\sqrt {Y} = 0 \]

3660

\[ {}y^{\prime } \sqrt {X} = \sqrt {Y} \]

3661

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

3662

\[ {}y^{\prime } \left (4 x^{3}+\operatorname {a1} x +\operatorname {a0} \right )^{\frac {2}{3}}+\left (\operatorname {a0} +\operatorname {a1} y+4 y^{3}\right )^{\frac {2}{3}} = 0 \]

3663

\[ {}X^{\frac {2}{3}} y^{\prime } = Y^{\frac {2}{3}} \]

3664

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

3665

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

3666

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

3667

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

3668

\[ {}\left (\operatorname {a0} +\operatorname {a1} \sin \left (x \right )^{2}\right ) y^{\prime }+\operatorname {a2} x \left (\operatorname {a3} +\operatorname {a1} \sin \left (x \right )^{2}\right )+\operatorname {a1} y \sin \left (2 x \right ) = 0 \]

3669

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

3670

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

3671

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

3672

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

3673

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

3674

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

3675

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

3676

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

3677

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

3678

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

3679

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

3680

\[ {}y^{\prime } y = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2} \]

3681

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

3682

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

3683

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

3684

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

3685

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

3686

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

3687

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

3688

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

3689

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

3690

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

3691

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

3692

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

3693

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

3694

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

3695

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

3696

\[ {}\left (x +y+1\right ) y^{\prime }+1+4 x +3 y = 0 \]

3697

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

3698

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

3699

\[ {}\left (3-x +y\right ) y^{\prime } = 11-4 x +3 y \]

3700

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