3.9.19 Problems 1801 to 1900

Table 3.543: First order ode linear in derivative

#

ODE

Mathematica

Maple

3749

\[ {}\left (1+x +9 y\right ) y^{\prime }+1+x +5 y = 0 \]

3750

\[ {}\left (8+5 x -12 y\right ) y^{\prime } = 3+2 x -5 y \]

3751

\[ {}\left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y = 0 \]

3752

\[ {}\left (3+9 x +21 y\right ) y^{\prime } = 45+7 x -5 y \]

3753

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

3754

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

3755

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

3756

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

3757

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

3758

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

3759

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

3760

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

3761

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

3762

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

3763

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

3764

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

3765

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

3766

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

3767

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

3768

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

3769

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

3770

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

3771

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

3772

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

3773

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

3774

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

3775

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

3776

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

3777

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

3778

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

3779

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

3780

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

3781

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

3782

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

3783

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

3784

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

3785

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

3786

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

3787

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

3788

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

3789

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

3790

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

3791

\[ {}2 x y y^{\prime }+1-2 x^{3}-y^{2} = 0 \]

3792

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

3793

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

3794

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

3795

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

3796

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

3797

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

3798

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

3799

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

3800

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

3801

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

3802

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

3803

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

3804

\[ {}2 x \left (2 x^{2}+y\right ) y^{\prime }+\left (12 x^{2}+y\right ) y = 0 \]

3805

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

3806

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

3807

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

3808

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

3809

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

3810

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

3811

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

3812

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

3813

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

3814

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

3815

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

3816

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

3817

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

3818

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

3819

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

3820

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

3821

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

3822

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

3823

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

3824

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

3825

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

3826

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

3827

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

3828

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

3829

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

3830

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

3831

\[ {}3 x^{2} y y^{\prime }+1+2 x y^{2} = 0 \]

3832

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

3833

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

3834

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

3835

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

3836

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

3837

\[ {}8 y^{\prime } y x^{3}+3 x^{4}-6 y^{2} x^{2}-y^{4} = 0 \]

3838

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

3839

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

3840

\[ {}x^{7} y y^{\prime } = 2 x^{2}+2+5 x^{3} y \]

3841

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

3842

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

3843

\[ {}\left (\operatorname {g0} \left (x \right )+y \operatorname {g1} \left (x \right )\right ) y^{\prime } = \operatorname {f0} \left (x \right )+\operatorname {f1} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\operatorname {f3} \left (x \right ) y^{3} \]

3844

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

3845

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

3846

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

3847

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

3848

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