4.9.13 Problems 1201 to 1300

Table 4.863: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

3545

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

3546

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

3547

\[ {} x y^{\prime } = \sqrt {16 x^{2}-y^{2}}+y \]

3548

\[ {} x y^{\prime }-y = \sqrt {9 x^{2}+y^{2}} \]

3549

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

3550

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

3551

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

3552

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

3553

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

3554

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

3555

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

3556

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

3557

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

3561

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

3562

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

3577

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

3578

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

3579

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

3580

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

3581

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

3582

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

3583

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

3586

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

3593

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

3594

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

3595

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

3596

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

3597

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

3598

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

3599

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

3600

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

3601

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

3602

\[ {} y^{\prime } = \frac {x^{2} y-32}{-x^{2}+16}+2 \]

3603

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

3604

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

3605

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

3606

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

3607

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

3608

\[ {} y^{\prime } = \frac {2 \sqrt {y-1}}{3} \]

3609

\[ {} m v^{\prime } = m g -k v^{2} \]

3610

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

3611

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

3612

\[ {} x^{2} y^{\prime }-4 x y = x^{7} \sin \left (x \right ) \]

3613

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

3614

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

3615

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

3616

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

3617

\[ {} y^{\prime }+\frac {y}{x \ln \left (x \right )} = 9 x^{2} \]

3618

\[ {} y^{\prime }-y \tan \left (x \right ) = 8 \sin \left (x \right )^{3} \]

3619

\[ {} t x^{\prime }+2 x = 4 \,{\mathrm e}^{t} \]

3620

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

3621

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

3622

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

3623

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

3624

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

3625

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

3626

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

3627

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

3628

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

3629

\[ {} y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right . \]

3630

\[ {} y^{\prime }-2 y = \left \{\begin {array}{cc} 1-x & x <1 \\ 0 & 1\le x \end {array}\right . \]

3632

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

3633

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

3634

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

3635

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

3636

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

3637

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

3638

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

3639

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

3640

\[ {} x y^{\prime } = \sqrt {16 x^{2}-y^{2}}+y \]

3641

\[ {} x y^{\prime }-y = \sqrt {9 x^{2}+y^{2}} \]

3642

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

3643

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

3644

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

3645

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

3646

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

3647

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

3648

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

3649

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

3650

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

3651

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

3652

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

3653

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

3654

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

3655

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

3656

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

3657

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

3658

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

3659

\[ {} y^{\prime }-\frac {3 y}{2 x} = 6 y^{{1}/{3}} x^{2} \ln \left (x \right ) \]

3660

\[ {} y^{\prime }+\frac {2 y}{x} = 6 \sqrt {x^{2}+1}\, \sqrt {y} \]

3661

\[ {} y^{\prime }+\frac {2 y}{x} = 6 x^{4} y^{2} \]

3662

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

3663

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

3664

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

3665

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

3666

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

3667

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

3668

\[ {} 2 y^{\prime }+y \cot \left (x \right ) = \frac {8 \cos \left (x \right )^{3}}{y} \]

3669

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

3670

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