5.1.42 Problems 4101 to 4200

Table 5.83: First order ode

#

ODE

Mathematica

Maple

8731

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

8732

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

8733

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

8734

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

8735

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

8736

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

8737

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

8738

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

8739

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

8740

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

8741

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

8742

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

8743

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

8744

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

8745

\[ {}p^{\prime } = a p-b p^{2} \]

8746

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

8747

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

8748

\[ {}x y^{\prime }-2 y+b y^{2} = c \,x^{4} \]

8749

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

8750

\[ {}u^{\prime }+u^{2} = \frac {1}{x^{{4}/{5}}} \]

8751

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

8756

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

8757

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

8758

\[ {}f^{\prime } = \frac {1}{f} \]

8770

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

8771

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

8789

\[ {}x^{\prime } = 4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x \]

8790

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

8791

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

8792

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

8793

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

8794

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

8796

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

8797

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

8798

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

8804

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

8860

\[ {}w^{\prime } = -\frac {1}{2}-\frac {\sqrt {1-12 w}}{2} \]

8886

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

8887

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

8889

\[ {}v v^{\prime } = \frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3} \]

8921

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

8922

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

8952

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

8976

\[ {}h^{2}+\frac {2 a h}{\sqrt {1+{h^{\prime }}^{2}}} = b^{2} \]

8980

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

8982

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

8984

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

8985

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

8986

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

8987

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

8988

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

8989

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

8990

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

8991

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

8992

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

8993

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

8994

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

8995

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

8996

\[ {}c y^{\prime } = 0 \]

8997

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

8998

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

8999

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

9000

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

9001

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

9002

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

9003

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

9004

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

9005

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

9006

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

9007

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

9008

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

9009

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

9010

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

9011

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

9012

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

9013

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

9014

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

9015

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

9016

\[ {}5 y^{\prime } = 0 \]

9017

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

9018

\[ {}\pi y^{\prime } = 0 \]

9019

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

9020

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

9021

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

9022

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

9023

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

9024

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

9025

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

9026

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

9027

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

9028

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

9029

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

9030

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

9031

\[ {}{y^{\prime }}^{n} = 0 \]

9032

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

9033

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

9034

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

9035

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

9036

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

9037

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