4.1.63 Problems 6201 to 6300

Table 4.125: First order ode

#

ODE

Mathematica

Maple

Sympy

14637

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

14638

\[ {} 8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime } = 0 \]

14639

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

14640

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

14641

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

14642

\[ {} y^{\prime } = \frac {2 x -7 y}{3 y-8 x} \]

14643

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

14644

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

14645

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

14646

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

14647

\[ {} 8+2 y^{2}+\left (-x^{2}+1\right ) y y^{\prime } = 0 \]

14648

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

14649

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

14650

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

14651

\[ {} y^{\prime } = \frac {2 x +7 y}{2 x -2 y} \]

14652

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

14653

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

14654

\[ {} \left (x +2\right ) y^{\prime }+y = \left \{\begin {array}{cc} 2 x & 0\le x \le 2 \\ 4 & 2<x \end {array}\right . \]

14655

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

14656

\[ {} 5 x y+4 y^{2}+1+\left (x^{2}+2 x y\right ) y^{\prime } = 0 \]

14657

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

14658

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

14659

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

14660

\[ {} 4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime } = 0 \]

14661

\[ {} 8 x^{2} y^{3}-2 y^{4}+\left (5 y^{2} x^{3}-8 x y^{3}\right ) y^{\prime } = 0 \]

14662

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

14663

\[ {} 3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime } = 0 \]

14664

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

14665

\[ {} 10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime } = 0 \]

14666

\[ {} 6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0 \]

14667

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

14668

\[ {} 2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime } = 0 \]

14669

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

14925

\[ {} -y+y^{\prime } = {\mathrm e}^{3 t} \]

14926

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

14985

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

14986

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

14987

\[ {} u^{\prime } = 4 t \ln \left (t \right ) \]

14988

\[ {} z^{\prime } = x \,{\mathrm e}^{-2 x} \]

14989

\[ {} T^{\prime } = {\mathrm e}^{-t} \sin \left (2 t \right ) \]

14990

\[ {} x^{\prime } = \sec \left (t \right )^{2} \]

14991

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

14992

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

14993

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

14994

\[ {} x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t} = {\mathrm e}^{-t} \]

14995

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

14996

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

14997

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

14998

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

14999

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

15000

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

15001

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

15002

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

15003

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

15004

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

15005

\[ {} x^{\prime }+p x = q \]

15006

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

15007

\[ {} i^{\prime } = p \left (t \right ) i \]

15008

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

15009

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

15010

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

15011

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

15012

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

15013

\[ {} x^{\prime }+t x = 4 t \]

15014

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

15015

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

15016

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

15017

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

15018

\[ {} x^{\prime }+5 x = t \]

15019

\[ {} x^{\prime }+\left (a +\frac {1}{t}\right ) x = b \]

15020

\[ {} T^{\prime } = -k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right ) \]

15021

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

15022

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

15023

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

15024

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

15025

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

15026

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

15027

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

15028

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

15029

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

15030

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

15129

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

15130

\[ {} 12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime } = 0 \]

15131

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

15132

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

15133

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

15134

\[ {} x^{\prime }+3 x = {\mathrm e}^{2 t} \]

15135

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

15136

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

15137

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

15138

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

15139

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

15140

\[ {} {y^{\prime }}^{2} = 9 y^{4} \]

15141

\[ {} x^{\prime } = {\mathrm e}^{\frac {x}{t}}+\frac {x}{t} \]

15142

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

15143

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

15144

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

15145

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

15146

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

15147

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