4.9.51 Problems 5001 to 5100

Table 4.725: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

12971

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

12973

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

12974

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

12975

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

12976

\[ {} u^{\prime } = \frac {1}{5-2 u} \]

12977

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

12978

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

12979

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

12980

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

12981

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

12982

\[ {} \theta ^{\prime } = t \sqrt {t^{2}+1}\, \sec \left (\theta \right ) \]

12983

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

12984

\[ {} R^{\prime } = \left (t +1\right ) \left (1+R^{2}\right ) \]

12985

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

12986

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

12987

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

12988

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

12989

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

12990

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

12991

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

12992

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

12993

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

12994

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

12995

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

12996

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

12997

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

12998

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

12999

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

13000

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

13002

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

13003

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

13004

\[ {} x^{\prime } = 2 t^{3} x-6 \]

13005

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

13006

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

13007

\[ {} 7 t^{2} x^{\prime } = 3 x-2 t \]

13008

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

13010

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

13011

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

13012

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

13013

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

13014

\[ {} \theta ^{\prime } = -a \theta +{\mathrm e}^{b t} \]

13015

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

13016

\[ {} x^{\prime }+\frac {5 x}{t} = t +1 \]

13017

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

13018

\[ {} R^{\prime }+\frac {R}{t} = \frac {2}{t^{2}+1} \]

13019

\[ {} N^{\prime } = N-9 \,{\mathrm e}^{-t} \]

13020

\[ {} \cos \left (\theta \right ) v^{\prime }+v = 3 \]

13021

\[ {} R^{\prime } = \frac {R}{t}+t \,{\mathrm e}^{-t} \]

13022

\[ {} y^{\prime }+a y = \sqrt {t +1} \]

13023

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

13024

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

13026

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

13027

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

13028

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

13029

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

13030

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

13031

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

13032

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

13033

\[ {} x^{\prime } = a x+b x^{3} \]

13034

\[ {} w^{\prime } = t w+t^{3} w^{3} \]

13035

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

13036

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

13037

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

13038

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

13039

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

13040

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

13113

\[ {} x^{\prime }+5 x = \operatorname {Heaviside}\left (t -2\right ) \]

13114

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

13122

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

13124

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

13125

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

13129

\[ {} x^{\prime }+3 x = \delta \left (t -1\right )+\operatorname {Heaviside}\left (-4+t \right ) \]

13175

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

13179

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

13180

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

13181

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

13182

\[ {} y^{\prime }+4 x y = 8 x \]

13187

\[ {} 2 y+y^{\prime } = 6 \,{\mathrm e}^{x}+4 x \,{\mathrm e}^{-2 x} \]

13191

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

13192

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

13198

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

13199

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

13200

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

13201

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

13202

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

13203

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

13204

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

13205

\[ {} 6 x y+2 y^{2}-5+\left (3 x^{2}+4 x y-6\right ) y^{\prime } = 0 \]

13206

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

13207

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

13208

\[ {} \frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}} = 0 \]

13209

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

13210

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

13211

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

13212

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

13213

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

13214

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

13215

\[ {} \frac {1+8 x y^{{2}/{3}}}{x^{{2}/{3}} y^{{1}/{3}}}+\frac {\left (2 x^{{4}/{3}} y^{{2}/{3}}-x^{{1}/{3}}\right ) y^{\prime }}{y^{{4}/{3}}} = 0 \]

13216

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

13217

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