3.1.60 Problems 5901 to 6000

Table 3.119: First order ode

#

ODE

Mathematica

Maple

12937

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

12938

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

12939

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

12940

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

12941

\[ {}\theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \]

12942

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

12943

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

12944

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

12945

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

12946

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

12947

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

12948

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

12949

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

12950

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

12951

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

12952

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

12953

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

12954

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

12955

\[ {}y^{\prime } = y^{2}-4 y-12 \]

12956

\[ {}y^{\prime } = y^{2}-4 y-12 \]

12957

\[ {}y^{\prime } = y^{2}-4 y-12 \]

12958

\[ {}y^{\prime } = y^{2}-4 y-12 \]

12959

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

12960

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

12961

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

12962

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

12963

\[ {}w^{\prime } = w \cos \left (w\right ) \]

12964

\[ {}w^{\prime } = w \cos \left (w\right ) \]

12965

\[ {}w^{\prime } = w \cos \left (w\right ) \]

12966

\[ {}w^{\prime } = w \cos \left (w\right ) \]

12967

\[ {}w^{\prime } = w \cos \left (w\right ) \]

12968

\[ {}w^{\prime } = \left (1-w\right ) \sin \left (w\right ) \]

12969

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

12970

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

12971

\[ {}w^{\prime } = 3 w^{3}-12 w^{2} \]

12972

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

12973

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

12974

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

12975

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

12976

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

12977

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

12978

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

12979

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

12980

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

12981

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

12982

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

12983

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

12984

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

12985

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

12986

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

12987

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

12988

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

12989

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

12990

\[ {}y^{\prime } = -4 y+9 \,{\mathrm e}^{-t} \]

12991

\[ {}y^{\prime } = -4 y+3 \,{\mathrm e}^{-t} \]

12992

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

12993

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

12994

\[ {}y^{\prime } = 3 y-4 \,{\mathrm e}^{3 t} \]

12995

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

12996

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

12997

\[ {}y^{\prime }-2 y = 3 \,{\mathrm e}^{-2 t} \]

12998

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

12999

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

13000

\[ {}y^{\prime }-2 y = 7 \,{\mathrm e}^{2 t} \]

13001

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

13002

\[ {}y^{\prime }+2 y = t^{2}+2 t +1+{\mathrm e}^{4 t} \]

13003

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

13004

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

13005

\[ {}y^{\prime }+y = \cos \left (2 t \right )+3 \sin \left (2 t \right )+{\mathrm e}^{-t} \]

13006

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

13007

\[ {}y^{\prime } = \frac {3 y}{t}+t^{5} \]

13008

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

13009

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

13010

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

13011

\[ {}y^{\prime }-\frac {2 y}{t} = t^{3} {\mathrm e}^{t} \]

13012

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

13013

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

13014

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

13015

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

13016

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

13017

\[ {}y^{\prime }-\frac {3 y}{t} = 2 t^{3} {\mathrm e}^{2 t} \]

13018

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

13019

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

13020

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

13021

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

13022

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

13023

\[ {}y^{\prime } = \frac {y}{\sqrt {t^{3}-3}}+t \]

13024

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

13025

\[ {}y^{\prime } = t^{r} y+4 \]

13026

\[ {}v^{\prime }+\frac {2 v}{5} = 3 \cos \left (2 t \right ) \]

13027

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

13028

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

13029

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

13030

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

13031

\[ {}y^{\prime } = -\sin \left (y\right )^{5} \]

13032

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

13033

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

13034

\[ {}y^{\prime } = \left (y-3\right ) \left (\sin \left (y\right ) \sin \left (t \right )+\cos \left (t \right )+1\right ) \]

13035

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

13036

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