3.9.51 Problems 5001 to 5100

Table 3.607: First order ode linear in derivative

#

ODE

Mathematica

Maple

12912

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

12913

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

12914

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

12915

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

12916

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

12917

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

12918

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

12919

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

12920

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

12921

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

12922

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

12923

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

12924

\[ {}\theta ^{\prime } = 2 \]

12925

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

12926

\[ {}v^{\prime } = -\frac {v}{R C} \]

12927

\[ {}v^{\prime } = \frac {K -v}{R C} \]

12928

\[ {}v^{\prime } = 2 V \left (t \right )-2 v \]

12929

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

12930

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

12931

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

12932

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

12933

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

12934

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

12935

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

12936

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

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

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