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Beliebt Rechnen >

y^{''}+4y^'+4y=12te^{-2t}+4t

Lösung

y^{^{''}} + 4 y^{^{'}} + 4 y = 12 t e^{- 2 t} + 4 t

Lösung

y = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} + 2 e^{- 2 t} t^{3} + t - 1

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) + 4 y = 12 t e^{- 2 t} + 4 t

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} + 2 e^{- 2 t} t^{3} + t - 1

y = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} + 2 e^{- 2 t} t^{3} + t - 1

Graph

Beliebte Beispiele

tangent (x+2)^2+(y-3)^2=37,(-1,9)

t an g e n t (x + 2)^{2} + (y - 3)^{2} = 37, (- 1, 9)

integral of tan(4x)sec^2(4x)

\int tan (4 x) sec^{2} (4 x) d x

derivative x^2-e^{y^2}

d er i v a t i v e x^{2} - e^{y^{2}}

derivative y=arctan(e^x)

d er i v a t i v e y = arctan (e^{x})

integral of 3x^2-6x

\int 3 x^{2} - 6 x d x