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Beliebt Rechnen >

x^{''}+4x^'+6x=1+e^{-t}

Lösung

x^{^{''}} + 4 x^{^{'}} + 6 x = 1 + e^{- t}

Lösung

x = e^{- 2 t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{1}{6} + \frac{1}{3} e^{- t}

Schritte zur Lösung

x^{''} (t) + 4 x^{'} (t) + 6 x = 1 + e^{- t}

Solve linear ODE:

x = e^{- 2 t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{1}{6} + \frac{1}{3} e^{- t}

x = e^{- 2 t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{1}{6} + \frac{1}{3} e^{- t}

Graph

Beliebte Beispiele

y^{''}+y=cos(at)

y^{^{''}} + y = cos (a t)

y^{'''}-2y^{''}-y^'+2y=-8e^x+6e^{-x}

y^{^{'''}} - 2 y^{^{''}} - y^{^{'}} + 2 y = - 8 e^{x} + 6 e^{- x}

y^{''}+2y^'+y=6e^{-t},y(0)=y

y^{^{''}} + 2 y^{^{'}} + y = 6 e^{- t}, y (0) = y

y^{''}+2y^'+y=e^{-x}*ln(x)

y^{^{''}} + 2 y^{^{'}} + y = e^{- x} \cdot ln (x)

y^{''}+2y^'+y=3

y^{^{''}} + 2 y^{^{'}} + y = 3