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Beliebt Rechnen >

x^{''}+8x^'+16x=e^{-t}sin(4t)

Lösung

x^{^{''}} + 8 x^{^{'}} + 16 x = e^{- t} sin (4 t)

Lösung

x = c_{1} e^{- 4 t} + c_{2} t e^{- 4 t} - \frac{7}{625} e^{- t} sin (4 t) - \frac{24}{625} e^{- t} cos (4 t)

Schritte zur Lösung

x^{''} (t) + 8 x^{'} (t) + 16 x = e^{- t} sin (4 t)

Solve linear ODE:

x = c_{1} e^{- 4 t} + c_{2} t e^{- 4 t} - \frac{7}{625} e^{- t} sin (4 t) - \frac{24}{625} e^{- t} cos (4 t)

x = c_{1} e^{- 4 t} + c_{2} t e^{- 4 t} - \frac{7}{625} e^{- t} sin (4 t) - \frac{24}{625} e^{- t} cos (4 t)

Graph

Beliebte Beispiele

y^{''}+y^'-y=sin(x)

y^{^{''}} + y^{^{'}} - y = sin (x)

y^{^{''}} + y^{^{'}} = 4 t

y^{'''}+y^{''}=4x^2+3e^x

y^{^{'''}} + y^{^{''}} = 4 x^{2} + 3 e^{x}

y^{''''}+2y^{''}+y=3x+4

y^{^{''''}} + 2 y^{^{''}} + y = 3 x + 4

y^{''}-18y^'+81y=480sin(x)-210cos(x)

y^{^{''}} - 18 y^{^{'}} + 81 y = 480 sin (x) - 210 cos (x)