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Beliebt Rechnen >

y^{''}+8y^'+16y=2sin(4t)

Lösung

y^{^{''}} + 8 y^{^{'}} + 16 y = 2 sin (4 t)

Lösung

y = c_{1} e^{- 4 t} + c_{2} t e^{- 4 t} - \frac{1}{16} cos (4 t)

Schritte zur Lösung

y^{''} (t) + 8 y^{'} (t) + 16 y = 2 sin (4 t)

Solve linear ODE:

y = c_{1} e^{- 4 t} + c_{2} t e^{- 4 t} - \frac{1}{16} cos (4 t)

y = c_{1} e^{- 4 t} + c_{2} t e^{- 4 t} - \frac{1}{16} cos (4 t)

Graph

Beliebte Beispiele

y^{''}+4y=14cos(2x)+21sin(2x)

y^{^{''}} + 4 y = 14 cos (2 x) + 21 sin (2 x)

y^{''}-y^'=e^xcos(x),y(0)=0,y^'(0)=0

y^{^{''}} - y^{^{'}} = e^{x} cos (x), y (0) = 0, y^{^{'}} (0) = 0

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

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

y^{^{''}} - y = 2 - x^{2}

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

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