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Beliebt Rechnen >

y^{''}+4y^'+16y=0,y(0)= 1/2 ,y^'(0)=0

Lösung

y^{^{''}} + 4 y^{^{'}} + 16 y = 0, y (0) = \frac{1}{2}, y^{^{'}} (0) = 0

Lösung

y = e^{- 2 t} (\frac{1}{2} cos (23 t) + \frac{1}{2 3} sin (23 t))

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = e^{- 2 t} (\frac{1}{2} cos (23 t) + \frac{1}{2 3} sin (23 t))

y = e^{- 2 t} (\frac{1}{2} cos (23 t) + \frac{1}{2 3} sin (23 t))

Graph

Beliebte Beispiele

y^{''}-10y^'+25y=0,y(0)=-2,y^'(0)=1

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = - 2, y^{^{'}} (0) = 1

1/2 y^{''}+2y=0

\frac{1}{2} y^{^{''}} + 2 y = 0

y^{'''}+6y^{''}=0

y^{^{'''}} + 6 y^{^{''}} = 0

y^{'''}-2y^{''}+5y^'=0,y(0)=0,y^'(0)=0

y^{^{'''}} - 2 y^{^{''}} + 5 y^{^{'}} = 0, y (0) = 0, y^{^{'}} (0) = 0

y^{''}+9y=0,y(0)=0

y^{^{''}} + 9 y = 0, y (0) = 0