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Beliebt Rechnen >

2y^{''}+16y^'+8y=0,y(0)=5,y^'(0)=0

Lösung

2 y^{^{''}} + 16 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

Lösung

y = (5 + \frac{5 ( 2 - 3 )}{2 3}) e^{2 (3 - 2) t} - \frac{5 ( 2 - 3 )}{2 3} e^{- 2 (2 + 3) t}

Schritte zur Lösung

2 y^{''} (t) + 16 y^{'} (t) + 8 y = 0

Solve linear ODE:

y = (5 + \frac{5 ( 2 - 3 )}{2 3}) e^{2 (3 - 2) t} - \frac{5 ( 2 - 3 )}{2 3} e^{- 2 (2 + 3) t}

y = (5 + \frac{5 ( 2 - 3 )}{2 3}) e^{2 (3 - 2) t} - \frac{5 ( 2 - 3 )}{2 3} e^{- 2 (2 + 3) t}

Graph

Beliebte Beispiele

(2 D^{2} - 5 D - 3) y = 0

y^{^{''}} + 1960 y = 0

y^{''}+9y^'+0y=0

y^{^{''}} + 9 y^{^{'}} + 0 y = 0

y^{'''}+9y^{''}+24y^'+16y=0

y^{^{'''}} + 9 y^{^{''}} + 24 y^{^{'}} + 16 y = 0

2x^{''}+16x^'+64x=0,x(0)=0,x^'(0)=0.2

2 x^{^{''}} + 16 x^{^{'}} + 64 x = 0, x (0) = 0, x^{^{'}} (0) = 0.2