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Beliebt Rechnen >

8y^{''}+8y^'+1/4 y=0,y(0)=2,y^'(0)=1

Lösung

8 y^{^{''}} + 8 y^{^{'}} + \frac{1}{4} y = 0, y (0) = 2, y^{^{'}} (0) = 1

Lösung

y = (2 + \frac{8 - 14}{14}) e^{\frac{( - 4 + 14 ) t}{8}} - \frac{8 - 14}{14} e^{- \frac{( 4 + 14 ) t}{8}}

Schritte zur Lösung

8 y^{''} (t) + 8 y^{'} (t) + \frac{1}{4} y = 0

Solve linear ODE:

y = (2 + \frac{8 - 14}{14}) e^{\frac{( - 4 + 14 ) t}{8}} - \frac{8 - 14}{14} e^{- \frac{( 4 + 14 ) t}{8}}

y = (2 + \frac{8 - 14}{14}) e^{\frac{( - 4 + 14 ) t}{8}} - \frac{8 - 14}{14} e^{- \frac{( 4 + 14 ) t}{8}}

Graph

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y^{''}+3y^'+2.25y=0