y^{''}+9y^'+αy=0,y(0)=1,y^'(0)=-4

Lösung

y^{^{''}} + 9 y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = - 4

y = e^{\frac{t ( - 9 + 81 - 4 α )}{2}} (1 + \frac{- - 4 α + 81 + 1}{2 81 - 4 α}) - \frac{e ^{\frac{t ( - 9 - 81 - 4 α )}{2}} ( - - 4 α + 81 + 1 )}{2 81 - 4 α}

Schritte zur Lösung

y^{''} (t) + 9 y^{'} (t) + α y = 0

Solve linear ODE:

y = e^{\frac{t ( - 9 + 81 - 4 α )}{2}} (1 + \frac{- - 4 α + 81 + 1}{2 81 - 4 α}) - \frac{e ^{\frac{t ( - 9 - 81 - 4 α )}{2}} ( - - 4 α + 81 + 1 )}{2 81 - 4 α}

y = e^{\frac{t ( - 9 + 81 - 4 α )}{2}} (1 + \frac{- - 4 α + 81 + 1}{2 81 - 4 α}) - \frac{e ^{\frac{t ( - 9 - 81 - 4 α )}{2}} ( - - 4 α + 81 + 1 )}{2 81 - 4 α}

y^{^{''}} + 0.05 y^{^{'}} - 0.0006 y = 0

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = - 1

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = - 5

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

3 x y^{^{'}} = 3 x y^{^{''}}