y^{''}-5y^'-14y=0,y(0)=α,y^'(0)=-14

Lösung

y^{^{''}} - 5 y^{^{'}} - 14 y = 0, y (0) = α, y^{^{'}} (0) = - 14

y = e^{7 t} (α + \frac{- 14 - 7 α}{9}) - \frac{e ^{- 2 t} ( - 14 - 7 α )}{9}

Schritte zur Lösung

y^{''} (t) - 5 y^{'} (t) - 14 y = 0

Solve linear ODE:

y = e^{7 t} (α + \frac{- 14 - 7 α}{9}) - \frac{e ^{- 2 t} ( - 14 - 7 α )}{9}

y = e^{7 t} (α + \frac{- 14 - 7 α}{9}) - \frac{e ^{- 2 t} ( - 14 - 7 α )}{9}

\frac{d ^{2} x}{d t ^{2}} + 12 \frac{d x}{d t} + 32 x = 0

y^{^{'''}} - 16 y = 0

y^{^{''}} + a \cdot y^{^{'}} + b \cdot y = 0

(3440.3669700000000 \dots) y^{^{''}} + (0) y^{^{'}} + (22500) y = 0

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = - \frac{6}{5}, y^{^{'}} (0) = - 3