y^{''}-(2α-1)y^'+α(α-1)y=0

Lösung

y^{^{''}} - (2 α - 1) y^{^{'}} + α (α - 1) y = 0

y = c_{1} e^{α t} + c_{2} e^{(α - 1) t}

Schritte zur Lösung

y^{''} (t) - (2 α - 1) y^{'} (t) + α (α - 1) y = 0

Solve linear ODE:

y = c_{1} e^{α t} + c_{2} e^{(α - 1) t}

y = c_{1} e^{α t} + c_{2} e^{(α - 1) t}

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = - 4, y^{^{'}} (0) = 3

y^{^{''}} + b y^{^{'}} + 64 y = 0, y (0) = 2, y^{^{'}} (0) = 0

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

y^{^{''''}} - 40 y^{^{'''}} + 400 y^{^{''}} = 0

x^{^{''}} + 2 x^{^{'}} + 8 x = 0