y^{''}-83y^'+αy=0,y(0)=1,y^'(0)=-73

Lösung

y^{^{''}} - 83 y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = - 73

y = e^{\frac{t ( 83 + 6889 - 4 α )}{2}} (1 + \frac{- - 4 α + 6889 - 229}{2 6889 - 4 α}) - \frac{e ^{\frac{t ( 83 - 6889 - 4 α )}{2}} ( - - 4 α + 6889 - 229 )}{2 6889 - 4 α}

Schritte zur Lösung

y^{''} (t) - 83 y^{'} (t) + α y = 0

Solve linear ODE:

y = e^{\frac{t ( 83 + 6889 - 4 α )}{2}} (1 + \frac{- - 4 α + 6889 - 229}{2 6889 - 4 α}) - \frac{e ^{\frac{t ( 83 - 6889 - 4 α )}{2}} ( - - 4 α + 6889 - 229 )}{2 6889 - 4 α}

y = e^{\frac{t ( 83 + 6889 - 4 α )}{2}} (1 + \frac{- - 4 α + 6889 - 229}{2 6889 - 4 α}) - \frac{e ^{\frac{t ( 83 - 6889 - 4 α )}{2}} ( - - 4 α + 6889 - 229 )}{2 6889 - 4 α}

x^{^{''}} - 9 x = 0

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (1) = 0, y^{^{'}} (1) = 1

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

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

2 y^{^{'''}} - 4 y^{^{''}} - 2 y^{^{'}} + 4 y = 0