y^{''}-(8)y^'+αy=0,y(0)=1,y^'(0)=-73

Lösung

y^{^{''}} - (8) y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = - 73

y = e^{t (4 + - α + 16)} (1 + \frac{- - α + 16 - 77}{2 16 - α}) - \frac{e ^{t (4 - - α + 16)} ( - - α + 16 - 77 )}{2 16 - α}

Schritte zur Lösung

y^{''} (t) - (8) y^{'} (t) + α y = 0

Solve linear ODE:

y = e^{t (4 + - α + 16)} (1 + \frac{- - α + 16 - 77}{2 16 - α}) - \frac{e ^{t (4 - - α + 16)} ( - - α + 16 - 77 )}{2 16 - α}

y = e^{t (4 + - α + 16)} (1 + \frac{- - α + 16 - 77}{2 16 - α}) - \frac{e ^{t (4 - - α + 16)} ( - - α + 16 - 77 )}{2 16 - α}

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

8 y^{^{''}} + y^{^{'}} + 128 y = 0, y (0) = 5, y^{^{'}} (0) = 8

\frac{1}{8} x^{^{''}} + 36 x = 0

\frac{d ^{2} y}{d x ^{2}} = - 4 y

\frac{d ^{2} y}{d t ^{2}} - y = 0