64y^{''}-y=0,y(-8)=1,y^'(-8)=-1

Lösung

64 y^{^{''}} - y = 0, y (- 8) = 1, y^{^{'}} (- 8) = - 1

y = (e - \frac{9 e}{2}) e^{\frac{t}{8}} + \frac{9 e ^{\frac{- t - 8}{8}}}{2}

Schritte zur Lösung

64 y^{''} (t) - y = 0

Solve linear ODE:

y = (e - \frac{9 e}{2}) e^{\frac{t}{8}} + \frac{9 e ^{\frac{- t - 8}{8}}}{2}

y = (e - \frac{9 e}{2}) e^{\frac{t}{8}} + \frac{9 e ^{\frac{- t - 8}{8}}}{2}

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = 0, y^{^{'}} (0) = - 7

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

y^{^{'''}} + 4 y^{^{''}} - 4 y^{^{'}} - 16 y = 0

y^{^{''''}} - y^{^{'''}} - 3 y^{^{''}} + 5 y^{^{'}} - 2 y = 0

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