16y^{''}-y=0,y(-4)=1,y^'(-4)=-1

Lösung

16 y^{^{''}} - y = 0, y (- 4) = 1, y^{^{'}} (- 4) = - 1

y = (e - \frac{5 e}{2}) e^{\frac{t}{4}} + \frac{5 e ^{\frac{- t - 4}{4}}}{2}

Schritte zur Lösung

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

Solve linear ODE:

y = (e - \frac{5 e}{2}) e^{\frac{t}{4}} + \frac{5 e ^{\frac{- t - 4}{4}}}{2}

y = (e - \frac{5 e}{2}) e^{\frac{t}{4}} + \frac{5 e ^{\frac{- t - 4}{4}}}{2}

y^{^{''}} + 16 y^{^{'}} + 64 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} = 0, y (0) = 6 - 6 e^{4}, y (1) = 0

y^{^{''}} - \frac{3}{2} y^{^{'}} - y = 0

y^{^{'''}} + 12 y^{^{''}} + 45 y^{^{'}} = 0

y^{^{''}} + 4 y = 0, y (\frac{π}{6}) = 4, y^{^{'}} (\frac{π}{6}) = - 8