y^{''}-2y^'-8y=0,y(0)=a,y^'(0)=5

Lösung

y^{^{''}} - 2 y^{^{'}} - 8 y = 0, y (0) = a, y^{^{'}} (0) = 5

y = e^{4 t} (a + \frac{5 - 4 a}{6}) - \frac{e ^{- 2 t} ( 5 - 4 a )}{6}

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) - 8 y = 0

Solve linear ODE:

y = e^{4 t} (a + \frac{5 - 4 a}{6}) - \frac{e ^{- 2 t} ( 5 - 4 a )}{6}

y = e^{4 t} (a + \frac{5 - 4 a}{6}) - \frac{e ^{- 2 t} ( 5 - 4 a )}{6}

x^{^{''}} + 4 x^{^{'}} + 29 x = 0

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (- 1) = 2, y^{^{'}} (- 1) = 2

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = \frac{33}{4}

81 y^{^{''}} = - 16 y

y^{^{''}} + (0) y^{^{'}} + 36 y = 0, y (0) = 3, y^{^{'}} (0) = 0