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

Lösung

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

y = e^{4 t} (a - \frac{2 ( a + 2 )}{3}) + \frac{2 e ^{- 2 t} ( a + 2 )}{3}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{4 t} (a - \frac{2 ( a + 2 )}{3}) + \frac{2 e ^{- 2 t} ( a + 2 )}{3}

y = e^{4 t} (a - \frac{2 ( a + 2 )}{3}) + \frac{2 e ^{- 2 t} ( a + 2 )}{3}

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

2 y^{^{''}} + 12 y^{^{'}} + 24 y = 0, y (0) = 1, y^{^{'}} (0) = 4

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

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = - 6, y^{^{'}} (0) = - 32

x^{^{''}} + 80 x = 0