The solution of f^(111)(x)-8f^(11)(x)=0 ...

The solution of `f^(111)(x)-8f^(11)(x)=0` satisfying `f(0)=(1)/(8),f^(1)(0)=0,f^(11)(0)=1` is `f(x)=lambda(e^(alpha x)+beta)-(x)/(alpha)`. Then `alpha, beta = ?`

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