$$\begin{gathered} The general solution of this kind of \\ differential eq. is y = e^{ax} \\ Let a function g\left(x\right) = e^{ax}f\left(x\right) \left(1\right) \\ differentiate eq. \left(1\right) thrice for getting g^{,,,}\left(x\right) \\ now for getting the same function as given \\ find a. you get the same function for \\ a = 1/2. clearly, for min 5 zeros of g\left(x\right), \\ there are min 2 zeros for g^{,,,}\left(x\right). \\ solve and inform if face any problem. \end{gathered}$$