# Question: consider the secondorder ordinary differential equation d2ydx2dydx2y0 a are...

###### Question details

Consider the second-order ordinary differential equation

$\frac{{d}^{2}y}{d{x}^{2}}-\frac{dy}{dx}-2y=0{*}$.

(a) Are the following statements true or false? Please explain.

(i) A non-trivial solution of ${*}$ will always grow exponentially.

(ii) A non-trivial solution of ${*}{}$will always exponentially decay.

(iii) A solution of ${*}{}$could grow linearly.

(iv) A solution of ${*}{}$may be oscillatory.