# 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.

(v) Whether a solution of ${*}{}{}$grows exponentially or decays exponentially depends on the initial conditions.

(vi) A solution of ${*}{}{}$may be a non-zero constant.

(vii) The only solution of ${*}{}{}$is the trivial solution $y\left(x\right)\equiv 0.$

(b) Now consider the differential equation ${*}{}{}$with the initial values $y\left(0\right)=1,\frac{dy}{dx}\left(0\right)=0.$

What is the value of y(1)?