Integrating factor (I.F.) of the differential equation $${{dy} \over {dx}} - {{3{x^2}} \over {1 + {x^3}}}y = {{{{\sin }^2}x} \over {1 + x}}$$ is

The differential equation of y = ae^bx (a & b are parameters) is

If $x=\int\limits_0^y \frac{1}{\sqrt{1+9 t^2}} d t$ and $\frac{d^2 y}{d x^2}=a y$, then $a$ is equal to