If $f(x)=10 \cos x+(13+2 x) \sin x$,then $f^{\prime \prime}(x)+f(x)$ is equal to

If $e^y + xy = e$,then the value of $\frac{d^2y}{dx^2}$ for $x = 0$ is

If ${y^2} = a{x^2} + bx + c$,then ${y^3}\frac{{{d^2}y}}{{d{x^2}}}$ is

If $y = {\left[ {x + \sqrt {{x^2} - 1} } \right]^{15}} + {\left[ {x - \sqrt {{x^2} - 1} } \right]^{15}}$,then $\left( {{x^2} - 1} \right)\frac{{{d^2}y}}{{d{x^2}}} + x\frac{{dy}}{{dx}}$ is equal to

If $f(x) = \sin(\sin x)$ and $f''(x) + \tan x f'(x) + g(x) = 0$,then $g(x)$ is

Let $f$ and $g$ be twice differentiable functions such that $f(x) \cdot g(x) = 1$ for all $x \in R$ and $f'$ and $g'$ are never zero. Then $\frac{f''(x)}{f(x)} + \frac{g''(x)}{g(x)}$ equals: