If $y=3 e^{5 x}+5 e^{3 x}$,then $\frac{d^{2} y}{d x^{2}}-8 \frac{d y}{d x}=$ (in $y$)

The equation $x^5 - 5x^3 + 5x^2 - 1 = 0$ has how many equal roots?

If $y = \frac{\alpha x + \beta}{\gamma x + \delta}$,then $2 y_1 y_3 =$

Let $f$ be a twice differentiable function such that $f^{\prime \prime}(x) = -f(x)$,$f^{\prime}(x) = g(x)$ and $h(x) = [f(x)]^2 + [g(x)]^2$. If $h(5) = 1$,then $h(10)$ is $\qquad$

If $y = e^{nx}$,then $\left( \frac{d^2y}{dx^2} \right) \left( \frac{d^2x}{dy^2} \right)$ is equal to

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