If $y = a \sin x + (5 + 2x) \cos x$,then $y'' + y =$

If $y = a{x^{n + 1}} + b{x^{ - n}},$ then ${x^2}\frac{{{d^2}y}}{{d{x^2}}}$ is equal to:

If $f: R \rightarrow R$ is an even function which is twice differentiable on $R$ and $f^{\prime \prime}(\pi)=1$,then $f^{\prime \prime}(-\pi)$ is equal to

If $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,then $\frac{d^2 y}{d x^2}$ is

Find the second order derivative of the function $f(x) = x^{20}$.

If $\frac{d^n y}{d x^n}=y_n$ and $y=e^{\sqrt{x}}+e^{-\sqrt{x}}$,then $4 x y_2+2 y_1=$