If $y = a{e^x} + b{e^{-x}} + c$ where $a, b, c$ are parameters,then $y''' = $

If $y=3 \cos (\log x)+4 \sin (\log x),$ show that $x^{2} y_{2}+x y_{1}+y=0$.

If $y=f(x)$ is a thrice differentiable function and a bijection,then $\frac{d^2 x}{d y^2}\left(\frac{d y}{d x}\right)^3+\frac{d^2 y}{d x^2}=$

If $f(x)=x^4-x^3+7x^2+14$,then what is the value of $f^{\prime \prime}(5)$?

If $p(x)$ is a polynomial of degree $3$ which satisfies $p^{\prime \prime}(1)=0$ and $p^{\prime \prime \prime}(1)=6$,then $p^{\prime \prime}(0)$ is equal to

$y=e^{a \sin ^{-1} x} \Rightarrow (1-x^2) y_{n+2}-(2 n+1) x y_{n+1}$ is equal to