Step 1:
We have $y=500e^{\large 7x}+600e^{\large-7x}$
Differentiating with respect to $x$
$\large\frac{dy}{dx}$$=500.7e^{\large 7x}+600.(-7)e^{\large -7x}$
Step 2:
$\large\frac{d^2y}{dx^2}$$=500\times 7\times 7e^{\large 7x}+600(-7)\times (-7)e^{\large-7x}$
$\quad\;=500e^{\large 7x}.49+600e^{\large -7x}.49$
$\quad\;=49[500e^{\large 7x}+600e^{-7x}]$
$\quad\;=49y$
Hence proved.