​ If y = 500e^7x + 600e^-7x, show that d^2y/dx^2 = 49y. ​

Question

If y = 500e^7x + 600e^-7x, show that \(\frac{d^2y}{dx^2}\) = 49y.

Answer 1

y = 500e^7x + 600e^-7x 

\(\frac{dy}{dx}\) = 500.7e^7x + 600(-7. e^-7x) 

\(\frac{d^2y}{dx^2}\) = 500(49e^7x) + 600(+49 .e^-7x) 

= 49 (500^7x + 600e^-7x) = 49y 

∴ \(\frac{d^2y}{dx^2}\) = 49y