Question

If y = 500 e^7x + 600 e^−7x, show that \[\frac{d^2 y}{d x^2} = 49y\] ?

Answer 1

Here,

\[y = 500 e^{7x} + 600 e^{- 7x} \]

\[\text { Differentiating w . r . t . x, we get }\]

\[\frac{d y}{d x} = 3500 e^{7x} - 4200 e^{- 7x} \]

\[ \text { Differentiating again w . r . t . x, we get}\]

\[\frac{d^2 y}{d x^2} = 24500 e^{7x} + 29400 e^{- 7x} \]

\[ = 49\left( 500 e^{7x} + 600 e^{- 7x} \right) = 49y\]