#### Question

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

#### Solution

Here,

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

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

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

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

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

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

Is there an error in this question or solution?

Solution If Y = 500 E7x + 600 E−7x, Show that D 2 Y D X 2 = 49 Y ? Concept: Simple Problems on Applications of Derivatives.