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# Solution for If Y = 500 E7x + 600 E−7x, Show that D 2 Y D X 2 = 49 Y ? - CBSE (Commerce) Class 12 - Mathematics

ConceptSimple Problems on Applications of Derivatives

#### Question

If y = 500 e7x + 600 e−7x, show that $\frac{d^2 y}{d x^2} = 49y$ ?

#### Solution

Here,

$y = 500 e^{7x} + 600 e^{- 7x}$

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

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

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

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

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

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Solution for question: If Y = 500 E7x + 600 E−7x, Show that D 2 Y D X 2 = 49 Y ? concept: Simple Problems on Applications of Derivatives. For the courses CBSE (Commerce), CBSE (Arts), PUC Karnataka Science, CBSE (Science)
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