If y= 5e^{7x}+6e^{-7x},  show that  \frac{d^{2}y}{dx^{2}}= 49y\cdot

 

 

 

 
 
 
 
 

Answers (1)

y= 5e^{7x}+6e^{-7x}---(ii)
\Rightarrow \frac{dy}{dx}= 35e^{7x}-42e^{-7x}
\Rightarrow \frac{d^{2}y}{dx^{2}}= 245e^{7x}+29\, 4e^{-7x}= 49\left ( 5e^{7x} +6e^{-7x}\right )
Hence  \frac{d^{2}y}{dx^{2}}= 49y

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