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If y=500\ e^(7x)+600\ e^(-7x) , show tha...

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

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`y=500e^(7x)+600e^(-7x)`
`implies(dy)/(dx)=(d)/(dx)(500e^(7x)+600e^(-7x))`
`=3500e^(7x)-4200e^(-7x)`
`implies(d^(2)y)/(dx^(2))=(d)/(dx)(3500e^(7x)-4200e^(-7x))`
`=24500e^(7x)+29400e^(-7x)`
`=49(500e^(7x)+600e^(-7x))=49y`
`implies(d^(2)y)/(dx^(2))=49y " " `Hence Proved.
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