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Find the differential equation of the fa...

Find the differential equation of the family of curves `y=A e^(2x)+B e^(-2x)` , where A and B are arbitrary constants.

Text Solution

Verified by Experts

The correct Answer is:
`(d^(2)y)/(dx^(2))=4y`
`y=Ae^(2x)+Be^(-2x)`
`therefore (dy)/(dx)=2Ae^(2x)-2Be^(-2x)`
or `(d^(2)y)/(dx^(2))=4Ae^(2x)+4Be^(-2x)` = `4(Ae^(2x)+Be^(-2x))`
`=4y`, which is the required differential equation.
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