The differential equation of the family of curves ` y= c_(1)e^(x) +c_(2)e^(-x)` is

Options

A. `(d^(2)y)/(dx^(2))+y=0`
B. `(d^(2)y)/(dx^(2))-y=0`
C. `(d^(2)y)/(dx^(2))+1=0`
D. `(d^(2)y)/(dx^(2))-1=0`

Answer

B

Explanation

`y=c_(1)e^(x)+c_(2)e^(-x)" …(i)"`
Differentiating w.r.t. x, we get
`(dy)/(dx)=c_(1)e^(x)-c_(2)e^(-x)" …(ii)"`
Again differentiating w.r.t. x, we get
`(d^(2)y)/(dx^(2))=c_(1)e^(x)-c_(2)e^(-x)" ...(iii)"`
`rArr" "(d^(2)y)/(dx^(2))=y" [Using (i)]"`
`rArr" "(d^(2)y)/(dx^(2))-y=0`