Which of the following differential equation has ` y = C_(1)e^(x) + C_(2)e^(-x)` as the general solution ?

Options

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

Answer

b

Explanation

Given , general solution is ` y = C_(1)e^(x) + C_(2)e^(-x)`
On differentiating twice w.r.t , we get
` y' = C_(1)e^(x) +C_(2)e^(-x)(-1)`
Again , on differentiating w.r.t x, we get
` y'' = C_(1)e^(x) - C_(2)e^(-x)(-1)`
` rArr y '' = C_(1)e^(x) + C_(2)e^(-x)`
` rArr y'' = y` [ from Eq.(i)
` rArr y' ' - y = 0 ` ltbRgt ` rArr (d^(2)y)/(dx^(2)) -y =0`