The solution of the differential eqution `(d^(2)y)/(dx^(2)) = e^(-2x)` is ` y = c_(1)e^(-2x) +c_(2)x + c_(3)` where `c_(1)` is

Options

A. 1
B. `1/4`
C. `1/2`
D. 2

Answer

b

Explanation

Given , ` (d^(2)y)/(dx^(2)) = e^(-2x)`
` rArr (dy)/(dx) = (e^(-2x))/(2) +c_(2)` [ integrating ]
`rArr y = (e^(-2x))/4 + c_(2)x + c_(3)` [ integrating]
But ` y = c(1)e^(-2x) + c_(2) x + c_(3) ` [given ]
` :. C_(1) = 1/4 `