If `(dy)/(dx)+y=2e^(2x)`, then y is equal to

Options

A. ` Ce^(x)+2/3e^(2x)`
B. ` (1-x)e^(-x)+2/3e^(2x)+C`
C. ` Ce^(-x)+2/3e^(2x)`
D. `e^(-x)+2/3e^(2x)+C`

Answer

a

Explanation

Given , ` (dy)/(dx) +y = 2e^(2x)`
This is linear differential equation
` :. IF = e^(int 1 dx) = e^(x)`
` :. " Required solution is "`
` ye^(x) = 2 int e^(2x) e^(x) dx + C = 2/3 e^(3x) +C`
` rArr y = 2/3 e^(2x) + Ce^(-x)`