The solution of `(dy)/(dx) + y = e^(x)` is

Options

A. ` 2y = e^(2x)+C`
B. `2ye^(x)=e^(2)+C`
C. `2ye^(x)=e^(2x)+C`
D. `2ye^(2x)=2e^(x)+C`

Answer

d

Explanation

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