If `(dy)/(dx)=y+3 and y(0)=2`, then y(ln 2) is equal to

Options

A. 5
B. 13
C. `-2`
D. 7

Answer

d

Explanation

Here, ` (dy)/(dx) = y + 3 gt and y (0) = 2`
` rArr int (dy)/(y+3) = int dx`
` rArr log | y + 3 | = x +C`
But , given `y(0) =2`
` rArr log | y + 3| = x + log_(e)5`
when ` x = log _(e)2`
` rArr log |y +3| = log_(e)2 + log_(e) 5 = log_(e) 10`
` :. y + 3 = 10`
` rArr y = 7`