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

Options

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

Answer

B

Explanation

We have
`(dy)/(dx)=y+3`
`rArr 1/(y+3)dy=dx`
`rArr " ln "|(y+3)|=x+"ln "c`, where ln c is a constant of integration
`(y+3)=ce^(x)`
Initially, when `x=0, y=2`
`rArr c=5`
Finally, the required solution is `y+3=5e^(x)`,
`rArr y("ln "2)=5e^("ln"2)-3=10-3=7`