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Question:

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

-2

7

5

13

Solution:

dy/dx = y+3
⇒ dy/(y+3) = dx
On integrating
ln|y+3| = x+c
∴ ln(y+3) = x+c
Since y(0)=2
∴ c = ln 5
⇒ ln(y+3) = x+ln 5
Substitute x = ln 2
⇒ ln(y+3) = ln 2 + ln 5
⇒ ln(y+3) = ln(2*5)
⇒ ln(y+3) = ln 10
⇒ y+3 = 10
⇒ y = 7
Hence, option '7' is correct.