If dy/dx = y + 3 > 0 and y(0) = 2

If dy/dx = y + 3 > 0 and y(0) = 2, then y(ln2) is equal to

  1. -13
  2. 5
  3. 7
  4. 2

Answer

dy/dx = y + 3

dy/y + 3 = dx

ln(y + 3) = x + c

Given at x = 0 , y = 2

ln5 = c

ln(y+3) = x + ln5

ln(y + 3/5) = x

y = 5ex - 3

The correct option is C.