If d y d x =y+3>0 and y(0)=2 then y( 2) is equal to

Step-by-step solution

The given differential equation is dy dx = y + 3 . Rearranging the terms to separate variables, we get dy y + 3 = dx . Integrating both sides, dy y + 3 = dx , which gives |y + 3| = x + C . Given y(0) = 2 , substituting x = 0 and y = 2 into the equation: |2 + 3| = 0 + C C = 5 . Thus, (y + 3) = x + 5 . Exponentiating both sides, y + 3 = 5e^x , so y = 5e^x - 3 . To find y( 2) , substitute x = 2 : y( 2) = 5e^ 2 - 3 = 5(2) - 3 = 10 - 3 = 7 . Answer: 7