If dy dx = y + 5 and y(0) = 4 then y( 2) is equal to

Step-by-step solution

Given differential equation is dy dx = y + 5 Separating the variables gives dy y + 5 = dx Integrating both sides gives dy y + 5 = dx |y + 5| = x + C Using the initial condition y(0) = 4 gives (4 + 5) = 0 + C C = 9 Substituting C back into the equation gives (y + 5) = x + 9 y + 5 = e^ x + 9 = 9e^x y = 9e^x - 5 Substituting x = 2 gives y( 2) = 9e^ 2 - 5 y( 2) = 9(2) - 5 = 13 Answer: 13