If y = f(x) is a monotonically increasing function such that ( dy dx )^2 = 6 - dy dx and y(0) = 5 , then y(3) =

Step-by-step solution

Let dy dx = p The given differential equation is p^2 + p - 6 = 0 (p+3)(p-2) = 0 p = -3 or p = 2 Since y = f(x) is a monotonically increasing function, dy dx > 0 Therefore, dy dx = 2 Integrating both sides, we get y = 2x + C Given y(0) = 5 , we have 5 = 2(0) + C C = 5 Thus, y = 2x + 5 Substituting x = 3 , we get y(3) = 2(3) + 5 = 11 Answer: 11