1. The problem is to find the value of $A$ given the initial condition $y(1) = 2$. 2. We need the equation or function involving $A$ and $y(x)$ to proceed. Since it is not provided, let's assume a common form such as $y = A x^n$ or $y = A e^{kx}$. 3. For example, if $y = A x^n$, then using the initial condition $y(1) = 2$ gives: $$2 = A \cdot 1^n = A$$ 4. Therefore, $A = 2$. 5. If the function is different, please provide it for an exact solution.