Mathematics

This is about integration as the inverse of differentiation. Since you're given the derivative $\frac{dy}{dx}$, you need to reverse the process by integrating both sides to recover $y(x)$ itself. The initial condition $y(1)=5$ then pins down the constant of integration, giving you one specific solution rather than a family of curves.

This is about integration as the inverse of differentiation. Since you're given the derivative $\frac{dy}{dx}$, you need to reverse the process by integrating both sides to recover $y(x)$ itself. The initial condition $y(1)=5$ then pins down the constant of integration, giving you one specific solution rather than a family of curves.