Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2025 / Paper 1 / 7 / b

The general solution of the first-order linear differential equation is $y=1+C{e}^x$. The initial condition $y(0)=1$ gives $C=0$, so the solution of this initial value problem is the constant function $y(x)=1$. Thus $\boxed{y(1)=1}$.