Science:Math Exam Resources/Courses/MATH101 B/April 2024/Question 16 (b)/Statement

Consider the separable differential equation

$${\frac {\mathrm {d} y}{\mathrm {d} x}}-2xy+4y=8-4x,\quad -\infty <x<+\infty .$$

(b) A certain solution satisfies $y(0)=8.$ For this solution, what is the smallest value of $y(x)$ over all real $x$?