Answer:
[tex]y=Ce^{2x}+\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]y'+2y=3\\\\\frac{dy}{dx}+2y=3\\ \\\frac{dy}{dx}=3-2y\\ \\dy=(3-2y)dx\\\\\frac{1}{3-2y}dy=dx\\ \\\int\limits {\frac{1}{3-2y}dy=\int dx}\\\\\frac{1}{2}ln(|3-2y|)=x+C\\\\ln(|3-2y|)=2x+C\\\\3-2y=e^{2x+C}\\\\3-2y=Ce^{2x}\\\\-2y=Ce^{2x}-3\\\\y=-\frac{Ce^{2x}}{2}+\frac{3}{2}\\ \\y=Ce^{2x}+\frac{3}{2}[/tex]
