Question

Problem 3: Solve the differential equation

`y' + 2y = 3`
​

Answer 1

`y=Ce^(2x)+(3)/(2)`

Explanation:

`y'+2y=3\\\\(dy)/(dx)+2y=3\\ \\(dy)/(dx)=3-2y\\ \\dy=(3-2y)dx\\\\(1)/(3-2y)dy=dx\\ \\\int\limits {(1)/(3-2y)dy=\int dx}\\\\(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=-(Ce^(2x))/(2)+(3)/(2)\\ \\y=Ce^(2x)+(3)/(2)`