Question 2.3.2: Solve the differential equation y'+2y = 4.

In this equation, p(t ) = 2, and therefore P(t ) = 2t . From (2.3.13), it follows that

y(t ) = e^{−P(t)} \int{e^{P(t)} f(t) dt}

=e^{−2t} \int{e^{2t}.4 dt}

= e^{−2t} (2e^{2t} +C)      (2.3.14)
= 2+Ce^{−2t}              (2.3.15)