Show that y1(t) + y2(t) solves the non-homogeneous equation

[DWill]

Homework Statement

Let y = y₁(t) be a solution of
y' + p(t)y = 0, (i)

and let y = y₂(t) be a solution of
y' + p(t)y = g(t). (ii)

Show that y = y₁(t) + y₂(t) is also a solution of Eq. (ii)

Homework Equations

The Attempt at a Solution

I'm not really sure how to start this one. Do I try to solve both (i) and (ii) first?

 

[Dick]

No. Just substitute y=y1(t)+y2(t) into the second equation and use the first one to simplify it.