Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution.
dy
dt
+ 25y = 45; y =
9
5
−
9
5
e−25t
When
y =
9
5
−
9
5
e−25t,
dy
dt
=
.
Thus, in terms of t,
dy
dt
+ 25y =
+ 25

9
5
−
9
5
e−25t


=
.