First look for the fundamental solutions by solving the homogeneous version of the ODE:

The characteristic equation is

with roots
and
, giving the two solutions
and
.
For the non-homogeneous version, you can exploit the superposition principle and consider one term from the right side at a time.

Assume the ansatz solution,



(You could include a constant term <em>f</em> here, but it would get absorbed by the first solution
anyway.)
Substitute these into the ODE:




is already accounted for, so assume an ansatz of the form



Substitute into the ODE:





Assume an ansatz solution



Substitute into the ODE:



So, the general solution of the original ODE is

37.6 - 25.49 =
12.11
now i round
12.10
The temperature got colder by 11 regress
Answer:
Commission: $3625.70
Total (sales + commission): $59405.70
Step-by-step explanation:
6.5% of 55780 = 0.065 × 55780 = 3625.7
55780 increase 6.5% =
55780 × (1 + 6.5%) = 55780 × (1 + 0.065) = 59405.7