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

128,147 that is in standard form
-3 and 5..................
Answer: 3 and 5 are called prime factor of 15
Step-by-step explanation:
Answer:
1150$
Step-by-step explanation:
2800$-500$=2300$÷2=1150$
hope this helped ; )