Answer:
{ x | x < 5}
Step-by-step explanation:
2(4 x + 3) < 5 x + 21
8x + 6 < 5x + 21
3x < 15
x < 5
Answer
{ x | x < 5}
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

Answer:
Yes. That is correct
Step-by-step explanation:
Answer:
12,321
Step-by-step explanation:
111 to the second power (basically 111 x 111) is 12,321. Multiply 111 by 111 since the exponent is 2. I hope this helps!