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:
(
0
,
2
)
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y and solve for x . To find the y-intercept, substitute in 0 for x and solve for y .
x-intercept(s): None
y-intercept(s): ( 0 , 2 )
Answer:
2 x 2 = 4
Step-by-step explanation:
Two cookies plus another two cookies is 4. You can also use a multiplication table. :)
Answer:
$225.50 (nearest cent)
Step-by-step explanation:
1 foot ≈ 0.3048 m
Width of room = 15 ft ≈ 15 x 0.3048 = 4.572 m
Length of room = 18 ft ≈ 18 x 0.3048 = 5.4864 m
Area of room = width x length = 4.572 x 5.4864 = 25.0938208... m²
Cost of carpet = $8.99 per m²
Total cost of carpet = 25.0938208 x 8.99 = $225.50 (nearest cent)