Use the method of "undetermined coefficients" to find a particular solution of the differential equation. (The solution found may not include any term that solves the corresponding homogeneous problem.)

y''(x) − 10y'(x) + 61y(x) = −3796 cos(5x) + 185e6x

The particular solution of the differential equation

=  +  

Step-by-step explanation:

Given differential equation y''(x) − 10y'(x) + 61y(x) = −3796 cos(5x) + 185e6x

The differential operator form

Rules for finding particular integral in some special cases:-

      the particular integral ≠ 0

      the particular integral  f(-a^2) ≠ 0

Given problem

Particular integral:-

P.I   =

we will apply above two conditions, we get

=

 on simplification we get

=

=

=

=

 Now particular solution

P.I   =

P.I  =    +  

the answer is b. 60. each interior angle in 120, so the exterior angle must be 60 in order to add up to 180

step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."