find the two values of k for which y(x)=ekx is a solution of the differential equation

y″−9y′+18y=0.

The 2 values of k are 3 and 6.

Step-by-step explanation:

If the given function  of y is a solution of the differential equation then it shall be able to satisfy it

Thus we have

Putiing in the above differential euation we get

Solving the above uadratic euation with the standard formula we get

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable   r   represents the radius of the circle,   h   represents the x-offset from the origin, and   k   represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at   ( h , k ) .

center:   ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center:   ( 3 , 1 ).

radius:   4