Answer:
yp = -x/8
Step-by-step explanation:
Given the differential equation: y′′−8y′=7x+1,
The solution of the DE will be the sum of the complementary solution (yc) and the particular integral (yp)
First we will calculate the complimentary solution by solving the homogenous part of the DE first i.e by equating the DE to zero and solving to have;
y′′−8y′=0
The auxiliary equation will give us;
m²-8m = 0
m(m-8) = 0
m = 0 and m-8 = 0
m1 = 0 and m2 = 8
Since the value of the roots are real and different, the complementary solution (yc) will give us
yc = Ae^m1x + Be^m2x
yc = Ae^0+Be^8x
yc = A+Be^8x
To get yp we will differentiate yc twice and substitute the answers into the original DE
yp = Ax+B (using the method of undetermined coefficients
y'p = A
y"p = 0
Substituting the differentials into the general DE to get the constants we have;
0-8A = 7x+1
Comparing coefficients
-8A = 1
A = -1/8
B = 0
yp = -1/8x+0
yp = -x/8 (particular integral)
y = yc+yp
y = A+Be^8x-x/8
Answer:
55
Step-by-step explanation:
took the test
Answer:
0
Step-by-step explanation:
look it up on google :)
Answer:
The estimate is less than the actual length of the CD.
Step-by-step explanation:
Consider the provided information.
Maurice's new CD has 12 songs. Each song lasts between 3 and 4 minutes.
That means the minimum length of the CD should be: 12×3=36 minutes.
The maximum length of the CD should be: 12×4=48 minutes
He estimates that the whole CD is about 30 minutes long.
30 minutes is less than 36 minutes.
That means, the estimate is less than the actual length of the CD.
Hence, the correct statement is: The estimate is less than the actual length of the CD.
Answer:
y = 2/5
Step-by-step explanation:
