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:
A. 
.
Step-by-step explanation:
We have been given an inequality 
. We are asked to solve the given inequality for x.
Using distributive property, we will get:
Subtract 2 from both sides:
Divide both sides by 7:
Therefore, option A is the correct choice.
8 (3)-10
24-10=14
Hope this helped :)
Answer:
x = - 14
Step-by-step explanation:
23 + 4 + x = 25 - 12
Combine like terms on both sides of the equation (by adding 23 and 4 on the left-hand side, and subtracting 12 from 25 on the right-hand side):
23 + 4 + x = 25 - 12
27 + x = 13
Next, subtract 27 from both sides to solve for x:
27 - 27 + x = 13 - 27
x = - 14
Please mark my answers as the Brainliest if you find this explanation helpful :)
Answer:
the answer is (-2,2)
Step-by-step explanation:
