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:
Ramiro is correct.
You cannot identify congruent triangles with only angles Angle-Angle-Angle is not one of the rules of congruence. They could have different sizes with the same angles which doesn't makes them congruent. They are similar though. Once you find the missing angles with the equations 62+39+C=180 and 39+79+X=180 the corresponding angles are congruent. So the triangles are not congruent, but are similar.
Answer:
1)https://answers4you-ph.com/math/question513389162
2)https://learning-ph.com/math/question512796522
Step-by-step explanation:
<span>-11 /7 * 7 /5</span>= -2(1/5)
