Answer:
y = (11x + 13)e^(-4x-4)
Step-by-step explanation:
Given y'' + 8y' + 16 = 0
The auxiliary equation to the differential equation is:
m² + 8m + 16 = 0
Factorizing this, we have
(m + 4)² = 0
m = -4 twice
The complimentary solution is
y_c = (C1 + C2x)e^(-4x)
Using the initial conditions
y(-1) = 2
2 = (C1 -C2) e^4
C1 - C2 = 2e^(-4).................................(1)
y'(-1) = 3
y'_c = -4(C1 + C2x)e^(-4x) + C2e^(-4x)
3 = -4(C1 - C2)e^4 + C2e^4
-4C1 + 5C2 = 3e^(-4)..............................(2)
Solving (1) and (2) simultaneously, we have
From (1)
C1 = 2e^(-4) + C2
Using this in (2)
-4[2e^(-4) + C2] + 5C2 = 3e^(-4)
C2 = 11e^(-4)
C1 = 2e^(-4) + 11e^(-4)
= 13e^(-4)
The general solution is now
y = [13e^(-4) + 11xe^(-4)]e^(-4x)
= (11x + 13)e^(-4x-4)
Answer:
7 = -x^2 +16
x^2 -16 = 7
x^2 -23 = 0
Using quadratic equation
x = -0 +- sqrt (23^2 - 4*1*23) / 2 * 1
x = sqrt (0 - -92) / 2
x = sqrt (92) / 2
x1 = 4.7958
x2 = -4.7958
(I tried to answer your question - even though you posted no question - AND you posted no graphics)
Step-by-step explanation:
Answer:
or 
Step-by-step explanation:
To find slope we use the slope formula
Two points on the line we can classify are (3,4) and (4,8)
