x*y' + y = 8x
y' + y/x = 8 .... divide everything by x
dy/dx + y/x = 8
dy/dx + (1/x)*y = 8
We have something in the form
y' + P(x)*y = Q(x)
which is a first order ODE
The integrating factor is 
Multiply both sides by the integrating factor (x) and we get the following:
dy/dx + (1/x)*y = 8
x*dy/dx + x*(1/x)*y = x*8
x*dy/dx + y = 8x
y + x*dy/dx = 8x
Note the left hand side is the result of using the product rule on xy. We technically didn't need the integrating factor since we already had the original equation in this format, but I wanted to use it anyway (since other ODE problems may not be as simple).
Since (xy)' turns into y + x*dy/dx, and vice versa, this means
y + x*dy/dx = 8x turns into (xy)' = 8x
Integrating both sides with respect to x leads to
xy = 4x^2 + C
y = (4x^2 + C)/x
y = (4x^2)/x + C/x
y = 4x + Cx^(-1)
where C is a constant. In this case, C = -5 leads to a solution
y = 4x - 5x^(-1)
you can check this answer by deriving both sides with respect to x
dy/dx = 4 + 5x^(-2)
Then plugging this along with y = 4x - 5x^(-1) into the ODE given, and you should find it satisfies that equation.
49 degree is the answer
tanø = 46/40
= 1.15
Ø = 49 degree
Answer:
Step-by-step explanation:
A) What is the speed of the pedestrian BC, CD, and DE?
Speed from B to C = distance/time = (40 - 20) / 4 = 20/4
= 5 km/h
Speed from C to D = distance/time = 0 / 2
= 0 km/h
Speed from D to E = distance/time = (20 - 0) / (10 - 6) = 20/4
= 5 km/h
B) After what time since the stop did he arrive at point E?
Since the stop at D, he arrived at E after (10 - 6) = 4 h
C) Write the formulas for function d(t) for sections BC, CD, and DE
For BC, d = 40 when t = 0 and d = 20 when t = 4
So d(t) = 40 - 5t
For CD, d = 20 when t = 4 and t = 6
So d(t) = 20
For DE, d = 20 when t = 6 and d = 0 when t = 10
So d(t) = 5 * (10 - t) or d(t) = 50 - 5t
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation: