Answer:
y = x*sqrt(Cx - 1)
Step-by-step explanation:
Given:
dy / dx = (x^2 + 5y^2) / 2xy
Find:
Solve the given ODE by using appropriate substitution.
Solution:
- Rewrite the given ODE:
dy/dx = 0.5(x/y) + 2.5(y/x)
- use substitution y = x*v(x)
dy/dx = v + x*dv/dx
- Combine the two equations:
v + x*dv/dx = 0.5*(1/v) + 2.5*v
x*dv/dx = 0.5*(1/v) + 1.5*v
x*dv/dx = (v^2 + 1) / 2v
-Separate variables:
(2v.dv / (v^2 + 1) = dx / x
- Integrate both sides:
Ln (v^2 + 1) = Ln(x) + C
v^2 + 1 = Cx
v = sqrt(Cx - 1)
- Back substitution:
(y/x) = sqrt(Cx - 1)
y = x*sqrt(Cx - 1)
Answer:
k12
Step-by-step explanation:
Answer:
The answer is "The cops were correct because the average speed would have been about 39.73 miles per hour as per the calculations."
Step-by-step explanation:
Finding the average skid distance:
Calculating the skid:
Answer:Bill
Step-by-step explanation:
Because Bill scored to the nearest 100
The parent function is y = x^2
There is a compression of 3:
y = 3x^2
There is a shift by 1 unit to the left:
y = 3(x + 1)^2
