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)
Hey there!
A reciprocal might be an unfamiliar vocab word, but the concept is really quite simple.
It's just a flipped fraction! Multiplying the flipped fraction by it's reciprocal gets you one, and that's how you check your answer.
So we have:
Reciprocal of 9/10 is 10/9, because 9/10 times 10/9 = 90/90 = 1
Reciprocal of 1/11 is 11/1, because 1/11 times 11/1 = 11/11 = 1
Reciprocal of 10(remember, it's 10/1) is 1/10, because 10/1 times 1/10 = 10/10 = 1
Hope this helps!
Answer:
5/9
Step-by-step explanation:
To solve for S, you would want to get rid of the denominator so multiply 360 onto both sides. then the equation is 360A=pi times r squared times S. Divide both sides by pi and r squared and you get S=360A/pi times r squared
Answer: sum=1 subtrahend=2
Step-by-step explanation:
