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:
|-2| + 2
Step-by-step explanation:
-4 / 2-5<em>i</em>
cos (<em>x</em>) / 1 - sin squared (<em>x</em>)
<u>|-2| + 2</u>
13/52= 1/4 or .25
If you have a scientific calculator it really helps with simplifying numbers to the lowest term.
Converse in discrete mathematics is switching the hypothesis and conclusion of a conditional statement.
So the correct answer will be that If a number is not divisible by two, then it is an odd number. Which is option D.
The math converse of a statement switches the if and then, resulting in a statement that may or may not be true so we have no guarantee that the preposition is true or not.
First you find how much weight it lost
500 - 350 = 150
Then, to find the mean change you divide the weight lost by the number of months
150 : 6 = 25
25 is the monthly change
