They are all correct good job
If you think about it, you have your answer in your question.
Convert 2/4 to 1/2 which in decimal form, is .5.
You’re final answer is -2.3,-2 2/4,-2.6.
I hope this helps!
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)
1. There is no "h" in f(x) = log(x). The question is nonsense.
2. The log function is defined for arguments greater than zero. You're probably expected to select D, though A and B could also be correct.
3. Same deal. The log function is defined for x > -2, but the domain could be restricted to x > 2. You're expected to select FALSE.
4. Same deal. Choose B, though D is also correct.
5. C is the proper choice. (See discussion of the log function, above.)
