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)
9514 1404 393
Answer:
the correct choices are shown
Step-by-step explanation:
<u>Statement</u> . . . . . <u>Reason</u>
1. c ║ d; ∠4 = ∠5 . . . . . Given
2. ∠4 = ∠7 . . . . . Alternate interior angles are equal
3. ∠5 = ∠8 . . . . . Vertical angles are equal
4. ∠7 = ∠8 . . . . . Substitution
Answer:
16
Step-by-step explanation:
first you get rid of the exponents and get
9+25-2×9
then you multiply and get
9+25-18
then you add And get
34-18
lastly you subtract to get your answer which is
16
Answer:
The least common denominator is 6.
Step-by-step explanation:
Answer:
21.4
Step-by-step explanation:
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