**9/
09/2014 **Express
*y*
as a function of *x*
alone. C is a positive number.

3
ln y = ½ ln (2x + 1) – ¼ ln (x + 4) + C **Scroll
down for the solution.**

**9/09/2014
**Solution.
Moving the ln terms to one side:

3
ln y – ½ ln (2x + 1) + ¼ ln (x + 4) =
C

Condensing:

ln y^{3}
– ln√(2x
+ 1) + ln ^{4}√(x
+ 4) = C

→
ln
[y^{3}·^{4}√(x
+ 4) /√(2x
+ 1)]
= C

Switching
to exponential form:

[y^{3}·^{4}√(x
+ 4) /√(2x
+ 1)]
= *e*^{C}

Cross-multiplying:

y^{3}
= *e*^{C}·√(2x
+ 1)/^{4}√(x
+ 4)

This
expression may be left alone as the answer *or
*one
may take the cube-root of it.