Question

Solve for Y

-2ln |y| + ln |2y-9| + ln|2y+9| = 162X + C

Answer 1

C is just an integration constant.

Answer 2

Recall that the sum of logs is the log of a product:

\[-2(ln\ y) + ln(2y-9) + ln(2y+9)\]\[=ln(\frac{4y^2 - 81}{y^2})\]\[\implies ln(\frac{4y^2 - 81}{y^2}) = 162x + C\]\[\implies 4 - \frac{81}{y^2} = Ce^{162x}\]

Answer 3

And continue from there to solve for y.