Antiderivative of dy/dx = 5x^2 - 6/(y - 2)

[degreeplus]

I need help taking the antiderivative of \(\displaystyle \
\frac{{dy}}{{dx}} = 5x^2 - \frac{6}{{y - 2}}
\\)

I seperated the parts
\(\displaystyle \
dy + \frac{6}{{y - 2}} = 5x^2 dx
\\)

and from here I'm unsure ...
i get

\(\displaystyle \
y + 6\ln \left| {y - 2} \right| = \frac{5}{3}x^3 + C
\\)

is this correct?

 

[nezenic]

This looks like a first order linear differential equation.

The standard form is represented by...

y' +P(x)y = Q(x)

The solution is as follows...

Consider u(x) = e ^ integral (P(x) dx)

y*u(x) = integral [ Q(x) * u(x) dx + C]

I included the constant because the integral is indefinite. I didn't solve the problem yet so don't hold me to this if it doesn't yield the correct answer but this is the formula I'd use to investigate first if I tried to solve it.