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**Hi, eveyone have been struggling to do this problem for a long time now, figured it is something very simple I am missing so thought I should ask here.**

1. Homework Statement

1. Homework Statement

Parker's solar wind equation is given after some manipulation as:

(v - (C

_{s}

^{2}/ v) dv/dr = 2 (C

_{s}

^{2}/ r

^{2}) (r - r

_{c})

where r

_{c}= GMm/4kT (the critical radius)

and

C

_{s}

^{2}= 2kT/m (coronal sound speed)

## The Attempt at a Solution

So using the usual method I separate the variables and integrate this equation to get:

v

^{2}/ 2 - C

_{s}

^{2}log(v) = 2C

_{s}

^{2}log(r) + (4C

_{s}

^{2}r

_{c}/ r) + C

where C is the constant of integration. However every solution

However every solution I see around the internet and indeed in my notes quotes the solution:

(v

^{2}/ C

_{s}

^{2}) - log(v

^{2}/ C

_{s}

^{2}) = 4log(r/r

_{c}) + 4(r/r

_{c})

and I cannot seem to figure out why. Am I missing something blindingly obvious here?

Thanks for your time, John.