Elementary Differential equations : seperable

[Mdhiggenz]

Homework Statement

Tan∅ dr + 2r d∅=0

Homework Equations

The Attempt at a Solution

∫1/2r dr +∫1/tan∅ d∅=0

1/2ln(2r)+ln(tan∅)=c
ln[r(tan∅)]=ln(c)

r(tan∅)=c

the solution in the book says the answer is rsin^2∅=c

Where did I go wrong?

Thank you

 

[Saitama]

Here's your mistake:
∫1/tan∅ d∅≠ln(tan∅)

 

[Mdhiggenz]

Here's your mistake:
∫1/tan∅ d∅≠ln(tan∅)

Wow I see it would be ∫cos∅/sin∅ d∅ and with some u substitution it would give us ln(sin∅) correct?

 

[Saitama]

Wow I see it would be ∫cos∅/sin∅ d∅ and with some u substitution it would give us ln(sin∅) correct?

Yep, that's right but you have done one more mistake.
∫1/2r dr≠(1/2)ln(2r). It is equal to (1/2)ln(r).