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Nano-Passion
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Homework Statement
Find 1-parameter family of solutions for the folloing differential equation:
dr/dβ cot (β) - r = 2
The Attempt at a Solution
dr/dβ cot β - r = 2
dr/β cot β = 2 + r
dr = (2+r) dβ/cot β
integral dr/2+r = integral tan β dβ
ln (2+r) = - ln (cos β) + c
I take everything to the e power
2+r = - cos β + e^c
r = c cos - 2
While the book has r = c sec - 2. I suspect this might be because of taking e^- ln, if it is, please explain why that happens.