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Question
Solve the differential equation:
dr = a r dθ − θ dr
Solution
dr = a r dθ − θ dr
∴ (1 + θ) dr = a r dθ
∴ `(dr)/r = a (dθ)/((1 + θ))`
Integrating on both sides, we get
`int (dr)/r = a int (dθ)/(1+θ)`
log | r | = a log | 1 + θ| + log | c |
∴ log | r | = log | c(1 + θ)a|
∴ r = c (1 + θ)a
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