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प्रश्न
Solve the following differential equation.
dr + (2r)dθ= 8dθ
उत्तर
dr + (2r)dθ= 8dθ
`(dr)/(dθ)` + 2r = 8
The given equation is of the form
`(dr)/(dθ) + Pr = Q`
where, P = 2 and Q = 8
I.F. = `e ^(int^(P^dθ) = e^(int^(2^dθ) = e^(2θ)`
Solution of the given equation is
`r(I.F.) = int Q (I.F.) dθ + c`
`re^(2θ) = int 8 e^(2θ) dθ + c`
`re^(2θ) = 8 int e^(2θ) dθ + c`
`re ^(2θ) = 8e^(2θ)/2 + c`
`re ^(2θ) = 4e^(2θ) + c`
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