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प्रश्न
The general solution of ex cosy dx – ex siny dy = 0 is ______.
विकल्प
ex cosy = k
ex siny = k
ex = k cosy
ex = k siny
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उत्तर
The general solution of ex cosy dx – ex siny dy = 0 is ex cosy = k.
Explanation:
The given differential equation is ex cosy dx – ex siny dy = 0
⇒ ex (cosy dx – siny dy) = 0
⇒ cosy dx – siny dy = 0 ......[∵ ex ≠ 0]
⇒ siny dy = cosy dx
⇒ `siny/cosy "d"y` = dx
Integrating both sides, we have
`int siny/cosy "d"y = int "d"x`
⇒ `-log|cosy| = x + log "k"`
⇒ `log 1/cosy - log "k"` = x
⇒ `log(1/("k" cosy))` = x
⇒ `1/("k" cosy)` = ex
⇒ `1/"k"` = ex cosy
⇒ ex cosy = c .....`["c" = 1/"k"]`
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