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प्रश्न
For the differential equation find a particular solution satisfying the given condition:
`cos (dx/dy) = a(a in R); y = 1` when x = 0
उत्तर
`dy/dx = cos^-1 a => dy = (cos^-1"a")` dx
On integrating
`int dy = int (cos^-1 a) dx`
`y = x cos^-1 a + C`
In this equation y = 1 if x = 0 is put in,
1 = 0 + C ⇒ C = 1
Putting this value of C in equation (i)
`y = x cos^-1 a + 1`
`(y - 1)/x = cos^-1 a`
`=> cos (y - 1)/x = a`
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