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Question
Integrating factor of the differential equation `(1 - x^2) ("d"y)/("d"x) - xy` = 1 is ______.
Options
– x
`x/(1 + x^2)`
`sqrt(1 - x^2)`
`1/2 log (1 - x^2)`
Solution
Integrating factor of the differential equation `(1 - x^2) ("d"y)/("d"x) - xy` = 1 is `sqrt(1 - x^2)`.
Explanation:
The given differential equation is `(1 - x^2) ("d"y)/("d"x) - xy` = 1
⇒ `("d"y)/("d"x) - x/(1 - x^2) * y = 1/(1 - x^2)`
Here, P = `x/(1 - x^2)` and Q = `1/(1 - x^2)`
∴ Integrating factor I.F. = `"e"^(int Pdx)`
= `"e"^(int (-x)/(1 - x^2) dx)`
= `"e"^(1/2 log(1 - x^2))`
= `sqrt(1 - x^2)`
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