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Solve : "Dy"/"Dx" = 1 - "Xy" + "Y" - "X" - Mathematics

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प्रश्न

Solve : `"dy"/"dx" = 1 - "xy" + "y" - "x"`

योग

उत्तर

`"dy"/"dx" = 1 - "xy" + "y" - "x"`

`"dy"/"dx" = (1 + "y") - "x" (1 + "y")`

`"dy"/"dx" = (1 + "y") (1 - "x")`

`"dy"/(1 + "y") = (1 - "x")"dx"`

Integrating bothe sides, we obtain

`int"dy"/(1 + "y") = int (1 - "x")"dx"`

log |1 + y| `= "x" - "x"^2/2 + "C"`

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2016-2017 (March) Set 1

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