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प्रश्न
Solve the differential equation: y dx + (x – y2)dy = 0
उत्तर
y dx + (x – y2)dy = 0
Reducing the given differential equation to the form `(dx)/(dy)` + Px = Q we get, `(dx)/(dy) + x/y` = y
I.F = `e^(intPdy)`
= `e^(int 1/y dy)`
= elog y
= y
The general solution is given by
x · IF = `int "Q" * "IF" "dy"`
⇒ xy = `int "y"^2 "dy"`
⇒ xy = `"y"^3/3 + C`, which is the required general solution
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