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प्रश्न
The general solution of the differential equation `(y dx - x dy)/y = 0` is ______.
पर्याय
xy = C
x = Cy2
y = Cx
y = Cx2
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उत्तर
The general solution of the differential equation `(y dx - x dy)/y = 0` is y = Cx.
Explanation:
Given the differential equation
`(y dx - x dy)/y = 0`
or `dx - y/x dy = 0`
and `dx/x - dy/y = 0`
On integrating,
⇒ log |x| - log |y| = log |C'|
⇒ `log |x/y| = log |C'|`
⇒ `x/y = C'`
⇒ `y = 1/C' x`
⇒ y = Cx
Where `1/C = C`
Which is the required solution.
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