Equation of curve passing through (3, 9) which satisfies the differential equation dydx=x+1x2, is
A
6xy=3x2−6x+29
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B
6xy=3x3−29x+6
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C
6xy=3x3+29x−6
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D
Noneofthese
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Solution
The correct option is C6xy=3x3+29x−6 dydx=x+1x2⇒∫dy=∫(x+1x2)dx⇒y=x22−1x+c Since it passes through (3, 9), therefore 9=92−13+c⇒c=296∴y=x22−1x+296⇒6xy=3x3+29x−6.