The equation of the curve passing through (3, 9) which satisfies
$\frac{d y}{d x} = \frac{x^{3} + 1}{x^{2}}$ is

6 x y = 3 x^{3} - 6 x + 29

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6 x y = 3 x^{2} - 29 x + 6

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6 x y = 3 x^{3} + 29 x - 6

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Solution

The correct option is C $6 x y = 3 x^{3} + 29 x - 6$
The given differential equation has variable separable so integrating, we have y = $\frac{x^{2}}{2} - \frac{1}{x} + C$ This will pass through $(3, 9) i f 9 = \frac{9}{2} - \frac{1}{3} + C \Rightarrow C = \frac{29}{6}$
Hence the required equation is $6 x y = 3 x^{3} + 29 x - 6$

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