Equation of the curve passing through (3, 9) which satisfies the differential equation $\frac{dy}{dx} = x + \frac{1}{x^2}$ is :

6xy = 3x2 – 6x + 29 6xy = 3x2 – 29x + 6 6xy = 3x3 – 29x – 6 None of these

6xy = 3x3 – 29x – 6

$\frac{d y}{d x}=x+\frac{1}{x^2} \Rightarrow y=\frac{x^2}{2}-\frac{1}{x}+c$ It passes through (3, 9) ∴ $9=\frac{9}{2}-\frac{1}{3}+c \Rightarrow c=\frac{29}{6}$ ∴ $y=\frac{x^2}{2}-\frac{1}{x}+\frac{29}{6}$ Hence (3) is the correct answer.