Equation of the curve passing through (3, 9) which satisfies the differential equation $\frac{dy}{dx} = x + \frac{1}{x^2}$ is :
Answer & explanation
Correct answer: option 3
$\frac{d y}{d x}=x+\frac{1}{x^2} \Rightarrow y=\frac{x^2}{2}-\frac{1}{x}+c$
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.