A) \[6xy=3{{x}^{2}}-6x+29\]
B) \[6xy=3{{x}^{3}}-29x+6\]
C) \[6xy=3{{x}^{3}}+29x-6\]
D) None of these
Correct Answer: C
Solution :
\[\frac{dy}{dx}=x+\frac{1}{{{x}^{2}}}\] Þ \[\int_{{}}^{{}}{dy}=\int_{{}}^{{}}{\left( x+\frac{1}{{{x}^{2}}} \right)}\text{ }dx\] Þ \[y=\frac{{{x}^{2}}}{2}-\frac{1}{x}+c\] Since it passes through (3, 9), therefore \[9=\frac{9}{2}-\frac{1}{3}+c\] Þ \[c=\frac{29}{6}\] \\[y=\frac{{{x}^{2}}}{2}-\frac{1}{x}+\frac{29}{6}\] Þ \[6xy=3{{x}^{3}}+29x-6\].
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