Differential Equations Question 78
Question: Equation of curve passing through (3, 9) which satisfies the differential equation $ \frac{dy}{dx}=x+\frac{1}{x^{2}} $ , is
[WB JEE 1986]
Options:
A) $ 6xy=3x^{2}-6x+29 $
B) $ 6xy=3x^{3}-29x+6 $
C) $ 6xy=3x^{3}+29x-6 $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{dy}{dx}=x+\frac{1}{x^{2}} $
Therefore $ \int _{{}}^{{}}{dy}=\int _{{}}^{{}}{( x+\frac{1}{x^{2}} )}dx $
Therefore $ y=\frac{x^{2}}{2}-\frac{1}{x}+c $
Since it passes through (3, 9), therefore $ 9=\frac{9}{2}-\frac{1}{3}+c $
Therefore $ c=\frac{29}{6} $
\ $ y=\frac{x^{2}}{2}-\frac{1}{x}+\frac{29}{6} $
Therefore $ 6xy=3x^{3}+29x-6 $ .
BETA
