Differential Equations Question 107
Question: The equation of a curve passing through $ ( 2,\frac{7}{2} ) $ and having gradient $ 1-\frac{1}{x^{2}} $ at $ (x,y) $ is
Options:
A) $ y=x^{2}+x+1 $
B) $ xy=x^{2}+x+1 $
C) $ xy=x+1 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ \frac{dy}{dx}=1-\frac{1}{x^{2}} $
Therefore $ y=x+\frac{1}{x}+c $
This passes through $ ( 2,\frac{7}{2} ) $ , \ $ \frac{7}{2}=2+\frac{1}{2}+c $
Therefore $ c=1 $
Thus the equation of the curve is $ y=x+\frac{1}{x}+1 $ or $ xy=x^{2}+x+1 $ .
BETA
