Differential Equations Question 24
Question: A curve passing through (2, 3) and satisfying the differential equation $ \int_0^{x}{ty(t)dt=x^{2}y(x),(x>0)} $ is
Options:
A) $ x^{2}+y^{2}=13 $
B) $ y^{2}=\frac{9}{2}x $
C) $ \frac{x^{2}}{8}+\frac{y^{2}}{18}=1 $
D) $ xy=c $
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Answer:
Correct Answer: D
Solution:
[d] Differentiate $ xy(x)=x^{2}y’(x)+2xy(x) $ or $ xy(x)+x^{2}y’(x)=0 $ or $ x\frac{dy}{dx}+y=0 $ or $ lny+lnx=lnc $
or $ xy=c $
BETA
