Differential Equations Question 13
Question: The differential equation which represents the three parameter family of circles $ x^{2}+y^{2}+2gx+2fy+c=0 $ is
Options:
A) $ y’’’=\frac{3y’y’{{’}^{2}}}{1+y{{’}^{2}}} $
B) $ y’’’=\frac{3y’{{’}^{2}}}{1+y{{’}^{2}}} $
C) $ y’’’=\frac{3y’}{1+y{{’}^{2}}} $
D) $ y’’’=\frac{3y’}{1-y{{’}^{2}}} $
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Answer:
Correct Answer: A
Solution:
[a] To eliminate the parameters g, f and c differentiate thrice w.r.t. x, $ x+yy’+g+fy’=0 $
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(1) $ 1+y{{’}^{2}}+yy’’+fy’’=0 $
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(2) $ 3y’y’’+yy’’’+fy’’’=0 $
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(3) (1) $ y’’’-(2)y’’ $ gives,
BETA
