Differential-Equations Question 382
Question: The solution of $ \frac{dy}{dx}={{( \frac{y}{x} )}^{1/3}} $ is
[EAMCET 2002]
Options:
A) $ {x^{2/3}}+{y^{2/3}}=c $
B) $ {x^{1/3}}+{y^{1/3}}=c $
C) $ {y^{2/3}}-{x^{2/3}}=c $
D) $ {y^{1/3}}-{x^{1/3}}=c $
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Answer:
Correct Answer: C
Solution:
$ \frac{dy}{dx}={{( \frac{y}{x} )}^{1/3}} $
Þ $ \frac{dy}{dx}=\frac{{y^{1/3}}}{{x^{1/3}}} $
Þ $ \frac{dy}{{y^{1/3}}}=\frac{dx}{{x^{1/3}}} $ Integrating both sides, $ \frac{{y^{2/3}}}{2/3}=\frac{{x^{2/3}}}{2/3}+c $ $ \frac{3}{2}\cdot {y^{2/3}}=\frac{3}{2}{x^{2/3}}+c $
Þ $ {y^{2/3}}-{x^{2/3}}=c $ .
BETA
