A) \[{{x}^{2}}y+\frac{{{x}^{3}}{{y}^{3}}}{3}=c\]
B) \[x{{y}^{2}}+\frac{{{x}^{3}}{{y}^{3}}}{3}=c\]
C) \[{{x}^{2}}y+\frac{{{x}^{4}}{{y}^{4}}}{4}=c\]
D) none of these
Correct Answer: A
Solution :
[a] \[(2x+x{{y}^{3}})dx+(x+{{x}^{2}}{{y}^{2}})dy=0\] Or \[(2ydx+xdy)+(x{{y}^{3}}dx+{{x}^{2}}{{y}^{2}}dy)=0\] Multiplying by x, we get \[(2xydx+{{x}^{2}}dy)+({{x}^{2}}{{y}^{3}}dx+{{x}^{3}}{{y}^{2}}dy)=0\] Or \[d({{x}^{2}}y)+\frac{1}{3}d({{x}^{3}}{{y}^{3}})=0\] Integrating, we get \[{{x}^{2}}y+\frac{{{x}^{3}}{{y}^{3}}}{3}=c\]
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