A) \[y(1-xy)=cx\]
B) \[{{y}^{3}}-x=cy\]
C) \[x(1-xy)=cy\]
D) \[x(1+xy)=cy\]
Correct Answer: B
Solution :
[b] \[{{y}^{3}}-x=cy\] \[\Rightarrow 3{{y}^{2}}\frac{dy}{dx}-1=c\frac{dy}{dx}\Rightarrow \frac{dy}{dx}(3{{y}^{2}}-c)=1\] \[\Rightarrow \frac{dy}{dx}\left( 3{{y}^{2}}-\frac{{{y}^{3}}-x}{y} \right)=1\] \[\Rightarrow \frac{dy}{dx}\left( \frac{3{{y}^{3}}-{{y}^{3}}+x}{y} \right)=1\Rightarrow \frac{dy}{dx}=\frac{y}{x+2{{y}^{3}}}\]
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