A) \[\left| f\left( y/x \right) \right|=c\left| x \right|,c\in R\]
B) \[\left| f\left( y/x \right) \right|=\left| x \right|+c,c>0\]
C) \[\left| f\left( y/x \right) \right|=c|x|,c>0\]
D) None of these
Correct Answer: C
Solution :
[c] \[\frac{dy}{dx}=\frac{y}{x}+\frac{f(y/x)}{f'(y/x)}\] ??.(i) Let \[\frac{y}{x}=V\] \[V+x\frac{dV}{dx}=V+\frac{f(V)}{f'(V)};\] \[\int{\frac{f'(V)}{f(V)}}dv=\int{\frac{dx}{x}}\] \[\Rightarrow In\left| f\left( y/x \right) \right|=In\left| x \right|+Inc\] \[\Rightarrow \left| f\left( y/x \right) \right|=c\left| x \right|,\text{ }where\text{ }c>0\]
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