A) \[(x+a)(x+ay)=cy\]
B) \[(x+a)(1-ay)=cy\]
C) \[(x+a)(1-ay)=c\]
D) None of these
Correct Answer: B
Solution :
\[y-x\frac{dy}{dx}=a\,\left( {{y}^{2}}+\frac{dy}{dx} \right)\] Þ \[y-a{{y}^{2}}=a\frac{dy}{dx}+x\frac{dy}{dx}\] Þ \[y(1-ay)=\left( a+x \right)\,.\frac{dy}{dx}\] Þ \[\frac{dx}{(a+x)}=\frac{dy}{y(1-ay)}\] Integrating both sides, \[\int{\frac{dx}{(a+x)}=}\int{\frac{dy}{y(1-ay)}}\] Þ \[\int{\frac{dx}{a+x}=\int{\left[ \frac{1}{y}+\frac{a}{(1-ay)} \right]\,dx}}\] \[\log (a+x)=\log y+\frac{a\log (1-ay)}{-a}\] Þ \[\log (a+x)=\log y-\log (1-ay)+\log c\] Þ \[\log (x+a)(1-ay)=\log cy\] Þ \[(x+a)(1-ay)=cy\].You need to login to perform this action.
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