The solution of the differential equation `x(dy)/(dx)=y+xtany/x ,` is `x y y_2+y1 2+y y_1=0` b. `x y y_2+x y1 2-y y_1=0` c. `x y y_2-x y1 2+y y_1=0` d. none of these

Explanation

Given : `x frac{d y}{d x}=y+x tan frac{y}{x} `


`Rightarrow frac{d y}{d x}=frac{y}{x}+tan frac{y}{x} ldots ldots(1) `


`text { Let } y=v x `


`Rightarrow frac{d y}{d x}=v+x frac{d v}{d x}`



Putt above value in equation (1), we obtain




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