Show that the differential equation `x(dy)/(dx)=y-x tan(y/x)` is homog – InterviewSolution

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1.	Show that the differential equation `x(dy)/(dx)=y-x tan(y/x)` is homogenous and solve it.
Answer» The given differential equation may be written as `(dy)/(dx)=y/x-tany/x`…………….(i) This is of the form, `(dy)/(dx)=f(y/x)`. So,the given differential equation is homogeneous. Putting, `y=vx` and `(dy)/(dx)=v+x(dv)/(dx)` in (i), we get `v+x(dv)/(dx)=v-tanv` `rArr x(dv)/(dx)=-tanv` `rArr (dv)/(tanv)=-(dx)/x` `rArr

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