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Consider the homogeneous differential eq...

Consider the homogeneous differential equation `(dy)/(dx)=f((y)/(x))` By putting `(y)/(x)=v`, the equation reduces to `(dv)/(f(v)-v)=(dx)/(x)`. Integrating we get `int(dv)/(f(v)-v)=int(dx)/(x)+c`
Solution of `(x+ycos""(y)/(x))dx=xcos""(y)/(x)dy` is

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