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Show that the differential equation xdy/dx sin(y/x) + x - y sin(y/x) = 0, is homogeneous. Find particular solution of this differential equation, given that x = 1 when y = pi/2

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The given differential equation is :

So, it is homogeneous.

Now, put y = vx in equation (i).

On differentiating both sides w.r.t. x, we get

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