# Show that the differential equation (xe^(y/x) + y)dx = x dy is homogeneous.

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Show that the differential equation (xey/x + y)dx = x dy is homogeneous. Find the particular solution of this differential equation, given that x = 1 when y = 1.

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The given differential equation is :

So this equation is homogeneous.

Now put y = vx in equation (i).

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