Question
Show that the given differential equation is homogeneous and solve it:
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Solution
The given differential equation is
or
...(1)
It is a differential equation of the form
Here,
Replacing x by
and y by 
, we get.
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or
...(1)It is a differential equation of the form
Here,
Replacing x by
and y by , we get.
∴ F(x, y) is a homogeneous function of degree zero.
∴ given differential equation is a homogeneous differential equation.
Put y = vx 
Substituting these values of y and 
in the given equation, we get
or 
Integrating, 
