Answer :


We need to solve the given differential equation












{ λ0= 1}


So, F(x, y) is a homogeneous function of degree zero


It is a homogeneous differential equation


Let y = vx


Differentiating with respect to x:














Integrating both sides:




Let 1 – 2v – v2 = t


(-2 – 2v) dv = dt




Now again put the value of t = 1 – 2v – v2:










{ log(ab) = log a + log b}




Hence, solution of the differential equation is


x2 – 2xy – y2 = c


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