Q. 164.5( 2 Votes )

# Solve the differe

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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