In each of the question, show that the given differential equation is homogeneous and solve each of them.

(x2 – y2)dx + 2xy dy = 0




Here, putting x = kx and y = ky




= k0.f(x,y)


Therefore, the given differential equation is homogeneous.





To solve it we make the substitution.


y = vx


Differentiating eq. with respect to x, we get










Integrating both sides, we get




Put 1 + v2 = t


2vdv = dt




log(t)


log(1 + v2) = -logx + logC ( From (i) eq.)





The required solution of the differential equation.


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