For each of the differential equations in question, find the particular solution satisfying the given condition:

x2dy + (xy + y2)dx = 0; y = 1 when x = 1


x2dy + (xy + y2)dx = 0



Here, putting x = kx and y = ky




= k0.f(x,y)


Therefore, the given differential equation is homogeneous.


x2dy + (xy + y2)dx = 0



To solve it we make the substitution.


y = vx


Differentiating eq. with respect to x, we get









Integrating both sides, we get













y = 1 when x = 1




3x2y = y + 2x


y + 2x = 3x2y


The required solution of the differential equation.


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