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

(x^{2} + xy)dy = (x^{2} + y^{2})dx

Here, putting x = kx and y = ky

= k^{0}.f(x,y)

Therefore, the given differential equation is homogeneous.

(x^{2} + xy)dy = (x^{2} + y^{2})dx

To solve it we make the substitution.

y = vx

Differentiating eq. with respect to x, we get

Integrating on both side,

- v - 2log|1 - v| = log|x| + logc

The required solution of the differential equation.

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