2. Consider a homogeneous differential equation, p(т, у) dx + q(z, у) dy %3D 0, where the coefficients p(x, y) and q(x, y) satisfy the homogeneity con- dition: p(Аг, Ау) — А"р(a, у); q(λ, λ) - λq(α, 9). Explain why it is always possible to express any such homogeneous differential equation in the form dy = F dx () HINT: You could start by first proving that p(x, y) = x°p(1,y/x), and q(x, y) = x°q(1,y/x).

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