Question: Explain why it is always possible to express any homogeneous differential equation M(x, y) dx + N(x, y) dy = 0 in the form dy/dx

Explain why it is always possible to express any homogeneous differential equation M(x, y) dx + N(x, y) dy = 0 in the form

dy/dx = F(y/x).

You might start by proving that

M(x, y) = xαM(1, y/x) and N(x, y) = xαN(1, y/x).

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