## Question

###### Explain why it is always possible to express any homogeneous differential equation $M(x, y) d x+N(x, y) d y=0$ in the form$$frac{d y}{d x}=Fleft(frac{y}{x}ight)$$You might start by proving that$$M(x, y)=x^{a} M(1, y / x) ext { and } N(x, y)=x^{alpha} N(1, y / x)$$

Explain why it is always possible to express any homogeneous differential equation $M(x, y) d x+N(x, y) d y=0$ in the form $$ frac{d y}{d x}=Fleft(frac{y}{x} ight) $$ You might start by proving that $$ M(x, y)=x^{a} M(1, y / x) ext { and } N(x, y)=x^{alpha} N(1, y / x) $$

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