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# 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$$frac{d y}{d x}=Fleft(frac{y}{x}ight)$$Yo...

## 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 $$M(x, y)=x^{a} M(1, y / x) ext { and } N(x, y)=x^{alpha} N(1, y / x)$$ #### Similar Solved Questions

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