The Cauchy homogeneous linear differential equation is given by(adsbygoogle = window.adsbygoogle || []).push({});

[itex]x^{n}\frac{d^{n}y}{dx^{n}} +k_{1} x^{n-1}\frac{d^{n-1}y}{dx^{n-1}} +...+k_{n}y=X [/itex]

where X is a function of x and [itex] k_{1},k_{2}...,k_{n}[/itex] are constants.

I thought for this equation to be homogeneous the right side should be 0. (i.e.) X=0.

But if X is a function of x then how can this be homogeneous?

Thanks a lot :)

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# Cauchy's homogeneous diff eqn

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