How to determine if a higher order ODE is homogeneous

kimkibun · May 2, 2012

how am i going to determine if a higher order differential equation is homogenous? example,

d⁴y/dx⁴+d²y/dx²=y

d³y/dx³-d²y/dx²=0

bigfooted · May 2, 2012

Homogeneous means all terms depend on y, no matter the order of the ODE. In your examples, both equations would be homogeneous. If you would add a term like 1 or f(x) it would become nonhomogeneous, i.e. y"=y is homogeneous, but y"=y+f(x) is nonhomogeneous.

How to determine if a higher order ODE is homogeneous

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How to determine if a higher order ODE is homogeneous

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