Originally Posted by

**physics** From what I gather from reading, homogenous differential equations of 2nd order or higher will have constant coefficients. Where they are nonhomogenous is where they will have undetermined coefficients. I believe how you tell the if it is homogeneous or non-homogenous is in its linear independence. If the Wronskian returns roots it is linearly dependent. If the Wronskian returns anything other than a zero, it is linearly indepedent and nonhomogenous.

Like in an equation, y^(4) + 10x^2y * y^(3) + y = g(x)y, you would plug in the functions of x or constants (x^2, 2, 3, etc) into the Wronskian, and test for linear independence or dependence. That will tell you whether it is homogenous or heterogenous, and homogenous higher order differential equations always have constant coefficients. It gets easier as you go along . IF there are any corrections anyone wants to make or parts that need further thought, please contribute as this thread as I believe it is important information.