Discussion
Linear differential equation of any order if there is no constant term is present is known as
Answer: A
A linear differential equation is homogeneous when every term carries the unknown function or one of its derivatives, so the right-hand side is zero:
\[ a_n y^{(n)} + \cdots + a_1 y' + a_0 y \;=\; 0 \]
Add a term that does not involve \( y \) and it becomes non homogeneous:
\[ a_n y^{(n)} + \cdots + a_0 y \;=\; f(x) \]
The distinction matters because a homogeneous equation's solutions form a vector space: any combination of solutions is itself a solution, which is false once \( f(x) \) is present.
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