# Revision history [back]

In this case, the function in the question has two parameters, so it describes a vector space of dimension 2 inside the space of functions from ℝ to ℝ.

So we might look for a linear differential equation of order two.

Then for each of the functions $x \mapsto e^{-x}$ and $x \mapsto x e^{-x}$, we can look for linear relations between the function, its derivative, and its second derivative.

Then we can find a common linear dependence relation that works for both.

That will be the desired differential equation.

In this case, the function in the question has two parameters, so it describes a vector space of dimension 2 inside the space of functions from ℝ to ℝ.

So we might look for a linear differential equation of order two.

Then for each of the functions $x \mapsto e^{-x}$ and $x \mapsto x e^{-x}$, we can look for linear relations between the function, its derivative, and its second derivative.