Kernel of a Transformation that is a differential equation

[FHamster]

Homework Statement

Calculate the kernel of https://webwork3.math.ucsb.edu/webwork2_files/tmp/equations/f7/04b646ac1797cdf54f4a373ce5ef431.png
Since T is a linear transformation on a vector space of functions, your kernel will have a basis of functions.
Give a basis for the kernel, you may enter a 0 in any box you believe you don't need.

Homework Equations

The Attempt at a Solution

I have little idea how to approach this problem. I know how to find the kernel and rank of a matrix transformation, but not a differential equation.

 

[clamtrox]

Kernel of any linear operator is defined in exactly the same way:
$$\ker(T) = \lbrace y \in X | T(y) = 0 \rbrace$$
In this case, X is the space of all (smooth enough) functions, and you need to find those which satisfy T(y) = 0.