Final answer:
The statement's validity depends on whether the differential equation is linear and homogeneous. For such equations, one solution can indeed be a linear combination of others, but this is not universally applicable.
Step-by-step explanation:
The statement that if three functions are solutions to the same differential equation, then one of them must be a linear combination of the other two can be true or false depending on the nature of the differential equation. For linear homogeneous differential equations, this statement is true due to the principle of superposition, which states that any linear combination of solutions is also a solution to the differential equation. However, for non-linear or non-homogeneous differential equations, this may not hold true, as solutions do not necessarily form a vector space where linear combinations are valid.