Answer:
The question discusses finding solutions to a homogeneous differential equation involving an independent variable 'x' and verification of these solutions.
Step-by-step explanation:
The question refers to a homogeneous differential equation dy/dx = xy - 18y². Solving this type of equation often involves separating variables or using an integrating factor. The solutions or functions sought in such a problem are usually expressed in terms of the independent variable, which is 'x' in this case. Identifying the general form of these solutions can involve verifying that a proposed function, when substituted into the differential equation, satisfies the equation.