To determine which function is a solution to the differential equation xy 2y 0, we first need to clarify the equation itself. It seems to indicate a relationship where xy multiplied by some function of y leads to a result of zero. This typically points to a scenario where either x or y (or both) must equal zero, or where the function does not change (is constant). Therefore, we consider the properties of functions that can satisfy this condition.
One common approach to solving such differential equations is to separate the variables or look for constants. We may also try substitution methods or exact equations, depending on the context. However, since the equation is somewhat vague, we can suggest testing functions like y = 0 or factors of the form y = k/x, where k is a constant, as potential candidates.
In conclusion, testing these candidates against the original equation should provide insights as to which function, if any, is a valid solution. Alternatively, graphical methods can showcase how different functions interact with the constraint given by the equation. Always remember to verify the results by plugging them back into the original equation.