My test says to make the "appropriate substitution," but one of the differential equations can be solved as a homogenous substitution and a bernoulli's substitution. Both yield different results. Is it ok to use either? This is the equation:
$$t^2\frac{dy}{dt} + y^2 = ty$$
Sure! Unless an exam/instructor asks/forces you to use a specific one.
Perhaps it would be more accurate to speak of making "an appropriate substitution" rather than "the appropriate substitution", since it may not be unique.
In any case: you can always try any substitution, but it will only turn out to be useful if it simplifies the equation or at least enables you to further solve the equation.