After selecting a character, the player then selects a starting stage through an overworld map.
To say that you have found the general homogeneous solution means that this function solves the homogeneous equation for every choice of the constant $C_1$ and every solution of the homogeneous equation is of this form for some choice of $C_1$. You can actually have more than one particular solution to a DEQ.
Differential algebra. Differential calculus Differential of a function, represents a change in the linearization of a function Total differential is its generalization for functions of multiple variables. Differential (infinitesimal) (e.g. dx, dy, dt etc.) are interpreted as infinitesimals. Differential topology.