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.
where f(t), the inhomogeneous term, is the forcing function. The transient solution to this differential equation is given by the solution to the homogeneous equation : y'' +j*y' + k*y = 0. while the long-term solution is the particular solution (particular integral). For instance, the equation: