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.
So, in other words, initial conditions are values of the solution and/or its derivative(s) at specific points. As we will see eventually, solutions to ânice enoughâ differential equations are unique and hence only one solution will meet the given conditions.