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.
1 If f(x) is a particular solution of (1), assume for v the above form multiplied by x. 2  The complete solution of (1) is given by y = u + v. This video demonstrates how to solve a more general second order linear differential equations.