We already know how to solve an initial value problem for a second-order homogeneous differential equation. Boundary value problems are very similar, but differ in a few important ways: 1) Initial value problems will always have a solution; boundary value problems may not, 2) The initial conditions given in an initial value problem relate to the general solution and its derivative; the initial conditions in a boundary value problem both relate to the general solution, not its derivative, and 3) The initial conditions given in an initial value problem are both for values of x0=0; the initial conditions given in a boundary value problem are for x0=a and x0=b.

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