Second Order Homogeneous DE
A linear second order homogeneous differential equation involves terms up to the second derivative of a function. For the case of constant multipliers, The equation is of the form
and can be solved by the substitution
The solution which fits a specific physical situation is obtained by substituting the solution into the equation and evaluating the various constants by forcing the solution to fit the physical boundary conditions of the problem at hand. Substituting gives
which leads to a variety of solutions, depending on the values of a and b.
