How to Solve Constant Coefficient Homogeneous Differential Equations
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One class of second order ODEs is particularly nice: constant coefficient homogeneous ones. That is, it is linear in the dependent variable and its coefficients, and the right hand side is just zero. For this class, we make a guess or ansatz that the solution is an exponential. Plug that it and you get something called the characteristic equation or the auxiliary equation. Solve that via the quadratic formula and the roots tell you the types of exponentials. It turns out that there are really three cases that can arise, and I'll break those three cases down in the next video. For now we do a full initial value problem (IVP) from start to finish to introduce the methodology
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