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GILBERT STRANG: OK, its time to move on to second order equations. First order equations, weve done pretty carefully. Second order equations are a step harder. But they come up in nature, they come in every application, because they include an acceleration, a second derivative. OK, so this would be a second order equation, because of that second derivative. Im often going to have constant a, b, and c. We have enough difficulties to it without allowing those to change. So a, b, c constants, and doing the null solution to start with. Later, therell be a forcing term on the right-hand side. But today, for this video, null solutions. And the point is, now, whats new is that there are two null solutions. So y null will be a combination of e-- and theyre both exponentials. Having constant coefficients there means exponentials in the solution. So e to the sum exponent, and another one to a, hopefully, different exponent. Sometimes if s1 equals s2, thatll be a special case and well ha
