Applied Mathematics 2270A/B Lecture Notes - Lecture 11: Horse Length, Product Rule
20 Oct 2018
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2nd order linear, homogeneous ode with constant coefficients. Now, nth order linear, homogeneous ode with constant coefficients an yn(x) + an-1 yn-1(x) + a1 y1(x) +a0 y(x) = 0. "recall: to solve a nth order linear, homogeneous ode, we knew (from 3. 2) that the general solution is a linearly independent set of functions y1(x), y2(x), y3(x) yn(x) n linearly independent solutions. That means the order is equal to the solution" "we guessed last section that a linearly independent solution to the homogeneous equation might be of the form y = erx " y"(x) = ex y""(x) = 2e2x y3 (x) = 3e3x yn(x) = nenx. "so to find the general solution, we have to find n roots because there will be n linearly independent solutions. And that was easy last section with our second order because finding the root was easy because quadratic formula"
