MATH215 : Notes Done in LaTeX
22 Dec 2011
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***how to solve first-order linear di erential equations . How to solve homogenous second-order linear di erential equation . ***how to solve particular solutions to nonhomogeneous di erential equations . First-order di erential equation (de): a rst-order di erential equation is y(cid:48) = f (x, y) or dy dx. = f (x, y) y = y (x) is a solution to the above di erential equation on an interval (i) if holds for all x i. dy (x) dx. Separable di erential equation: a rst-order di erential equation such that we can separate x and y: dy dx dy g(y) A general solution to a de is a solution that contains all possible solutions. Seperate all y (independent) and x (dependent) variables onto the left and right hand side: Make sure the derivates (dy and dx) are in the numerator of any faction and intergrate f (y) dy = g(x) dx g(x) dx f (y) dy =
