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Warm–up Problems 1) Find the general solution of y – 5y + 6y = 8 + 2sin x. 2) How would your work change if the equation was y + y = 8 + 2sin x? Variation of Parameters –– Another Method for Finding yp 1) Find yc = c1y1 + c2y2 2) Find the Wronskian, W, of y1 and y2. 3) Put the DE in the form y + Py + Qy = f (x) 0 y2 y1 0 4) Find W1 and W2 f x y2 y1 f x W1 W2 dx 5) Find u1 dx and u2 W W 6) yp = u1y1 + u2y2 Ex. Solve y – 4y + 4y = (x + 1)e2x Ex. Solve 4y + 36y = csc 3x For higher order: y1 y2 y3 W y1 y2 y3 y1 y2 y3 y1 W2 y1 y1 W1 0 y2 y3 0 y2 y3 f x y2 y3 0 y3 y1 y2 0 0 y3 W3 y1 y2 0 f x y3 y1 y2 f x Ex. Solve y + 4y = sec 2x Practice Problems Section 4.6 Problem 2