Working Backwanls Write the standard form (equation (16) with leading coefficient an = 11) of the nth
Question:
1. y" + 4v = 0, y(0) = 1 , y'(0) = -1
2. y" - 4y' + 13y = 0, y(0) = 1 . y'(0) = 0
3. y" + 2y' + 2y = 0, y(0) = 1 , y'(0) = 0
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InitialValue Problems 1 y 4y 0 y 0 1 y0 1 The characteristic equation is r 2 4 0 which has roots 2i The general solution is y t c 1 cos2t c 2 sin 2t Substituting this into the initial conditions gives y 0 c 1 1 y0 2c 2 1 Hence the solution of the initialvalue problem is y t cos2t c 2 sin 2t 2 y 4y 13y 0 y 0 1 y0 0 The characteristic equation is r 2 4r 13 0 which has roots 2 ...View the full answer
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Related Book For
Differential Equations and Linear Algebra
ISBN: 978-0131860612
2nd edition
Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West
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