Question: Working Backwanls Write the standard form (equation (16) with leading coefficient an = 11) of the nth order linear homogeneous differential equation with real coefficients

Working Backwanls Write the standard form (equation (16) with leading coefficient an = 11) of the nth order linear homogeneous differential equation with real coefficients whose roots are given in Problems 1-3?
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 full answer

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