Chem Differential Eq HW Solutions Fall 2011 181

Chem Differential - Section A.3 Linear Ordinary Dierential Equations with Nonconstant Coecients A181 Solutions to Exercises A.3 1 We apply the

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Section A.3 Linear Ordinary Differential Equations with Nonconstant Coefficients A181 Solutions to Exercises A.3 1. We apply the reduction of order formula and take all constants of integration equal to 0. y ±± +2 y ± - 3 y =0 ,y 1 = e x ; p ( x )=2 , ± p ( x ) dx =2 x, e - ± p ( x ) dx = e - 2 x ; y 2 = y 1 ± e - ± p ( x ) dx y 2 1 dx = e x ± e - 2 x e 2 x dx = e x ± e - 4 x dx = e x ² - 1 4 e - 4 x ³ = - 1 4 e - 3 x . Thus the general solution is y = c 1 e x + c 2 e - 3 x . 5. y ±± +4 y 1 = cos 2 x . y ±± y 1 = cos 2 x ; p ( x )=0 , ± p ( x ) dx ,e - ± p ( x ) dx =1; y 2 = y 1 ± e - ± p ( x ) dx y 2 1 dx = cos 2 x ± 1 cos 2 2 x dx = cos 2 x ± sec 2 2 xdx = cos 2 x ² 1 2 tan 2 x ³ = 1 2 sin 2 x. Thus the general solution is
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This note was uploaded on 12/22/2011 for the course MAP 3305 taught by Professor Stuartchalk during the Fall '11 term at UNF.

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