Chem Differential Eq HW Solutions Fall 2011 175

Chem Differential Eq HW Solutions Fall 2011 175 - Section...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Section A.2 Linear Ordinary Differential Equations with Constant Coefficients A175 25. Equation: y ±± - 4 y ± +3 y = e 2 x ; Homogeneous equation: y ±± - 4 y ± y =0 ; Characteristic equation: λ 2 - 4 λ +3 = 0 ( λ - 1)( λ - 3) = 0; Characteristic roots: λ 1 =1 2 =3 ; Solution of homogeneous equation: y h = c 1 e x + c 2 e 3 x . To Fnd a particular solution, we apply the method of undetermined coefficients. Accordingly, we try y p = Ae 2 x ; y ± p =2 Ae 2 x ; y ±± p =4 Ae 2 x . Plug into the equation y ±± - 4 y ± y = e 2 x : 4 Ae 2 x - 4(2 Ae 2 x )+3 Ae 2 x = e 2 x - Ae 2 x = e 2 x ; A = - 1 . Hence y p = - e 2 x and so the general solution y g = c 1 e x + c 2 e 3 x - e 2 x . 29. Equation: y ±± - 4 y ± y = xe - x ; Homogeneous equation: y ±± - 4 y ± y ; Characteristic equation: λ 2 - 4 λ ( λ - 1)(
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/22/2011 for the course MAP 3305 taught by Professor Stuartchalk during the Fall '11 term at UNF.

Ask a homework question - tutors are online