Chem Differential Eq HW Solutions Fall 2011 177

Chem Differential Eq HW Solutions Fall 2011 177 - Section...

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Section A.2 Linear Ordinary Differential Equations with Constant Coefficients A177 Plug into the equation y ±± - y ± - 2 y = x 2 - 4: 2 A - 2 Ax - B - 2 2 - 2 Bx - 2 C = x 2 - 4; - 2 A =1 ; A = - 1 2 ; - 2 A - 2 B =0 1 - 2 B ; B = 1 2 ; 2 A - 2 C - B =4 ⇒- 1 2 - 1 2 - 2 C C = 5 4 . Hence y p = - 1 2 x 2 + 1 2 x + 5 4 ; and so the general solution y g = c 1 e - x + c 2 e 2 x - 1 2 x 2 + 1 2 x + 5 4 . 41. 2 y ± - y = e 2 x . Equation: 2 y ± - y = e 2 x ; Homogeneous equation: 2 y ± - y ; Characteristic equation: 2 λ - 1=0 Characteristic root: λ 1 = 1 2 ; Solution of homogeneous equation: y h = c 1 e x/ 2 . For a particular solution, try y p = Ae 2 x ; y ± p =2
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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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