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Example > y" = 9x + 2x -1 D =0 = , =r, =0 = y, =Cx+C, y, =x(Ax+ Bx+C)

Example > y" = 9x + 2x -1 D =0 = , =r, =0 = y, =Cx+C, y, =x(Ax+ Bx+C)

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Example > y" = 9x +2x-1 D' =0 = =r, = 0 = y, Cx+C, y, =x(Ax + Bx+c) > y -y' =x D -D = 0 D(D-1) = 0 = = 0 and r, =1 = y, = G +C,e* y, = x(Ax + B) > y" - 5y = 3e" -2x+1 D -5 = 0 (D-5)(D+5)= 0 = = 15 and r, =-5 y, =Ce + Ce B y, = Ae" + Bx + C > y" - 4y' +3y = e" +2 D -4D+3 =0 (D-3)(D-1) = 0 =3 and r, =1 y, = Ce +C,e y, = Axe" + B 11 Mathematics Electrical & Electronic Engineering Department Second Year Dr. Atheer Alaa Sabri > y" + y = 6e" +6cos(x) D' +1=0 = = j and r, =-j = a = 0, B =1 y, = C, cos(x)+ C, sin(x) y, = Ae" + x(B cos(x) +Csin(x)) > y" - 2y'+ y = xe* D - 2D+1=0 (D-1) =0 = = r, =1 = y, = (C,x+C, )e* y, =(Ax+ B)(x'e") > y" + y = x' sin(2x) D' +1=0 r, = j and r, =-j = a = 0, B =1 y, = C, cos(x)+ C, sin(x) y, = (Ax + Bx +C) (cos(2x)+sin(2x))
Transcribed Image Text:Example > y" = 9x +2x-1 D' =0 = =r, = 0 = y, Cx+C, y, =x(Ax + Bx+c) > y -y' =x D -D = 0 D(D-1) = 0 = = 0 and r, =1 = y, = G +C,e* y, = x(Ax + B) > y" - 5y = 3e" -2x+1 D -5 = 0 (D-5)(D+5)= 0 = = 15 and r, =-5 y, =Ce + Ce B y, = Ae" + Bx + C > y" - 4y' +3y = e" +2 D -4D+3 =0 (D-3)(D-1) = 0 =3 and r, =1 y, = Ce +C,e y, = Axe" + B 11 Mathematics Electrical & Electronic Engineering Department Second Year Dr. Atheer Alaa Sabri > y" + y = 6e" +6cos(x) D' +1=0 = = j and r, =-j = a = 0, B =1 y, = C, cos(x)+ C, sin(x) y, = Ae" + x(B cos(x) +Csin(x)) > y" - 2y'+ y = xe* D - 2D+1=0 (D-1) =0 = = r, =1 = y, = (C,x+C, )e* y, =(Ax+ B)(x'e") > y" + y = x' sin(2x) D' +1=0 r, = j and r, =-j = a = 0, B =1 y, = C, cos(x)+ C, sin(x) y, = (Ax + Bx +C) (cos(2x)+sin(2x))
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