Page 119 - Schaum's Outline of Differential Equations

102 THE METHOD OF UNDETERMINED COEFFICIENTS [CHAP. 11

In Problems 11.27 through 11.36, determine the form of a particular solution to \-(y) = tj>(x) for <j>(x) as given if the solution
5x
to the associated homogeneous equation \-(y) = 0 is y h = c^ x cos 3x + C 2e sin 3x.

In Problems 11.37 through 11.43, determine the form of a particular solution to L(x) = <j>(t) for <j>(t) as given if the solution
to the associated homogeneous equation L(x) = 0 is x h = Cj + c 2e' + c 3te'.

In Problems 11.44 through 11.52, find the general solutions to the given differential equations.

2
44. y"-2y' + y = x -! 11.45. /'- -2y' + y = 36^
,46. y" - 2y' + y = 4 cos x 11.47. /'- -2y' + y = 3e*

,48. y"-2y' + y = xe x 11.49. /- -y = e*
2x
,50. y' -y = xe + 1 11.51. y' -- y = sin x + cos 2x

11.,52. y'" -3y" + 3y'-y = if+l