- #1
ProPatto16
- 326
- 0
solve y''+y'+y=cosx-x2ex
y= yc+yp
yc:
characteristic eq gives r2+r+1=0
using quadratic formula i got r=-1/2+[(sqrt3)/2]i and r=-1/2-[(sqrt3)/2]i
so yc=e-x/2(c1cos(sqrt3/2)x+c2sin(sqrt3/2)x
but i have no idea of a particular solution that makes any sense.
i tried a general approach, the functions and their derivitives on the RHS include terms cosx, sinx, x2ex, xex, ex
so i good start would be yp=Acosx+Bsinx+Cx2ex+Dxex+Eex
then find y'p and y''p and sub into original equation.
but it becomes so dam monstrous there must be another way.
y= yc+yp
yc:
characteristic eq gives r2+r+1=0
using quadratic formula i got r=-1/2+[(sqrt3)/2]i and r=-1/2-[(sqrt3)/2]i
so yc=e-x/2(c1cos(sqrt3/2)x+c2sin(sqrt3/2)x
but i have no idea of a particular solution that makes any sense.
i tried a general approach, the functions and their derivitives on the RHS include terms cosx, sinx, x2ex, xex, ex
so i good start would be yp=Acosx+Bsinx+Cx2ex+Dxex+Eex
then find y'p and y''p and sub into original equation.
but it becomes so dam monstrous there must be another way.