- #1
Calu
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I have a differential equation
y'' + y' -2y = 3e-2x + 5cosx
y = yc + yp
I found
yc = Ae-2x + Bex
for A, B arb. Const.
Then when selecting a trial function to find the particular integral, yp I came up with:
yp = ae-2x + bcosx + csinx
However the correct trial function to choose is:
yp = axe-2x + bcosx + csinx
Where the ae-2x has been multiplied by x. I was wondering in what instance I would have to multiply the term in the yp equation by x or x2.
y'' + y' -2y = 3e-2x + 5cosx
y = yc + yp
I found
yc = Ae-2x + Bex
for A, B arb. Const.
Then when selecting a trial function to find the particular integral, yp I came up with:
yp = ae-2x + bcosx + csinx
However the correct trial function to choose is:
yp = axe-2x + bcosx + csinx
Where the ae-2x has been multiplied by x. I was wondering in what instance I would have to multiply the term in the yp equation by x or x2.