I need to solve this equation :
y'' + 2y' + y = xe^-x
I found the complimentary solution which i will dub yc(x) and i know that the solution is the complimentary plus the particular ( yc(x) + yp(x) ) but I am having trouble finding the particular. I know it will have the form
y = (Ax + B)*e^-x
y' = e^-x * (A - Ax + B)
y'' = -e^-x * (2A - Ax + B)
right?
Then when i plug back in everything cancels out except 2B * e^-x = xe^-x
This can't be right. Any help appreciated.
y'' + 2y' + y = xe^-x
I found the complimentary solution which i will dub yc(x) and i know that the solution is the complimentary plus the particular ( yc(x) + yp(x) ) but I am having trouble finding the particular. I know it will have the form
y = (Ax + B)*e^-x
y' = e^-x * (A - Ax + B)
y'' = -e^-x * (2A - Ax + B)
right?
Then when i plug back in everything cancels out except 2B * e^-x = xe^-x
This can't be right. Any help appreciated.