Find a particular solution yp using undetermined coefficient

Find a particular solution y_p using undetermined coefficients, for y\" - 2y\' + y = 80 e^5t

Solution

This method computes a particular solution based on the inhomoengeous part ie: 80 exp(5t)

The guess is:

yp=A exp(5t)

Substituting gives

yp\'\'-2yp\'+yp=80 exp(5t)

25A exp(5t)-10 Aexp(5t)+A exp(5t)=80 exp(5t)

16A=80

A=5

HEnce,

yp=5 exp(5t)