Find a particular solution Use the method of variation of pa

Find a particular solution?
Use the method of variation of parameters to find a particular solution of y\"-5y\'+6y=2e^t.

Solution

A particular solution is evident. If you have exponential function on the right side of the equation yuo can look for a particular solution in the form:

y = A et

since all derivatives give you the same function, Substitute this function into the left side of the eqaution.

It gives you (after dividing by et)):

A - 5A + 6A = 2 or A = 1

Thus y = et .   

You don\'t need to use r =2,3. This is about general solution for the homogeneous equation.