variation of parameter method

solve xy" - 4y' = x^4 by method of variation of parameter
make the coefficient of y" unity by dividing by x

find CF in the form Ay1 + By2 (using trial and error or some other method)
find the wronskian
and then find the PI as shown below

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solving a second order differential equation

solve y"-y'+y = 1

rewrite the equation as (D²-D+1)y = 1
replace D with m to get the auxilary equation
write the C.F. and then proceed to the particular integral (PI)