Who can help me?
Variation of parameters
\[y''-2y'+y=e^{2x}\]
\[r^2-2r+1=0\]
\[(r-1)^2=0\]
\[r=1\]
\[y_c(x)=c_1e^x+c_2xe^x\]
\[y_p(x)=u_1e^x+u_2xe^x\]
\[y_p'(x)=u_1'e^x+u_2'xe^x+u_1e^x+u_2e^x+u_2xe^x\]
\[u_1'e^x+u_2'xe^x=0\]
\[y_p'=u_1e^x+u_2e^x+u_2xe^x\]
\[y_p''(x)=u_1e^x+u_1e^x+u_2'e^x+u_2e^x+u_2'xe^x+u_2e^x+u_2xe^x\]
what am I looking for when I compare the coeffients....sorry don't mean to ask dumb questions...but what is my eventual goal? Do I have to manipulate the coeffients if they're diffferent?
I solved it using undetermined coefficients and I got \[y=y_c+y_p\]
\[y=c_1e^x+c_2xe^x+e^{2x}\]
and then I was asked to solve the same problem using variation of parameters