## JenniferSmart1 2 years ago Who can help me? Variation of parameters \[y''-2y'+y=e^{2x}\] \[r^2-2r+1=0\] \[(r-1)^2=0\] \[r=1\] \[y_c(x)=c_1e^x+c_2xe^x\] \[y_p(x)=u_1e^x+u_2xe^x\] \[y_p'(x)=u_1'e^x+u_2'xe^x+u_1e^x+u_2e^x+u_2xe^x\] \[u_1'e^x+u_2'xe^x=0\] \[y_p'=u_1e^x+u_2e^x+u_2xe^x\] \[y_p''(x)=u_1e^x+u_1e^x+u_2'e^x+u_2e^x+u_2'xe^x+u_2e^x+u_2xe^x\]

1. JenniferSmart1

@UnkleRhaukus

2. JenniferSmart1

3. JenniferSmart1

@hartnn I'm almost done with the question

4. JenniferSmart1

glad to see you my friend =D

5. JenniferSmart1

the next step...everything I did so far seems right

6. JenniferSmart1

ohhh...I plug them back into the original formula!!!

7. hartnn

and then compare the co-efficients.

8. JenniferSmart1

and then I....? Yeah that's where I'm stuck :P

9. JenniferSmart1

oh ok

10. JenniferSmart1

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?

11. JenniferSmart1

sry :S

12. JenniferSmart1

13. JenniferSmart1

oh sorry I forgot to write \[y_p'=u_1e^x+u_2e^x+u_2xe^x\]

14. oldrin.bataku

Hey, is that the Stewart book?

15. JenniferSmart1

yes

16. JenniferSmart1

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

17. UnkleRhaukus

you have y_p, y'_p and y''_p insert them into t your original DE and simplify