## lilMissMindset 3 years ago i am stuck with this DE problem. help please, anybody. (D^2 - D -2)y=6x+6e^(-x)

1. zepdrix

|dw:1350355096186:dw| So what kind of complimentary solution did you get? Was there any overlap? :)

2. mahmit2012

D=-1 , 2 Yp=Ax+B+Cxe-x find A B C

3. zepdrix

Woops I should have called the exponential term C, sorry about that.

4. mahmit2012

but you mentioned Yp1 and its ok.

5. mahmit2012

so Yp2=Cxe-x

6. lilMissMindset

Yp2 is the same as in the auxillary eqtn

7. mahmit2012

no it has x so xe-x

8. lilMissMindset

yes, multiplied it with x, and then?

9. lilMissMindset

what will be the value of C?

10. mahmit2012

then put in DE and find the values of A B C Y=c1e-x + c2e2x + Ax+B+Cxe-x c1 & c2 are unknown , but A B C is exactly known

11. mahmit2012

Tricky it is -2

12. lilMissMindset

how is that so? i keep on getting 3/2

13. mahmit2012

I found it with Laplace !

14. lilMissMindset

teach me master. what is laplace?

15. mahmit2012

no it is 6/(-1-2)=-2

16. mahmit2012

Don't pay attention that just put in DE and find out A B C especially C. C=-2

17. lilMissMindset

i get it. jeeeeeez, stupid mistake.

18. lilMissMindset

thanks a lot!

19. mahmit2012

for A B 0-A-2(Ax+B)=6x A=-3 B=3/2