## lilMissMindset Group Title (D^2 + 9)y =5e^x - 162x i need to check if my answer is right. one year ago one year ago

1. lilMissMindset Group Title

@AnimalAin this.

2. partyrainbow276 Group Title

Awesome! u did it write

3. lilMissMindset Group Title

this is my answer: 2Ae^x + B + Cx = 5e^x -162x

4. partyrainbow276 Group Title

lets see...... AWESOME AWESOME :) thats right good job

5. AnimalAin Group Title

It's been a minute since I've done these, but I think the way is to consider the homogeneous solution by using an auxilliary (sp?) equation, then fit a particular solution that will match the RHS.

6. partyrainbow276 Group Title

lilmissmindset is right thats what i got for my answer

7. AnimalAin Group Title

That's the problem we did before.....

8. lilMissMindset Group Title

yes yes, this is the first question i asked. it's just that the book says the general solution for this is $=C _{1} \cos 3x+ C _{2} \sin3x + \frac{ 1 }{ 2 } e ^{x} -18xy$

9. lilMissMindset Group Title

there's no y after -18x SORRY

10. AnimalAin Group Title

Lets look at this in more detail.

11. lilMissMindset Group Title

and our answer is 5/2 e^x -162x

12. lilMissMindset Group Title

i thought, maybe there's something wrong with me, getting the solution after all

13. AnimalAin Group Title

$(D^2 + 9)y =5e^x - 162x$Consider$(D^2 + 9)y =0$Aux equation$r^2+9=0 \implies r= \pm 3i \implies y _{h}=C _{1} \cos 3x +C_2 \sin3x$OK so far?

14. lilMissMindset Group Title

yeps. ok.

15. lilMissMindset Group Title

ok with that part,

16. AnimalAin Group Title

Then we find the particular solution. Consider the first part of the RHS by itself, so$(D^2 + 9)y_p =5e^x \implies y_p=\frac{e^x}{2}$

17. AnimalAin Group Title

This is true since the derivative of the e^x term is always itself. That means the second derivative is the same as the original function. Added to the nine copies of the original function, we get 10ysubp=5e^x.

18. lilMissMindset Group Title

owwww. i understand,

19. AnimalAin Group Title

Now consider the polynomial part. The second derivative of a linear function is zero, so we get$9y_{p2} =- 162x \implies y_{p2} =-19x$

20. AnimalAin Group Title

So we get something like$y=y_h+y_p=C_1\cos 3x+C_2\sin3x+\frac{e^x}{2}-19x$

21. lilMissMindset Group Title

i forgot to multiply $y _{p}$ with 9 when i substitute, right? that's why i did ot get the answer,

22. lilMissMindset Group Title

not*

23. AnimalAin Group Title

Actually, my division is horrible today.... should be 18 in the last term; exactly as your text had said.

24. AnimalAin Group Title

I hope you've got this; you're wearing me out....LOL

25. lilMissMindset Group Title

actually, it's the same for the two of us. LOL hey, thanks a lot. you've been helping me large. Sorry for the stress,

26. lilMissMindset Group Title

SORRY!

27. lilMissMindset Group Title

i get it, i'm just confused on some parts.

28. AnimalAin Group Title

No stress. It's fun working with students that work hard and get it. Do math every day.

29. lilMissMindset Group Title

i'll practice harder, :)

30. AnimalAin Group Title

I'm sure you'll get it.

31. lilMissMindset Group Title

i hope i get it the soonest possible, my exam is tomorrow. O.O