## anonymous 5 years ago anyone a pro with differential equations? It has been too long and I need some help

1. anonymous

I feel ok with them, not pro but hopefully I can help

2. anonymous

$y'''+y=0$ where y(o)=0 , y'(0) =1, y''(0)= 0 thank you please help

3. anonymous

sorry I cannot help, havent done 3rd order ones.

4. anonymous

Ok how about find all solutions to y'-2y=1 thank you for trying

5. anonymous

you can multiply with an integrating factor, do you remember that?

6. anonymous

I will get a pen and paper

7. anonymous

thank you I know its alot of work

8. anonymous

ok I solved it

9. anonymous

so do you know the technique of integrating factor?

10. anonymous

you r the best lets see if I get it :)

11. anonymous

you want to make a full derivative out of the left hand side

12. anonymous

for this you need to have something like dy/dx+ some y=whatever

13. anonymous

my computer is slowing down sorry ...yes I remeber that

14. anonymous

no problem, what is the integrating factor here?

15. anonymous

ok

16. anonymous

after we integrate x dx on the other side

17. anonymous

it is $e ^{\int\limits_{}^{} the multiplier of y}dx$

18. anonymous

that is -2 here

19. anonymous

the integral of -2 is -2x (you dont need the constant here) so multiply through by $e ^{-2}$

20. anonymous

-2x

21. anonymous

Im sorry the computer wont let me type

22. anonymous

It keeps stopping but I am here reading...Yes I remeber now the -2x

23. anonymous

the result is $e ^{-2x}$ dy/dx -2 e^{-2x} y=e ^{-2x}

24. anonymous

do you recognise the full derivative now?

25. anonymous

yes it is coming back to me

26. anonymous

what about when we have a trig function like y''+4y=cos x

27. anonymous

this is harder but my favourite :)

28. anonymous

better your fav than mine :) :) i have not done these in 17 years it is so hard to remember you r a big help

29. anonymous

first you have to think of the homogeneous equation (meaning y''+4y=0) you have to find the general solution for that, for this we use the auxiliary equation. that just says that ay''+by'+cy=0 and write a quadratic equation for it,$a \lambda ^{2}+b \lambda +c=0$

30. anonymous

where lambda=e^x

31. anonymous

or in the form of e^x

32. anonymous

here you will have to solve y^2+4=0

33. anonymous

do you know how to?

34. anonymous

I will be back in 5 min

35. anonymous

i have no idea Im trying to follow along with you and my book but so confused I need to watch a tutorial i think and i will be bac

36. anonymous

you can only solve this with complex numbers

37. anonymous

38. anonymous

you had enough? How is it that after 17 years you are doing this again?

39. anonymous

40. anonymous

i am a teacher but needed 2 credits of advanced math i truly didnt want to take up your time

41. anonymous

I will have an exam about this in 2weeks so it is not a waste of time for me

42. anonymous

I need alot of explanation and my computer is not cooperating ...to be honest this work is due tomorrow and my brain is blank we can continue if u want to help me..

43. anonymous

well it is up to you, I am free now for an hour

44. anonymous

Consider the equation y' + (cos x) y= e^-sinx find the solution that satisfies $\phi$($\pi$ ) = pi

45. anonymous

what is the end bit? that isnt clear

46. anonymous

I guess you have to use the integrating factor here as well. it will be e^integral(cosx) so e^sinx.

47. anonymous

that way you get $(e ^{sinx}y)'=1$

48. anonymous

so the LHS= x+C y=(x+C)/e^sinx