anonymous 4 years ago does anyone understand Differential equations

1. lalaly

yes

2. amistre64

einstein did i think

3. amistre64

newton faked it lol

4. Mr.Math

lol

5. anonymous

i just begun D.E. and i am totally lost. find a function, y=f(x) satisfying the given differential equation and the prescribed initial condition. dy/dx= 2x+1; y(0)=3 where do i start

6. amistre64

with integration id assume

7. lalaly

multiply both sides by dx .. then integrate both sides

8. amistre64

$y' = 2x+1$ $\int y' = \int 2x+1$ $y=x^2+x +C$

9. amistre64

plug in x=0 and y=3 to solve for C

10. lalaly

this is a seperable DE

11. amistre64

yeah, semantics :)

12. lalaly

:D:D

13. anonymous

you do these just like seperable this is 2 sections before seperable

14. lalaly

Initial Value problem?

15. anonymous

intergrals as general and particular solutions

16. lalaly

forget what i said, its done the way amistre showd u

17. amistre64

yay!!

18. lalaly

hehehe

19. anonymous

ok appreciate it!

20. amistre64

$Y(x)=\int y'\ dx$ $Y(x)=\int (2x+1)dx$ stuff like that

21. anonymous

it just shows you the equation and intial condition and you have to choose what to do. So when you work it out it becomes what you are doing with the integral

22. lalaly

$\frac{dy}{dx}=2x+1$$dy=(2x+1)dx$now integrate both sides$\int\limits{dy}=\int\limits{(2x+1)dx}$$y=x^2+x+c$

23. anonymous

yea, just like that, thanks,

24. lalaly

:)

25. anonymous

i need help with intergals, it has been 2 yrs since i have done them. x times sq. root of x^2+9

26. lalaly

let u=x^2+9 du=2x so integration becomes$\frac{1}{2} \int\limits{ \sqrt u}du$

27. lalaly

integrate sqrt u then substitute the x back

28. lalaly

du=2xdx **

29. lalaly

I am really sorry, i have to leave now. Post a new question and someone else could help you

30. anonymous

thanks

31. anonymous

is $^{?} \int\limits_{?}^{?} xe ^{-x}$ u substitution or by parts integral

32. amistre64

or simply recognize that your missing a -1 in front

33. amistre64

34. amistre64

by parts with that one

35. anonymous

alright

36. amistre64

e^-x + x -e^-x | -1 e^-x | = x e^-x - e^-x +0 -----

37. amistre64

+C if youaint got bounds

38. amistre64

$-xe^{-x}-e^{-x}\ or\ -e^{-x}(x+1)$