## kirbykirby Group Title x^2*y' + 3xy = 1 (Linear DE) one year ago one year ago

1. kirbykirby Group Title

I divide by x^2 to get y' + (3/x)y=1/x^2 My integration factor though gives me |x|^3

2. kirbykirby Group Title

I dunno what to do with this absolute value :S

3. shamim Group Title

is it $x ^{2}y \prime +3xy=1$

4. kirbykirby Group Title

yes

5. nubeer Group Title

have you tried Cautiy Eiller..?

6. kirbykirby Group Title

WHat's Cautiy Eiller?

7. chemENGINEER Group Title

basically Put the differential equation in the correct initial form Find the integrating factor Multiply everything in the differential equation by and verify that the left side becomes the product rule and write it as such. Integrate both sides, make sure you properly deal with the constant of integration. Solve for the solution y(t).

8. kirbykirby Group Title

(I tried seeing what wolfram alpha does, but they always do Integral (1/x) as ln x, but we are supposed to do it as ln |x|)

9. nubeer Group Title

mm no.. sorry that won't work here..

10. kirbykirby Group Title

I get $|x|^3y' +\frac{3|x|^3}{x}=\frac{|x|^3}{x^2}$

11. kirbykirby Group Title

after multiplying te integration factor

12. chemENGINEER Group Title

the final step is then d/dx[x^3y]=int(x) which is simple.

13. chemENGINEER Group Title

excuse me it is x^3y=int(x) which is to say d/dx[x^3y]=x^3/x^2

14. kirbykirby Group Title

But we hae absolute values no? Integral (1/x) = ln|x|

15. chemENGINEER Group Title

this yields x^3y=x^2/2 then jus divide by x^3 to get y=1/2(x^-1)

16. kirbykirby Group Title

How do you know if the x is always positive?

17. chemENGINEER Group Title

Try reading some outside resources like http://tutorial.math.lamar.edu/Classes/DE/Linear.aspx !!! I liked this site when i was a rook!

18. kirbykirby Group Title

COuld it be because if we say x>0, then the drop the absolute value, but if x <0, then you put -x^3 everywhere (but since the whole equation is negative, you just "divide by -1" o_o?

19. chemENGINEER Group Title

otherwise though this solution looks correct..any problems you see?

20. kirbykirby Group Title

No I was mainly concerned about the absolute value

21. kirbykirby Group Title

Thanks though !

22. shubhamsrg Group Title

Ignore the absolute value.

23. UnkleRhaukus Group Title

yeah.

24. SWAG Group Title

Yup