## anonymous 5 years ago I need to find the partivular solution to the differential equation dy/dx=(1+y)/x Given the initial conditon f(-1)=1

1. bahrom7893

I love diff equations! =) So first of all see if its separable

2. bahrom7893

it is!

3. bahrom7893

So separate it: $dy/dx = (1+y)/x$

4. bahrom7893

Sorry, I keep crashing on here but i will always reply: So multiply both sides by dx and divide both sides by 1+y

5. bahrom7893

You will have: $dy/(1+y) = dx/x$

6. anonymous

can't you think of it as dy/(1+y) you're in good hands later.

7. bahrom7893

Integrate both sides: Left side will be just Ln|1+y| and the right side will be Ln|x|

8. bahrom7893

So: Ln|1+y| = Ln|x| + C

9. bahrom7893

Raise e to both sides to get rid of Ln: $e^{Ln|1+y|} = e^{Ln|x|+C}$

10. bahrom7893

Rewrite and simplify: $e^{Ln|1+y|} = e^{Ln|x|}*e^C$ $1+y = Kx$

11. bahrom7893

(e to some constant is another constant so I just let that other constant be K) Now apply initial conditions: f(-1)=1: 1+1 = -1K; 2 = -K; K = -2

12. bahrom7893

13. bahrom7893

Im taking a differential equations course! IT IS FUN!! P.S.: Please click on become a fan if I helped, I really want to get to the next level!! Thanks =)

14. anonymous

why do you multiply by e^c

15. bahrom7893

there's a property: $A^{B+C} = A^B * A^C$, so in our case: $e^{Ln|x|+C} = e^{\ln|x|} * e^C$

16. bahrom7893

and e to some constant is another constant so I said let that constant be K. Any other questions?

17. anonymous

no and thanks for your help