## anonymous 5 years ago can smeone give the general solution of y'= x+y/(2x+2y+3)

1. anonymous

it is under exact differential equations

2. anonymous

are u sure its not (x+y)/(2x+2y+3) ?

3. anonymous

yes it is

4. anonymous

the take x+y=z and proceed. that is a useful substitution.

5. anonymous

ok will try

6. anonymous

then what?

7. anonymous

do u have an idea about exact differential equations

8. anonymous

yups but this substitution solves THIS particular sum. if you want a solution with exact differentials i can give u. but u may try this substitution.

9. anonymous

i have but the function will be in z and dy/dx then what should i do

10. anonymous

u will have $\frac{dz}{dx}=\frac{3z+3}{2z+3}$ Integrate!

11. anonymous

dont understand as dy/dx=z/(2z+3) so did u get dz/dx

12. anonymous

use $x+y=z \implies 1+\frac{dy}{dx}=\frac{dz}{dx}$ in case u r wondering how i got $\frac{dz}{dx}$

13. anonymous

oh u can do that, thanks, u made my day

14. anonymous

I solved it without using the concept of exact differential equations!

15. anonymous

yeah but is it ok to do that? will the answers be the same