Question

can smeone give the general solution of y'= x+y/(2x+2y+3)

Answer 1

it is under exact differential equations

Answer 2

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

Answer 3

yes it is

Answer 4

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

Answer 5

ok will try

Answer 6

then what?

Answer 7

do u have an idea about exact differential equations

Answer 8

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.

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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