anonymous
  • anonymous
can smeone give the general solution of y'= x+y/(2x+2y+3)
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
it is under exact differential equations
anonymous
  • anonymous
are u sure its not (x+y)/(2x+2y+3) ?
anonymous
  • anonymous
yes it is

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anonymous
  • anonymous
the take x+y=z and proceed. that is a useful substitution.
anonymous
  • anonymous
ok will try
anonymous
  • anonymous
then what?
anonymous
  • anonymous
do u have an idea about exact differential equations
anonymous
  • 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.
anonymous
  • anonymous
i have but the function will be in z and dy/dx then what should i do
anonymous
  • anonymous
u will have \[\frac{dz}{dx}=\frac{3z+3}{2z+3}\] Integrate!
anonymous
  • anonymous
dont understand as dy/dx=z/(2z+3) so did u get dz/dx
anonymous
  • anonymous
use \[x+y=z \implies 1+\frac{dy}{dx}=\frac{dz}{dx}\] in case u r wondering how i got \[\frac{dz}{dx}\]
anonymous
  • anonymous
oh u can do that, thanks, u made my day
anonymous
  • anonymous
I solved it without using the concept of exact differential equations!
anonymous
  • anonymous
yeah but is it ok to do that? will the answers be the same

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