Solve the DE: (3x-y)dx + (x+y)dy = 0
I've tried it using integrating factors, but (dM/dy - dN/dx)/N = -2/(x+y) & (dN/dy - dM/dx)/M = 0

Question

Solve the DE: (3x-y)dx + (x+y)dy = 0
I've tried it using integrating factors, but (dM/dy - dN/dx)/N = -2/(x+y) & (dN/dy - dM/dx)/M = 0

anonymous · Answer

ops i meant to say  (dM/dy - dN/dx)/N = -2/(x+y) & (dN/dx - dM/dy)/M = 0

anonymous · Answer

just noticed that  (dN/dx - dM/dy)/M = 2/(3x-y)

anonymous · Answer

im trying this problem with a different aproach, here is what i got:$$-(3x-y)/(x+y)= dy/dx$$$$0= (dy/dx)(x+y)+3-y$$ Im kind of lost regarding of what to do next.

unklerhaukus · Answer

can you arrange the origional DE in to the form 

dy/dx = f (y/x)

unklerhaukus · Answer

$$\frac{dy}{dx}=\frac{-(3x-y)}{x+y}\\qquad=-\frac{3x/x-y/x}{x/x+y/x}\=$$

anonymous · Answer

I still don't see how i could solve$$\frac{ 3-y/x }{ 1+y/x }$$

unklerhaukus · Answer

try the subsitution   
 
  y/x = v
  y = vx
dy = ...+...

anonymous · Answer

oooo, i think i can work from there on, thanks for the help.

unklerhaukus · Answer

**


dy/dx  = ... + ...

unklerhaukus · Answer

have you found dy/dx?

dumbcow · Answer

this is not an exact diff equ ... you can't explicitly solve for "y" in terms of "x"

dumbcow · Answer

look at solution http://www.wolframalpha.com/input/?i=%283x-y%29dx+%2B+%28x%2By%29dy+%3D+0