Problem goes as follows :
(y^2 + x^2)dx + (2xy)dy = 0
Now I can clearly see it is homogeneous but my problem starts once I get it in derivative form. Once in derivative form, I subbed u = y/x , y = ux , dy/dx = (du/dx) x + u.
Once I subbed it all in, I was left with
u + du/dx = - (1 + u^2) / (2u)
Can someone help me proceed from here?
multiply by 3, moving the to the RHS and exponentiating
which after substituting and simplifying gives the answer
Since is a constant then which we'll call
same answer. So why did I use . I saw that I was going to multiply by 3 and exponentiate.
I hate to ask this but could you show me in more detailed steps or least tell me in more detail how you went from after integrating and then getting
(1 + 3u^2)x^3.
I get that e^3c is just another constant so that'll equal C later but i'm at an absolute loss as to how you got what I typed above. If you multiply both sides by 3, you should end up with
ln(1+3u^2) = -3lnx + 3c
If you take e to the both sides, you should get
(1 + 3u^2) = - 1/x^3 + e^3c
now I can get this far... and I just can't see how you're able to get
(1 + 3u^2)x^3 on the left hand side and e^3c on the right hand side.
I mean supposing you DID multiply both sides by x^3, THEN I can see you getting that for the left side but on the right side you'll end up with -1 + (x^3)(e^3c)
.......If you don't mind could you show it to me in clearer steps? I've been racking my brains for over a day on this problem and I can't seem to get it to how you're able to get it to. THanks.