(2xy+3y^2)/(2xy+x^2)=dy/dx y(1)=1 private solution ?

Question

(2xy+3y^2)/(2xy+x^2)=dy/dx   y(1)=1 private solution ?

myininaya · Answer

without trying to myself
we could try y=vx 
which means y'=v'x+v
this could help or this may not help
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if that doesn't work, maybe we can see if it is exact

myininaya · Answer

actually first way seems to work

calculusfunctions · Answer

@rubcksy do you understand? @myininaya is correct because what you have is a homogenous equation of degree zero. Thus you can start with y = vx.

anonymous · Answer

y=vx
dy=xdv+vdx        i applied this transform but i cannot get the answers.maybe i have some mistakes at the other steps

calculusfunctions · Answer

First if$$y =vx$$then differentiating with respect to x yields$$\frac{ dy }{ dx}= x \frac{ dv }{ dx }+v$$