Question

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

Answer 1

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

Answer 2

actually first way seems to work

Answer 3

@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.

Answer 4

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

Answer 5

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