Differential substitution question

[boneill]

Hi guys,
In one of my lecture notes examples on substitution methods for ODE's

I have a DE

dy/dx = (2y^4+x^4) / (xy^3)

It then says to use the substitution y=xv.

The next line then becomes

v+x dv/dx = (2(xv)^4+x^4) / (x(xv)^3)

Now I see on the right hand side the substitution y=xv.


what I don't understand is the LHS.

How did they go from dy/dx to v+x dv/dx ??

[zaza]

Chain rule.

y = x.v(x), so you need to differentiate both parts.