http://i.snag.gy/hMVVv.jpg
Can someone explain how you perform that step, with the black arrow next to it?
THANKS
Can someone explain how you perform that step, with the black arrow next to it?
THANKS
-
As you probably know, the product rule states that if
P(x) = u(x)*v(x)
dP/dx = udv/dx + vdu/dx = uv' + vu'
As part of your solution you had v = y/x = yx^-1, so, applying the above rule,
dv/dx = y*-x^-2 + x^-1*dy/dx which can be rearranged as
dv/dx = (1/x)y' - (1/x)(y/x)
Just recognise that y/x = v and you have it
dv/dx = (1/x)y' - (1/x)v, or,
v' = (1/x)(y' - v)
and so on to
v'x + v = y' = -2v^3 + v (from earlier)
Cancelling v on both sides
xdv/dx = -2v^3 and separating variables
dv/v^3 = -2dx/x etc etc
Regards - Ian H
P(x) = u(x)*v(x)
dP/dx = udv/dx + vdu/dx = uv' + vu'
As part of your solution you had v = y/x = yx^-1, so, applying the above rule,
dv/dx = y*-x^-2 + x^-1*dy/dx which can be rearranged as
dv/dx = (1/x)y' - (1/x)(y/x)
Just recognise that y/x = v and you have it
dv/dx = (1/x)y' - (1/x)v, or,
v' = (1/x)(y' - v)
and so on to
v'x + v = y' = -2v^3 + v (from earlier)
Cancelling v on both sides
xdv/dx = -2v^3 and separating variables
dv/v^3 = -2dx/x etc etc
Regards - Ian H