Hi there, We got a problem in Dynamics lecture,

Consider motion in a central force field, mr''=F(r,theta)*e_r where r
and e_r are vectors.
In this case, for F(r,theta), textbook derives the formula below,
v^2=(r')^2+(h_0/r)^2 where v is velocity, h_0 is r(cross
product)v=specific angular momentum,
Those processes are not problems, but when considering a special case
for F=F(r) only,
The problem can be described by a potential V, V(r)=-int{F(r)dr}

From energy conservation,

0.5mv^2+V(r)=T_0+V_0=E_0=0.5m{(r'^2+(h_0/r)^2+V(r)}
Transpose and process bilaterial, we get,
dr 2 mh_0^2
(------)^2 = ----(E_0 - V(r) - --------------) = (blablabla)
dt m 2r^2
(The formula is so BEAUTIFUL that I call them (blablabla),
The problem is when we remove square of left-hand side, should
right-hand side be
denoted as a square root? That is,
dr
(------)= + - (blablabla)^0.5
dt
My textbook show us just positive square root and then solve the ODE,
but I don't
know why it neglects the minus sign.