Transformer operation question

The primary winding of a transformer consists of two parts:

1- Primary leakage inductance Lp1

2-Primary coupling inductance L1

neglect the wiring resistance.

So the total primary inductance Lp=Lp1 + L1

The voltage across L1 must be constnat all the time = N1*d@m/dt

where @m is the mutual magnetizing flux, which is constant for all loads.

Now,if the primary is connected into a constant AC supply voltage V1 and the secondary is connected into resistive load,then:

V1 = Lp1*d i1/dt + N1*d@m/dt

V1 and N1*d@m/dt are constants while the first term of the equation Lp1*d i1/dt

is variable depends on the primary current !

Any one can explain that conflict in the equation ?

Thanks