differentiate with respect to time m.v/t=q.E+q.B.v where m = mass

Question

v= velocity, t = time,   q,b,E are constant

Answer 1

mv/t=qE+qBv, mv=qEt+qBvt, mv-qBvt=qEt, v(m-qBt)=qEt, v=qEt/(m-qBt).

mdv/dt=qE+qB(v+tdv/dt),

mdv/dt-qBtdv/dt=qE+qBv,

dv/dt(m-qBt)=qE+qBv,

dv/dt=q(E+Bv)/(m-qBt).

This can also be written:

dv/dt=q(E+BqEt/(m-qBt))/(m-qBt),

dv/dt=qEm/(m-qBt)².