Plz help me to finish this physics question?

The equation describes the motion of the proton is,
m(dV/dt) = q(V x B)
[Note: Capital letters of V and B stand for Vector V and Vector B]
i.e. dV/dt = (q/m)(V x B)

But (V x B) = [(vox)i + (voy).cos(wt)j - (voy)sin(wt)k] x (bi)
where (vox) and (voy) are the initial x and y components of the velocity V; b is the magnitude of the magnetic field B]
After expanding the cross product and simplify,
i.e. (V x B) = -b(voy)[sin(wt)j + cos(wt)k]

Hence, right-hand-side of the equation
= -(qb/m).(voy)[sin(wt)j + cos(wt)k] --------- (1)

Now, consider the left-hand side of the equation (dV/dt),
dV/dt = d[(vox)i + (voy).cos(wt)j - (voy).sin(wt)k]/dt
dV/dt = -(voy)w.sin(wt)j - (voy)w.cos(wt)k
i.e. dV/dt = -(voy)w[sin(wt)j + cos(wt)k]
Given that w = qb/m, we have,
dV/dt = -(qb/m).(voy)[sin(wt)j + cos(wt)k] ----------- (2)

By comparing equations (1) and (2), it shows that the given expression for V satisfies the equation
dV/dt = (q/m)(V x B).
Therefore, it is a possible velocity solution of the equation.