Question on lasers and einstein's co-efficents

just wondering on what the simple re-arrangement of this is
(dN2/dt)=-A21.N2 to get the answer N2(t) = ????
its a maths question more-so but my lecturer gave an answer that seemed wrong, perhaps a typo
he gave it to be N2(t)=N20e^(-A21t)

It's a Differential Equation:
dN₂/dt=-A₂₁*N₂
Separation of variables:
dN₂/N₂ = -A₂₁*dt
Integrate both sides:
ln(N₂) = -A₂₁*t + C
N₂(t) = exp(-A₂₁*t)*exp(C)
If we set exp(C) to be some other constant B, and use the initial condition N₂(0) = N₀, then B = N₀ and the equation becomes:
N₂(t) = N₀exp(-A₂₁*t)