I need to solve this differential equation initial value problem: Q' = -rQ, Q(0) = Q_0 (Q_0 0). I got y = Ce^(-rt) but it's not the same as the answer book answer. Can anyone briefly do this problem so I can see where my mistake was?

Question

I need to solve this differential equation initial value problem: Q' = -rQ, Q(0) = Q_0 (Q_0 > 0). I got y = Ce^(-rt) but it's not the same as the answer book answer. Can anyone briefly do this problem so I can see where my mistake was?

turingtest · Answer

Q'=dQ/dt=-rQ
dQ/Q=-rdt
integrate both sides from Q_0 to Q, and 0 to t
ln(Q/Q_0)=-rt
Q=Q_0*e^(-rt)
what does your book have?