The problem says,"Solve the differential equation. Assume a, b, and k are nonzero constants."

dP

dt = P - a

Here is how I tried to solve the problem:

dP

dt = P - a

multiply both sides by dt:

dp = P - a dt

divide both sides by P:

1/P dP = -a dt

take integral of both sides:

(integral sign) 1/P dP = (integral sign) -a dt

ln|P| = -at + C

exponentiate both sides to get rid of natural log:

e^(ln|P|) = e^(-at) * e^(C)

<----This is my answer, where C is just a constant.P = Ce^(-at)

However, my book says that the answer is P = a + Ae^(t). Please let me know what I did wrong. Thank you