Differentials calculus

Question

Find a solution to dA/dt=7A if A(0)=5. 

A(t)=?

Answer 1

dA/dt = 7A

Separate variables to get (1/A)dA = 7dt

Integrate both sides: lnA = 7t + C

Since t = 0 when A = 5, we have ln5 = 7(0) + C. So, C = ln5.

Therefore, lnA = 7t + ln5

lnA - ln5 = 7t

ln(A/5) = 7t

A/5 = e^7t

A (t) = 5e^7t