Question

Find the solution for the differential equation
(dP/dt)=(0.8-0.2*t)*P
When P(0)=1000,
Thanks in advance

Answer 1

first group or separate the variables

dP/P = .8 -.2t dt
integrate both sides

ln(P) = .8t -.1t^2 +C
take e raised to both sides to cancel natural log

P(t) = k*e^(.8t-.1t^2), where k is some constant

Now apply initial conditions: P(0) = 1000
1000 = k*e^0 --> k = 1000

P(t) = 1000*e^(.8t-.1t^2)

Answer 2

Fuuark, thanks a lot man :)! Can't believe I didn't get it

Answer 3

how did u do the elimination of log?

Answer 4

e^ln(x) = x

Answer 5

ok,thanks