Question 1012678
From dx/dt=-3x/(1+t)^2, I'm thinking to solve this by separation of variables...thus, we can rearrange and get
(1/x) dx = -3 dt / (t+1)^2
Now integrate
ln x = 3/(t+1) + C
Now exponentiate
x(t) = Ce^(3/(t+1))
Now apply initial conditions...
x(0) = 1000 = Ce^3 so that
C = 1000/e^3 = 1000e^(-3)
and then
x(t) = 1000e^(-3)*e^(3/(t+1))
Now combine exponents and you get
x(t) = 1000e^(-3t/(1+t))