Integration with two variables?

Question

Velocity = dx/dt = x^2e^(-3t)
x = Distance
When t = 0, x = 2
Find x when t = 4

Answer 1

dx/x^2 =e^-3t dt
so -1/x = -1/3 e^-3t +C
at t=0 x=2 so -1/2=-1/3+C so C=1/3-1/2 =-1/6
and
1/x= 1/3 e^-3t+1/6
if t=4
1/x= 1/3 e^-12 +1/6 so x=6 as e^-12 is very small compared with 1/6

Answer 2

given : dx/dt=x^2e^(-3t)
now lets use variable seprable method
dx/(x^2)=e^(-3t)dt
nw integrating both sides
we get
-1/x=e^(-3t)/(-3)+c
where c is a const
now put x=2 nd t=0
we get
-1/2=-1/3+c
c=-1/6
nw
1/x=e^(-3t)+1/6
nw put t=4 and find x!!!!