Question 1012678
{{{dx/dt=-3x/(1+t)^2}}}
{{{dx/x=-3(1+t)^(-2)*dt}}}
Use a substitution,
{{{u=1+t}}}
{{{du=dt}}}
So,
{{{dx/x=-3u^(-2)du}}}
Integrating both sides,
{{{ln(x)=3u^(-1)+C}}}
{{{ln(x)=3/(1+t)+C}}}
{{{x=Ce^(3/(1+t))}}}
When {{{t=0}}},{{{x=1000}}}
{{{1000=Ce^(3/(1+0))}}}
{{{C=1000/e^3}}}
{{{x=(1000/e^3)*e^(3/(1+t))}}}
Check your problem setup because our functions don't match.