# section 2.1
# problem 1
ode:=diff(y(t),t)+3*y(t)=t+exp(-2*t);
ans:=dsolve(ode);
limit(ans,t=infinity);
# problem 10
ode:=t*diff(y(t),t)-y(t)=t^2*exp(-t);
ans:=dsolve(ode);
limit(ans,t=infinity);
# problem 11
ode:=diff(y(t),t)+y(t)=5*sin(t);
ans:=dsolve(ode);
limit(ans,t=infinity);
# problem 17
ode:=diff(y(t),t)-2*y(t)=exp(2*t);
ics:=y(0)=2;
ans:=dsolve({ode,ics},y(t));
# problem 28
ode:=diff(y(t),t)+2*y(t)/3=1-t/2;
ics:=y(0)=y0;
ans:=dsolve({ode,ics},y(t));
limit(ans,t=infinity);
diff(ans,t);
a:=solve(rhs(ans)+3*diff(rhs(ans),t)/2,t);
solve(eval(rhs(ans),t=a)=0,y0);