Exercises

  1. Solve the ODE: with a=5 and g=0.1. However, solve the ODE with the intial condition y(0)=100 and then solve with the initial condition y(0)=10. Then plot both solutions on an appropriate time scale(x) to see the steady state behavior of both solutions on the same plot.

    ODE1:=diff(y(x), x) = a*y(x)-g*y(x)^2
    ODE2:=subs(a=5, g=0.1, ODE1)
    sol1:=dsolve({ODE2, y(0)=100}, y(x))
    sol2:=dsolve({ODE2, y(0)=10}, y(x))
    plot([rhs(sol1), rhs(sol2)], x=0..1.5, color=[red,blue])

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