library(deSolve)
parameters<-c(r=1.5,K=100) 
state<-c(X=50) 
logistic <- function(t, state, parameters){ 
 with(as.list(c(state, parameters)), 
 { 
 dX=r*X*(K-X)/K
 return(list(dX)) 
}) 
}
 times <- seq(1,100,by=0.01) 
 out<-as.data.frame(ode(y=state,times=times, func=logistic,parms=parameters))
plot(out$X)