# TA2 - Graphic, Numeric, Analytic
# -----------------------------------------------------
library(ggplot2)

# Q7
# ---------

Dt = 
numericSolution = data.frame(t = seq(0,1,Dt), 
                             x = numeric(length = length(seq(0,1,Dt))), 
                             dxdt = numeric(length = length(seq(0,1,Dt))), 
                             dxdtDt = numeric(length = length(seq(0,1,Dt))))

numericSolution$x[1] = 1

for(row in 1:length(seq(0,1,Dt))){
  if(row > 1) {
    numericSolution$x[row] = numericSolution$x[row-1]+numericSolution$dxdtDt[row-1]
  }
  numericSolution$dxdt[row] = (3/numericSolution$x[row])+1
  numericSolution$dxdtDt[row] = numericSolution$dxdt[row]*Dt
}

ggplot(numericSolution, aes(x = t, y = x)) +
  geom_point() +
  geom_line() +
  labs(title = paste0("X as a function of t - Dt = ",Dt)) +
  theme_light()

ggplot(numericSolution, aes(x = t, y = dxdt)) +
  geom_point() +
  geom_line() +
  labs(title = paste0("dx/dt as a function of t - Dt = ",Dt)) +
  theme_light()

ggplot(numericSolution, aes(x = x, y = dxdt)) +
  geom_point() +
  geom_line() +
  labs(title = paste0("dx/dt as a function of x - Dt = ",Dt)) +
  theme_light()