save_figs = FALSE

# Plot the solution:
# 
ts = seq(0, 2*pi, length.out=200 )
ys = -(1/5) * exp(-ts) * cos(2*ts) - (1/10) * exp(-ts) * sin(2*ts) + 1/5
c = -(1/5)*(1 + exp(pi/2))
mask = ts > pi/2
ys[mask] = c * exp(-ts[mask]) * cos(2*ts[mask]) + (c/2) * exp(-ts[mask]) * sin(2*ts[mask]) 

# Plot the right-hand-side:
#
rhs = rep(1, length(ts))
rhs[mask] = 0

y_min = min( c(ys, rhs) )
y_max = max( c(ys, rhs) )

if( save_figs ){ postscript("../../WriteUp/Graphics/Chapter3/chap_3_sect_5_prob_32_plot.eps", onefile=FALSE, horizontal=FALSE) }
plot(ts, ys, type='l', ylim=c(y_min, y_max), xlab='t', ylab='y(t)', main='Question 32')
lines(ts, rhs, type='l', col='red')
grid()
if( save_figs ){ dev.off() }