3.33 How to make phase plot of first order ODE?
Make a phase plot of
\[ y'(x) = \sqrt {y(x)^{2}-1} \]
The phase plot has \(x\) on the x axis and has \(y\) on the y axis. It shows the family of solutions
for different initial conditions.
restart;
ode:=diff(y(x), x) = sqrt(y(x)^2 - 1);
DEtools:-DEplot(ode,y(x),x=-2..2,y=1..3)
To show specific solution curve that passes via some initial conditions such as \(y(0)=2\) then
do
restart;
ode:=diff(y(x), x) = sqrt(y(x)^2 - 1);
DEtools:-DEplot(ode,y(x),x=-2..2,y=1..3,[y(0)=2])