Plotting a solution of a differential equation : plotode odeplot

Let f (t, y) be an expression depending of two variables t and y.

• plotode(f (t, y),[t,y],[t0,y0]) draws the solution of the differential equation y' = f (t, y) crossing through the point (t0,y0) (i.e. such that y(t₀) = y₀)
• By default, t goes in both directions. The range of value of t may be specified by the optional argument t=tmin..tmax.
• We can also represent, in the space or in the plane, the solution of a differential equation y' = f (t, y) where y = (X, Y) is a vector of size 2. Just replace y by the variable names X, Y and the initial value y₀ by the two initial values of the variables at time t₀.

Input :

plotode(sin(t*y),[t,y],[0,1])

Output :

The graph of the solution of y'=sin(t,y) crossing through the point (0,1)

Input :

S:=odeplot([h-0.3*h*p, 0.3*h*p-p], [t,h,p],[0,0.3,0.7])

Output, the graph in the space of the solution of :

[h, p]' = [h - 0.3h*p, 0.3h*p - p]    [h, p](0) = [0.3, 0.7]

To have a 2-d graph (in the plane), use the option plane

S:=odeplot([h-0.3*h*p, 0.3*h*p-p], [t,h,p],[0,0.3,0.7],plane)

To compute the values of the solution, see the section .