Plotting solutions of differential equations

### 19.8.3 Plotting solutions of differential equations

The plotode or odeplot command draws solutions of differential equations.

- plotode takes three mandatory arguments and one optional argument:
  - expr an expression depending on two or three variables, a time variable and one or two dependent variables.
  - vars, a list of the time variable and the dependent variable. The time variable can optionally have a range of values, such as t=a..b. The dependent variable can also be a vector of size two.
  - init, the initial values of the variables.
  - Optionally, for when there are two dependent variables, plane, the symbol, to draw the solution in the plane.
- plotode(expr,vars,init) draws the solution of the differential equation y′=expr (where y is the dependent variable) passing through the initial point init.

To compute the values of the solutions, see Section 23.4.1.

#### Examples

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

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

Input for a 2D graph in the plane:

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