Differential equations functions, Jan 2023
diffeq_slopefield(function, [options])
Draws a slopefield for the given differential equation.
function: For a first order ODE, like dy/dx=x*y^2, use a single string, like "x*y^2"
.
For an autonomous system, like x'=x+y, y'=y-2x, list both parts, like "x+y,y-2x"
options is an optional associative array of parameters. You can define none or several of them. There are two common ways to define these:
Inline: $g = diffeq_slopefield("xy",['dx'=>0.5, 'arrows'=>1])
As a separate array:
$ops['dx'] = 0.5 $ops['arrows'] = 1 $g = diffeq_slopefield("xy",$ops)
The options you can set are:
diffeq_comparegensoln(expr1, expr2, vars, constants, [tolerance, domain])
Compares two general solutions to an ODE which contain arbitrary constants. They are compared in a way that allows swapping which constant goes where, and accomodates absorbed constants.
expr1: the first general solution, like "cos(t)+c_1*e^t+c_2*e^(-t)"
expr2: the second general solution
vars: the independent variables in the expression, like "t"
constants: the arbitrary constants in the expression, like "c_1,c_2"
tolerance: the relative tolerance to compare with. Default 0.001.
domain: the domain to compare on. Default "-10,10".