Plotting Slope Fields using Graph

y' = x² + y² - r²  (r = 0, 1, 2, ..., 7)

y' = (x + y)/(x - y)  (method 1)

y' = (x + y)/(x - y)  (method 2)

y' = sin(x)/y + sin(y)/x

y' = cos(x) + cos(y)

y' = cos(x) sqrt(1+x²) + cos(y) sqrt(1+y²)

Download Examples:

• slope_field.zip

( Mathematical software used: Graph )

A Monster Equation

x² + y² - a[exp(sin³(x-y)) + exp(sin³(-x-y))]² = c

• x and y are variables.
• a and c are parameters.

(a = 3, c = 0.5)

Scilab script:

clear;
clf();
xset("wdim",400,400);
xset("fpf"," ");
xset("thickness", 2);
square(-8.2,-8.2,8.2,8.2);

a = 3;
c = 0.5;
function z = fun(x,y)
   z = x^2 + y^2 - a*(exp(sin(x-y)^3) + exp(sin(-x-y)^3))^2 - c;
endfunction
data = linspace(-8.2, 8.2, 2000);

contour2d(data, data, fun, [0,0], style=color("red"), axesflag=0);

(a = -1, c = 24)

(a = -2, c = 50)

( Mathematical software used: Scilab )