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[01] Various Functions
1. f(x,y) = x^4 + xy - y^4
15. f(x,y) = x^3 - 3xy + y^3
18. f(x,y) = x^3 + 3xy + y^3
2. f(x,y) = (y - x^2)^2 + x^5
3. f(x,y) = x^2y^2 / (x^2 + y^2), f(0,0) = 0.0
4. f(x,y) = (x - y) / (x + y)
5. f(x,y) = |x|^y, f(0,y) = 0.0
6. f(x,y) = xy*log(x^2 + y^2), f(0,0) = 0.0
7. f(x,y) = exp(-|x + y|*(x^2 + y^2))
8. f(x,y) = sqrt(|xy|)
9. f(x,y) = sqrt(x^2 + y^2)
10. f(x,y) = xy / sqrt(x^2 + y^2), f(0,0) = 0.0
11. f(x,y) = xy * sin( 1 / sqrt(x^2 + y^2)), f(0,0) = 0.0
12. f(x,y) = x^y * y^x
13. f(x,y) = e^(-abs(x + y)/(x^2 + y^2)), f(0,0) = 0.0
14. f(x,y) = log(x^2 + y^2), f(0, y) = - infty
16. f(x,y) = exp(-(x^2 + y^2) * sin(x + y))
17. f(x,y) = x^4 + 2*x^2*y^2 - 6*x^2*y + y^2
19. f(x,y) = x^2 + xy + y^2 - 4x - 2y
20. f(x,y) = x*sin(y / x), f(0,y) = 0.0
21. f(x,y) = exp(-(x^3 + y^3) * sin(x + y))
22. f(x,y) = x^4 + y^4 - 2(x^2 + y^2)
23. f(x,y) = sqrt((x^2 - y^2 - 1)^2 + 4 * x^2 * y^2)
[02] Complex Functions (Absolute Value)
f(x,y) = |sin(ω)|, ω = x + iy
f(x,y) = |cos(ω)|, ω = x + iy
f(x,y) = |Γ(ω)|, ω = x + iy
[03] Functions Covered in "Differential Equations: Plotting Trajectory of Solutions
;01. f(x,y) = (x^2 + y^2 + a^2)^2 - 4a^2x^2 - b^4, a = 0.6, b=0.4 Cassini Ovals
03. f(x,y) = cos(y) - cos(x)
[09] User Defined
01. User Defined
02. Sample 1: Function shown in the example of input
03. Sample 2: Function shown in long formula

$f(x, y) = $

$\quad$ where, $\quad r = $

Coefficient

$a:$ $d:$
$b:$ $e:$
$c:$ $f:$

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