Yum
a Math problem
y'
y x -> kx - y ...
x,y = c [0 1 k k^2-1 k^3-2k k^4-3k^2+1 ...] and j = c^2
e.g. k = 4: 0 1 4 15 56 209 ... see below graph
... ky-x <- y x
x'
30 _| /
| p(y,x) = y^2 - 4 x y + x^2-1 = 0 => p(y',x)=0, y' = 4x-y
| / p(y,x')=0, x' = 4y-x
| y = 2 x +- sqrt(3 x^2 + 1)
| /
| ~= ( 2 +- sqrt(3)) x ~= {3.73, 0.27} x
20 _| /
|
| / 4,15 <== 4 + 56 = 4(15) <== 56,15
| #. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .#
| /. || x' + x = 4 y _ -
| . \/ _ -
10 _| / . _ -
| . _ -
| / . _ - 0 <- 1 <- 4 <- 15 <- 56
| . 15,4 _ -
1,4 |# . _ # 1,0 <== 4,1 <== 4,15 <== 56,15
|/ . _ -
|#---#-------------------------------------------------------------
1,0 <= 4,1 | | | | |
. 10 20 30 40 50
.
... y' + y = 4 x
1 + 15 = 4(4)
|