Uppgift A:15 

restart; -1; with(plots); -1 

`:=`(ode, {y(1) = 1, diff(y(x), x) = `+`(1, `*`(`^`(y(x), 3)))}) 

{y(1) = 1, diff(y(x), x) = `+`(1, `*`(`^`(y(x), 3)))} (4.1)
 

`:=`(sol, dsolve(ode, numeric, range = 1 .. 1.37)) 

proc (x_rkf45) local _res, _dat, _vars, _solnproc, _xout, _ndsol, _pars, _n, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if `<`(1, nargs) then error (4.2)
 

sol(1.1) 

[x = 1.1, y(x) = 1.23914482887952415] (4.3)
 

sol(1.2) 

[x = 1.2, y(x) = 1.62685503035695867] (4.4)
 

`:=`(p1, odeplot(sol, x = 1 .. 1.37, thickness = 2)) 

PLOT(CURVES(Array(1..50, 1..2, {(1, 1) = 1.0, (1, 2) = 1.0, (2, 1) = 1.0075510204082, (2, 2) = 1.0152761751564243, (3, 1) = 1.0151020408163, (3, 2) = 1.0309132915702637, (4, 1) = 1.0226530612245, (4, ... (4.5)
 

assume(n, integer) 

`:=`(y[0], 1) 

1 (4.6)
 

for n from 0 to 2 do `:=`(y[`+`(n, 1)], `+`(1, int(`+`(1, `*`(`^`(y[n], 3))), x = 1 .. x))) end do 

 

 

`+`(`-`(1), `*`(2, `*`(x)))
`+`(`*`(2, `*`(`^`(x, 4))), `-`(`*`(4, `*`(`^`(x, 3)))), `*`(3, `*`(`^`(x, 2))))
`+`(`-`(`/`(157, 910)), x, `*`(`/`(8, 13), `*`(`^`(x, 13))), `-`(`*`(4, `*`(`^`(x, 12)))), `*`(12, `*`(`^`(x, 11))), `-`(`*`(`/`(104, 5), `*`(`^`(x, 10)))), `*`(22, `*`(`^`(x, 9))), `-`(`*`(`/`(27, 2)... (4.7)
 

eval(y[3], x = 1.1) 

1.238671413 (4.8)
 

eval(y[3], x = 1.2) 

1.60863384 (4.9)
 

`:=`(p2, plot(y[3], x = 1 .. 1.5, color = BLUE, thickness = 2)) 

PLOT(CURVES([[1., .99999999999999956], [1.01089857708333342, 1.02216275393958345], [1.02038137072916668, 1.04207070779054778], [1.03104576395833325, 1.06520621960700090], [1.04178084770833323, 1.08935... (4.10)
 

display(p1, p2) 

Plot_2d