nm

6778 Reputation

18 Badges

10 years, 34 days

MaplePrimes Activity


These are answers submitted by nm

There are many ways,. Here are two 

restart;

ode:=diff(y(x),x$2)+diff(y(x),x)+y(x)=0;
sol:=dsolve(ode);

diff(diff(y(x), x), x)+diff(y(x), x)+y(x) = 0

y(x) = _C1*exp(-(1/2)*x)*sin((1/2)*3^(1/2)*x)+_C2*exp(-(1/2)*x)*cos((1/2)*3^(1/2)*x)

diff(rhs(sol),x)

-(1/2)*_C1*exp(-(1/2)*x)*sin((1/2)*3^(1/2)*x)+(1/2)*_C1*exp(-(1/2)*x)*3^(1/2)*cos((1/2)*3^(1/2)*x)-(1/2)*_C2*exp(-(1/2)*x)*cos((1/2)*3^(1/2)*x)-(1/2)*_C2*exp(-(1/2)*x)*3^(1/2)*sin((1/2)*3^(1/2)*x)

sol := unapply(rhs(sol),x);

proc (x) options operator, arrow; _C1*exp(-(1/2)*x)*sin((1/2)*3^(1/2)*x)+_C2*exp(-(1/2)*x)*cos((1/2)*3^(1/2)*x) end proc

diff(sol(x),x)

-(1/2)*_C1*exp(-(1/2)*x)*sin((1/2)*3^(1/2)*x)+(1/2)*_C1*exp(-(1/2)*x)*3^(1/2)*cos((1/2)*3^(1/2)*x)-(1/2)*_C2*exp(-(1/2)*x)*cos((1/2)*3^(1/2)*x)-(1/2)*_C2*exp(-(1/2)*x)*3^(1/2)*sin((1/2)*3^(1/2)*x)

diff(sol(x),x$2)

-(1/2)*_C1*exp(-(1/2)*x)*sin((1/2)*3^(1/2)*x)-(1/2)*_C1*exp(-(1/2)*x)*3^(1/2)*cos((1/2)*3^(1/2)*x)-(1/2)*_C2*exp(-(1/2)*x)*cos((1/2)*3^(1/2)*x)+(1/2)*_C2*exp(-(1/2)*x)*3^(1/2)*sin((1/2)*3^(1/2)*x)

 

Download diff.mw

You can also make y(x) itself a function. But I think it is better to use sol and keep y as free variable.

restart;

ode:=diff(y(x),x$2)+diff(y(x),x)+y(x)=0;
sol:=dsolve(ode);

diff(diff(y(x), x), x)+diff(y(x), x)+y(x) = 0

y(x) = _C1*exp(-(1/2)*x)*sin((1/2)*3^(1/2)*x)+_C2*exp(-(1/2)*x)*cos((1/2)*3^(1/2)*x)

y := unapply(rhs(sol),x);
diff(y(x),x)

proc (x) options operator, arrow; _C1*exp(-(1/2)*x)*sin((1/2)*3^(1/2)*x)+_C2*exp(-(1/2)*x)*cos((1/2)*3^(1/2)*x) end proc

-(1/2)*_C1*exp(-(1/2)*x)*sin((1/2)*3^(1/2)*x)+(1/2)*_C1*exp(-(1/2)*x)*3^(1/2)*cos((1/2)*3^(1/2)*x)-(1/2)*_C2*exp(-(1/2)*x)*cos((1/2)*3^(1/2)*x)-(1/2)*_C2*exp(-(1/2)*x)*3^(1/2)*sin((1/2)*3^(1/2)*x)

 

Download diff2.mw

looks like numerical issue. Try

restart;
sol:=[solve((20 + 20*T + 2*T*(T + 1))*exp(-T) - 10*exp(-2*T) - 2*T - 10 = 0,T)];
evalf~(sol)

Gives

         [-10.0000000000, -0.0000000000]

PDEtools gives just zero as answer

restart;
sol:=PDEtools:-Solve((20 + 20*T + 2*T*(T + 1))*exp(-T) - 10*exp(-2*T) - 2*T - 10 = 0,T);
evalf(sol)

This is hard to solve exactly, so use root finder

restart;
eq:=(20 + 20*T + 2*T*(T + 1))*exp(-T) - 10*exp(-2*T) - 2*T - 10 = 0;
Student:-Calculus1:-Roots(eq, 0..2);

 

         [0, 1.4114548230]

 

Maple 2022.1 on windows 10.

 

Try to see if this works for you.   Maple 2022.1

 

restart;
with(Statistics):
with(stats):
y_a:=t->piecewise(0<=t and t<=1,DynamicSystems:-Sine(1.5*t,10*Pi,0,0),1<=t and t<=2,DynamicSystems:-Sine(1.5*(2-t),10*Pi,0,0));
plot(y_a(t),t=0..2);
mu:=t->statevalf[pdf,normald[1,2*4.47]](t);
plot(mu(t),t=0..2);
y:=t->y_a(t)+mu(t);
plot(y(t),t=0..2)

 

type

ssystem("powershell.exe get-process")

restart;

ode:=diff(y(x),x$2)+ 4*diff(y(x),x) + 4*y(x) = sin(x);
ic:=y(0) = 1 , D(y)(0)=0;
sol_analytic:=dsolve([ode,ic]);
sol_numeric:=dsolve([ode,ic], numeric, method = gear,output=listprocedure):
sol_numeric := eval(y(x),sol_numeric):

diff(diff(y(x), x), x)+4*(diff(y(x), x))+4*y(x) = sin(x)

y(0) = 1, (D(y))(0) = 0

y(x) = (29/25)*exp(-2*x)+(11/5)*exp(-2*x)*x-(4/25)*cos(x)+(3/25)*sin(x)

p1:=plot(rhs(sol_analytic),x=0..10,title="analytic",gridlines,color=blue):

p2:=plot(sol_numeric(x),x=0..10,title="numerical",gridlines,color=red):

[p1,p2]

[INTERFACE_PLOT(CURVES(Matrix(400, 2, {(1, 1) = 0.125e-1, (1, 2) = 1.0000423877313804, (2, 1) = 0.375e-1, (2, 2) = .9973327142, (3, 1) = 0.625e-1, (3, 2) = .9928472474, (4, 1) = 0.875e-1, (4, 2) = .986464337, (5, 1) = .1125, (5, 2) = .978394552, (6, 1) = .1375, (6, 2) = .9688324054, (7, 1) = .1625, (7, 2) = .9579574074, (8, 1) = .1875, (8, 2) = .9459350565, (9, 1) = .2125, (9, 2) = .9329177703, (10, 1) = .2375, (10, 2) = .9190457616, (11, 1) = .2625, (11, 2) = .9044478513, (12, 1) = .2875, (12, 2) = .8892422422, (13, 1) = .3125, (13, 2) = .8735372392, (14, 1) = .3375, (14, 2) = .8574319204, (15, 1) = .3625, (15, 2) = .8410167742000001, (16, 1) = .3875, (16, 2) = .8243742917000001, (17, 1) = .4125, (17, 2) = .8075795233, (18, 1) = .4375, (18, 2) = .7907005984, (19, 1) = .4625, (19, 2) = .7737992144, (20, 1) = .4875, (20, 2) = .7569310936, (21, 1) = .5125, (21, 2) = .74014641, (22, 1) = .5375, (22, 2) = .7234901913, (23, 1) = .5625, (23, 2) = .7070026915000001, (24, 1) = .5875, (24, 2) = .6907197426, (25, 1) = .6125, (25, 2) = .6746730816, (26, 1) = .6375, (26, 2) = .6588906583, (27, 1) = .6625, (27, 2) = .6433969196, (28, 1) = .6875, (28, 2) = .6282130779, (29, 1) = .7125, (29, 2) = .613357362, (30, 1) = .7375, (30, 2) = .5988452491, (31, 1) = .7625, (31, 2) = .5846896836, (32, 1) = .7875000000000001, (32, 2) = .5709012795999999, (33, 1) = .8125, (33, 2) = .5574885112, (34, 1) = .8375, (34, 2) = .5444578901, (35, 1) = .8625, (35, 2) = .5318141283, (36, 1) = .8875, (36, 2) = .5195602935, (37, 1) = .9125, (37, 2) = .5076979519, (38, 1) = .9375, (38, 2) = .4962273016, (39, 1) = .9625, (39, 2) = .4851472953, (40, 1) = .9875, (40, 2) = .4744557567, (41, 1) = 1.0125, (41, 2) = .46414948840000003, (42, 1) = 1.0375, (42, 2) = .4542243701, (43, 1) = 1.0625, (43, 2) = .444675452, (44, 1) = 1.0875, (44, 2) = .4354970398, (45, 1) = 1.1125, (45, 2) = .4266827761, (46, 1) = 1.1375, (46, 2) = .4182257127, (47, 1) = 1.1625, (47, 2) = .41011838, (48, 1) = 1.1875, (48, 2) = .4023528497, (49, 1) = 1.2125, (49, 2) = .3949207939, (50, 1) = 1.2375, (50, 2) = .3878135398, (51, 1) = 1.2625, (51, 2) = .3810221188, (52, 1) = 1.2875, (52, 2) = .3745373137, (53, 1) = 1.3125, (53, 2) = .3683497007, (54, 1) = 1.3375, (54, 2) = .3624496893, (55, 1) = 1.3625, (55, 2) = .3568275585, (56, 1) = 1.3875, (56, 2) = .3514734893, (57, 1) = 1.4125, (57, 2) = .346377596, (58, 1) = 1.4375, (58, 2) = .3415299548, (59, 1) = 1.4625, (59, 2) = .336920628, (60, 1) = 1.4875, (60, 2) = .3325396891, (61, 1) = 1.5125, (61, 2) = .328377243, (62, 1) = 1.5375, (62, 2) = .3244234463, (63, 1) = 1.5625, (63, 2) = .32073589950000003, (64, 1) = 1.5875, (64, 2) = .3171027922, (65, 1) = 1.6125, (65, 2) = .3137166588, (66, 1) = 1.6375, (66, 2) = .310500651, (67, 1) = 1.6625, (67, 2) = .3074454201, (68, 1) = 1.6875, (68, 2) = .3045417542, (69, 1) = 1.7125, (69, 2) = .3017805873, (70, 1) = 1.7375, (70, 2) = .2991530082, (71, 1) = 1.7625, (71, 2) = .2966502679, (72, 1) = 1.7875, (72, 2) = .2942637866, (73, 1) = 1.8125, (73, 2) = .2919851599, (74, 1) = 1.8375, (74, 2) = .2898061636, (75, 1) = 1.8625, (75, 2) = .2877187584, (76, 1) = 1.8875, (76, 2) = .2857150935, (77, 1) = 1.9125, (77, 2) = .2837875106, (78, 1) = 1.9375, (78, 2) = .2819285456, (79, 1) = 1.9625, (79, 2) = .2801309317, (80, 1) = 1.9875, (80, 2) = .2783876008, (81, 1) = 2.0125, (81, 2) = .2766916847, (82, 1) = 2.0375, (82, 2) = .2750365164, (83, 1) = 2.0625, (83, 2) = .2734156305, (84, 1) = 2.0875, (84, 2) = .2718227635, (85, 1) = 2.1125, (85, 2) = .2702518534, (86, 1) = 2.1375, (86, 2) = .2686970404, (87, 1) = 2.1625, (87, 2) = .2671526653, (88, 1) = 2.1875, (88, 2) = .265613269, (89, 1) = 2.2125, (89, 2) = .2640735921, (90, 1) = 2.2375, (90, 2) = .2625285729, (91, 1) = 2.2625, (91, 2) = .2609733467, (92, 1) = 2.2875, (92, 2) = .2594032438, (93, 1) = 2.3125, (93, 2) = .2578137881, (94, 1) = 2.3375, (94, 2) = .2562006955, (95, 1) = 2.3625, (95, 2) = .254559872, (96, 1) = 2.3875, (96, 2) = .2528874112, (97, 1) = 2.4125, (97, 2) = .2511795931, (98, 1) = 2.4375, (98, 2) = .2494328808, (99, 1) = 2.4625, (99, 2) = .2476439197, (100, 1) = 2.4875, (100, 2) = .2458095339, (101, 1) = 2.5125, (101, 2) = .2439267247, (102, 1) = 2.5375, (102, 2) = .2419926678, (103, 1) = 2.5625, (103, 2) = .240004711, (104, 1) = 2.5875, (104, 2) = .2379603716, (105, 1) = 2.6125, (105, 2) = .2358573341, (106, 1) = 2.6375, (106, 2) = .2336934474, (107, 1) = 2.6625, (107, 2) = .2314667223, (108, 1) = 2.6875, (108, 2) = .2291753291, (109, 1) = 2.7125, (109, 2) = .2268175947, (110, 1) = 2.7375, (110, 2) = .2243919999, (111, 1) = 2.7625, (111, 2) = .2218971774, (112, 1) = 2.7875, (112, 2) = .219331908, (113, 1) = 2.8125, (113, 2) = .2166951191, (114, 1) = 2.8375, (114, 2) = .2139858818, (115, 1) = 2.8625, (115, 2) = .211203407, (116, 1) = 2.8875, (116, 2) = .2083470442, (117, 1) = 2.9125, (117, 2) = .2054162784, (118, 1) = 2.9375, (118, 2) = .2024107273, (119, 1) = 2.9625, (119, 2) = .1993301377, (120, 1) = 2.9875, (120, 2) = .196174385, (121, 1) = 3.0125, (121, 2) = .1929434681, (122, 1) = 3.0375, (122, 2) = .1896375084, (123, 1) = 3.0625, (123, 2) = .1862567461, (124, 1) = 3.0875, (124, 2) = .1828015384, (125, 1) = 3.1125, (125, 2) = .1792723556, (126, 1) = 3.1375, (126, 2) = .17567582646954935, (127, 1) = 3.1625, (127, 2) = .1719945016, (128, 1) = 3.1875, (128, 2) = .1682473168, (129, 1) = 3.2125, (129, 2) = .1644291248, (130, 1) = 3.2375, (130, 2) = .1605409252, (131, 1) = 3.2625, (131, 2) = .1565838155, (132, 1) = 3.2875, (132, 2) = .1525589883, (133, 1) = 3.3125, (133, 2) = .1484677289, (134, 1) = 3.3375, (134, 2) = .144311412, (135, 1) = 3.3625, (135, 2) = .1400914997, (136, 1) = 3.3875, (136, 2) = .1358095388, (137, 1) = 3.4125, (137, 2) = .1314671577, (138, 1) = 3.4375, (138, 2) = .1270660644, (139, 1) = 3.4625, (139, 2) = .1226080431, (140, 1) = 3.4875, (140, 2) = .1180949527, (141, 1) = 3.5125, (141, 2) = .1135287228, (142, 1) = 3.5375, (142, 2) = .1089113522, (143, 1) = 3.5625, (143, 2) = .104244906, (144, 1) = 3.5875, (144, 2) = 0.9953151258e-1, (145, 1) = 3.6125, (145, 2) = 0.9477336139e-1, (146, 1) = 3.6375, (146, 2) = 0.8997270075e-1, (147, 1) = 3.6625, (147, 2) = 0.851318342e-1, (148, 1) = 3.6875, (148, 2) = 0.8025311905999999e-1, (149, 1) = 3.7125, (149, 2) = 0.7533896322e-1, (150, 1) = 3.7375, (150, 2) = 0.7039182246e-1, (151, 1) = 3.7625, (151, 2) = 0.6541419858e-1, (152, 1) = 3.7875, (152, 2) = 0.6040863626e-1, (153, 1) = 3.8125, (153, 2) = 0.5537772081e-1, (154, 1) = 3.8375, (154, 2) = 0.5032407561e-1, (155, 1) = 3.8625, (155, 2) = 0.4525035926e-1, (156, 1) = 3.8875, (156, 2) = 0.4015926362e-1, (157, 1) = 3.9125, (157, 2) = 0.3505351112e-1, (158, 1) = 3.9375, (158, 2) = 0.2993585227e-1, (159, 1) = 3.9625, (159, 2) = 0.2480906275e-1, (160, 1) = 3.9875, (160, 2) = 0.1967594199e-1, (161, 1) = 4.0125, (161, 2) = 0.1453930939e-1, (162, 1) = 4.0375, (162, 2) = 0.940200324e-2, (163, 1) = 4.0625, (163, 2) = 0.42668773e-2, (164, 1) = 4.0875, (164, 2) = -0.86320121e-3, (165, 1) = 4.1125, (165, 2) = -0.59853539e-2, (166, 1) = 4.1375, (166, 2) = -0.110966938e-1, (167, 1) = 4.1625, (167, 2) = -0.161943276e-1, (168, 1) = 4.1875, (168, 2) = -0.2127535808e-1, (169, 1) = 4.2125, (169, 2) = -0.263368862e-1, (170, 1) = 4.2375, (170, 2) = -0.3137601363e-1, (171, 1) = 4.2625, (171, 2) = -0.3638984493e-1, (172, 1) = 4.2875, (172, 2) = -0.4137548998e-1, (173, 1) = 4.3125, (173, 2) = -0.4633006585e-1, (174, 1) = 4.3375, (174, 2) = -0.5125069947e-1, (175, 1) = 4.3625, (175, 2) = -0.5613452929e-1, (176, 1) = 4.3875, (176, 2) = -0.6097870823e-1, (177, 1) = 4.4125, (177, 2) = -0.6578040492000001e-1, (178, 1) = 4.4375, (178, 2) = -0.7053680646e-1, (179, 1) = 4.4625, (179, 2) = -0.7524512039e-1, (180, 1) = 4.4875, (180, 2) = -0.7990257641e-1, (181, 1) = 4.5125, (181, 2) = -0.8450642912e-1, (182, 1) = 4.5375, (182, 2) = -0.8905395922e-1, (183, 1) = 4.5625, (183, 2) = -0.9354247617e-1, (184, 1) = 4.5875, (184, 2) = -0.9796931984e-1, (185, 1) = 4.6125, (185, 2) = -.1023318624, (186, 1) = 4.6375, (186, 2) = -.1066275104, (187, 1) = 4.6625, (187, 2) = -.1108537064, (188, 1) = 4.6875, (188, 2) = -.1150079313, (189, 1) = 4.7125, (189, 2) = -.1190874138678, (190, 1) = 4.7375, (190, 2) = -.1230905903, (191, 1) = 4.7625, (191, 2) = -.1270141917, (192, 1) = 4.7875, (192, 2) = -.1308561597, (193, 1) = 4.8125, (193, 2) = -.1346141912, (194, 1) = 4.8375, (194, 2) = -.1382860313, (195, 1) = 4.8625, (195, 2) = -.141869475, (196, 1) = 4.8875, (196, 2) = -.1453623686, (197, 1) = 4.9125, (197, 2) = -.1487626114, (198, 1) = 4.9375, (198, 2) = -.1520681571, (199, 1) = 4.9625, (199, 2) = -.1552770152, (200, 1) = 4.9875, (200, 2) = -.1583872522, (201, 1) = 5.0125, (201, 2) = -.1613969932, (202, 1) = 5.0375, (202, 2) = -.1643044233, (203, 1) = 5.0625, (203, 2) = -.1671077887, (204, 1) = 5.0875, (204, 2) = -.1698053976, (205, 1) = 5.1125, (205, 2) = -.172395622, (206, 1) = 5.1375, (206, 2) = -.1748768984, (207, 1) = 5.1625, (207, 2) = -.177247729, (208, 1) = 5.1875, (208, 2) = -.1795066826, (209, 1) = 5.2125, (209, 2) = -.1816523959, (210, 1) = 5.2375, (210, 2) = -.1836835743, (211, 1) = 5.2625, (211, 2) = -.1855989926, (212, 1) = 5.2875, (212, 2) = -.1873974962, (213, 1) = 5.3125, (213, 2) = -.1890780016, (214, 1) = 5.3375, (214, 2) = -.1906394973, (215, 1) = 5.3625, (215, 2) = -.1920810446, (216, 1) = 5.3875, (216, 2) = -.1934017779, (217, 1) = 5.4125, (217, 2) = -.1946009058, (218, 1) = 5.4375, (218, 2) = -.1956777115, (219, 1) = 5.4625, (219, 2) = -.1966315528, (220, 1) = 5.4875, (220, 2) = -.1974618634, (221, 1) = 5.5125, (221, 2) = -.1981681527, (222, 1) = 5.5375, (222, 2) = -.1987500066, (223, 1) = 5.5625, (223, 2) = -.1992070873, (224, 1) = 5.5875, (224, 2) = -.1995391338, (225, 1) = 5.6125, (225, 2) = -.1997459627, (226, 1) = 5.6375, (226, 2) = -.199827467, (227, 1) = 5.6625, (227, 2) = -.1997836179, (228, 1) = 5.6875, (228, 2) = -.1996144632, (229, 1) = 5.7125, (229, 2) = -.1993201286, (230, 1) = 5.7375, (230, 2) = -.198900817, (231, 1) = 5.7625, (231, 2) = -.1983568088, (232, 1) = 5.7875, (232, 2) = -.1976884608, (233, 1) = 5.8125, (233, 2) = -.1968962078, (234, 1) = 5.8375, (234, 2) = -.1959805604, (235, 1) = 5.8625, (235, 2) = -.1949421063, (236, 1) = 5.8875, (236, 2) = -.1937815088, (237, 1) = 5.9125, (237, 2) = -.1924995069, (238, 1) = 5.9375, (238, 2) = -.1910969155, (239, 1) = 5.9625, (239, 2) = -.1895746235, (240, 1) = 5.9875, (240, 2) = -.1879335945, (241, 1) = 6.0125, (241, 2) = -.1861748654, (242, 1) = 6.0375, (242, 2) = -.1842995468, (243, 1) = 6.0625, (243, 2) = -.1823088209, (244, 1) = 6.0875, (244, 2) = -.180203942, (245, 1) = 6.1125, (245, 2) = -.1779862354, (246, 1) = 6.1375, (246, 2) = -.1756570961, (247, 1) = 6.1625, (247, 2) = -.1732179888, (248, 1) = 6.1875, (248, 2) = -.1706704459, (249, 1) = 6.2125, (249, 2) = -.168016068, (250, 1) = 6.2375, (250, 2) = -.1652565213, (251, 1) = 6.2625, (251, 2) = -.162393538, (252, 1) = 6.2875, (252, 2) = -.1594304279691601, (253, 1) = 6.3125, (253, 2) = -.1563645099, (254, 1) = 6.3375, (254, 2) = -.1532022461, (255, 1) = 6.3625, (255, 2) = -.1499441053, (256, 1) = 6.387499999999999, (256, 2) = -.1465921299, (257, 1) = 6.4125, (257, 2) = -.1431484201, (258, 1) = 6.4375, (258, 2) = -.1396151335, (259, 1) = 6.4625, (259, 2) = -.1359944834, (260, 1) = 6.4875, (260, 2) = -.1322887376, (261, 1) = 6.512499999999999, (261, 2) = -.1285002166, (262, 1) = 6.5375, (262, 2) = -.1246312924, (263, 1) = 6.5625, (263, 2) = -.1206843874, (264, 1) = 6.5875, (264, 2) = -.1166619725, (265, 1) = 6.6125, (265, 2) = -.1125665652, (266, 1) = 6.637499999999999, (266, 2) = -.1084007287, (267, 1) = 6.6625, (267, 2) = -.1041670702, (268, 1) = 6.6875, (268, 2) = -0.9986823885e-1, (269, 1) = 6.7125, (269, 2) = -0.9550692464e-1, (270, 1) = 6.7375, (270, 2) = -0.9108585629e-1, (271, 1) = 6.762499999999999, (271, 2) = -0.8660779972e-1, (272, 1) = 6.7875, (272, 2) = -0.8207555649e-1, (273, 1) = 6.8125, (273, 2) = -0.7749196174e-1, (274, 1) = 6.8375, (274, 2) = -0.7285988257e-1, (275, 1) = 6.8625, (275, 2) = -0.6818221638e-1, (276, 1) = 6.887499999999999, (276, 2) = -0.6346188896e-1, (277, 1) = 6.9125, (277, 2) = -0.58701852590000006e-1, (278, 1) = 6.9375, (278, 2) = -0.5390508423e-1, (279, 1) = 6.9625, (279, 2) = -0.4907458378e-1, (280, 1) = 6.9875, (280, 2) = -0.4421337196e-1, (281, 1) = 7.012499999999999, (281, 2) = -0.3932448909e-1, (282, 1) = 7.0375, (282, 2) = -0.3441099193e-1, (283, 1) = 7.0625, (283, 2) = -0.2947595321e-1, (284, 1) = 7.0875, (284, 2) = -0.2452245864e-1, (285, 1) = 7.1125, (285, 2) = -0.1955360572e-1, (286, 1) = 7.137499999999999, (286, 2) = -0.1457250118e-1, (287, 1) = 7.1625, (287, 2) = -0.958225946e-2, (288, 1) = 7.1875, (288, 2) = -0.45860007e-2, (289, 1) = 7.2125, (289, 2) = 0.41315132e-3, (290, 1) = 7.2375, (290, 2) = 0.541207109e-2, (291, 1) = 7.262499999999999, (291, 2) = 0.1040763327e-1, (292, 1) = 7.2875, (292, 2) = 0.1539671462e-1, (293, 1) = 7.3125, (293, 2) = 0.2037619616e-1, (294, 1) = 7.3375, (294, 2) = 0.2534296469e-1, (295, 1) = 7.3625, (295, 2) = 0.302939153e-1, (296, 1) = 7.387499999999999, (296, 2) = 0.352259529e-1, (297, 1) = 7.4125, (297, 2) = 0.4013599408e-1, (298, 1) = 7.4375, (298, 2) = 0.450209695e-1, (299, 1) = 7.4625, (299, 2) = 0.4987782534e-1, (300, 1) = 7.4875, (300, 2) = 0.547035254e-1, (301, 1) = 7.512499999999999, (301, 2) = 0.594950532e-1, (302, 1) = 7.5375, (302, 2) = 0.6424941334e-1, (303, 1) = 7.5625, (303, 2) = 0.6896363389e-1, (304, 1) = 7.5875, (304, 2) = 0.7363476794e-1, (305, 1) = 7.6125, (305, 2) = 0.7825989556e-1, (306, 1) = 7.637499999999999, (306, 2) = 0.8283612557e-1, (307, 1) = 7.6625, (307, 2) = 0.873605975e-1, (308, 1) = 7.6875, (308, 2) = 0.9183048314e-1, (309, 1) = 7.7125, (309, 2) = 0.9624298843e-1, (310, 1) = 7.7375, (310, 2) = .1005953553, (311, 1) = 7.762499999999999, (311, 2) = .1048848629, (312, 1) = 7.7875, (312, 2) = .1091088304, (313, 1) = 7.8125, (313, 2) = .1132646172, (314, 1) = 7.8375, (314, 2) = .1173496259, (315, 1) = 7.8625, (315, 2) = .121365550997, (316, 1) = 7.887499999999999, (316, 2) = .1252971409, (317, 1) = 7.9125, (317, 2) = .1291546795, (318, 1) = 7.9375, (318, 2) = .1329315078, (319, 1) = 7.9625, (319, 2) = .1366252649, (320, 1) = 7.9875, (320, 2) = .140233642, (321, 1) = 8.0125, (321, 2) = .1437543838, (322, 1) = 8.0375, (322, 2) = .1471852897, (323, 1) = 8.0625, (323, 2) = .1505242151, (324, 1) = 8.0875, (324, 2) = .153769073, (325, 1) = 8.1125, (325, 2) = .1569178355, (326, 1) = 8.1375, (326, 2) = .1599685342, (327, 1) = 8.1625, (327, 2) = .1629192624, (328, 1) = 8.1875, (328, 2) = .1657681757, (329, 1) = 8.2125, (329, 2) = .1685134936, (330, 1) = 8.2375, (330, 2) = .1711535001, (331, 1) = 8.2625, (331, 2) = .173686545, (332, 1) = 8.2875, (332, 2) = .1761110451, (333, 1) = 8.3125, (333, 2) = .1784254851, (334, 1) = 8.3375, (334, 2) = .1806284182, (335, 1) = 8.3625, (335, 2) = .1827184676, (336, 1) = 8.3875, (336, 2) = .1846943271, (337, 1) = 8.412500000000001, (337, 2) = .1865547614, (338, 1) = 8.4375, (338, 2) = .1882986078, (339, 1) = 8.4625, (339, 2) = .1899247764, (340, 1) = 8.4875, (340, 2) = .1914322507, (341, 1) = 8.5125, (341, 2) = .1928200885, (342, 1) = 8.537500000000001, (342, 2) = .1940874223, (343, 1) = 8.5625, (343, 2) = .1952334599, (344, 1) = 8.5875, (344, 2) = .196257485, (345, 1) = 8.6125, (345, 2) = .1971588576, (346, 1) = 8.6375, (346, 2) = .1979370142, (347, 1) = 8.6625, (347, 2) = .1985914685, (348, 1) = 8.6875, (348, 2) = .1991218113, (349, 1) = 8.7125, (349, 2) = .1995277111, (350, 1) = 8.7375, (350, 2) = .1998089142, (351, 1) = 8.7625, (351, 2) = .1999652445, (352, 1) = 8.7875, (352, 2) = .1999966047, (353, 1) = 8.8125, (353, 2) = .1999029747, (354, 1) = 8.8375, (354, 2) = .1996844133, (355, 1) = 8.8625, (355, 2) = .1993410568, (356, 1) = 8.8875, (356, 2) = .1988731199, (357, 1) = 8.9125, (357, 2) = .1982808949, (358, 1) = 8.9375, (358, 2) = .1975647518, (359, 1) = 8.9625, (359, 2) = .1967251382, (360, 1) = 8.9875, (360, 2) = .1957625788, (361, 1) = 9.0125, (361, 2) = .194677675, (362, 1) = 9.0375, (362, 2) = .193471105, (363, 1) = 9.0625, (363, 2) = .1921436227, (364, 1) = 9.0875, (364, 2) = .1906960576, (365, 1) = 9.1125, (365, 2) = .1891293146, (366, 1) = 9.1375, (366, 2) = .1874443726, (367, 1) = 9.1625, (367, 2) = .1856422847, (368, 1) = 9.1875, (368, 2) = .183724177, (369, 1) = 9.2125, (369, 2) = .1816912485, (370, 1) = 9.2375, (370, 2) = .1795447692, (371, 1) = 9.2625, (371, 2) = .1772860811, (372, 1) = 9.2875, (372, 2) = .1749165954, (373, 1) = 9.3125, (373, 2) = .1724377932, (374, 1) = 9.3375, (374, 2) = .1698512233, (375, 1) = 9.3625, (375, 2) = .1671585025, (376, 1) = 9.3875, (376, 2) = .1643613135, (377, 1) = 9.4125, (377, 2) = .16147334919122835, (378, 1) = 9.4375, (378, 2) = .1584605879, (379, 1) = 9.4625, (379, 2) = .1553607387, (380, 1) = 9.4875, (380, 2) = .1521637948, (381, 1) = 9.5125, (381, 2) = .1488717537, (382, 1) = 9.5375, (382, 2) = .1454866729, (383, 1) = 9.5625, (383, 2) = .1420106681, (384, 1) = 9.5875, (384, 2) = .1384459116, (385, 1) = 9.6125, (385, 2) = .134794631, (386, 1) = 9.6375, (386, 2) = .1310591087, (387, 1) = 9.6625, (387, 2) = .1272416787, (388, 1) = 9.6875, (388, 2) = .1233447273, (389, 1) = 9.7125, (389, 2) = .1193706896, (390, 1) = 9.7375, (390, 2) = .1153220494, (391, 1) = 9.7625, (391, 2) = .1112013368, (392, 1) = 9.7875, (392, 2) = .1070111272, (393, 1) = 9.8125, (393, 2) = .1027540395, (394, 1) = 9.8375, (394, 2) = 0.9843273396e-1, (395, 1) = 9.8625, (395, 2) = 0.9404991135e-1, (396, 1) = 9.8875, (396, 2) = 0.8960831078e-1, (397, 1) = 9.9125, (397, 2) = 0.851107082e-1, (398, 1) = 9.9375, (398, 2) = 0.8055991428e-1, (399, 1) = 9.9625, (399, 2) = 0.7595877328e-1, (400, 1) = 9.9875, (400, 2) = 0.7131016054e-1}, datatype = float[8])), COLOUR(RGB, 0., 0., 1.00000000), TITLE("analytic"), AXESLABELS(x, ""), _AXIS[1](_GRIDLINES(DEFAULT)), _AXIS[2](_GRIDLINES(DEFAULT)), VIEW(0. .. 10., DEFAULT, _ATTRIBUTE("source" = "mathdefault")), _ATTRIBUTE("input" = [TABLE([1 = plot, 2 = [(29/25)*exp(-2*x)+(11/5)*exp(-2*x)*x-(4/25)*cos(x)+(3/25)*sin(x)], 3 = (x = 0 .. 10), 4 = (title = "analytic"), 5 = (color = blue), 6 = (gridlines = true)]), "originalview" = [0.125000000000000007e-1 .. 9.98750000000000071, -.199827467000000009 .. 1.00004238773138043]])), INTERFACE_PLOT(CURVES(Matrix(206, 2, {(1, 1) = .0, (1, 2) = 1.0, (2, 1) = 0.657200628125e-2, (2, 2) = .9999144176901015, (3, 1) = 0.131440125625e-1, (3, 2) = .9996608396568744, (4, 1) = 0.1971601884375e-1, (4, 2) = .999243948007427, (5, 1) = 0.26288025125e-1, (5, 2) = .9986683311918757, (6, 1) = 0.394320376875e-1, (6, 2) = .9970588173642065, (7, 1) = 0.5257605025e-1, (7, 2) = .99486719411864, (8, 1) = 0.7544912035e-1, (8, 2) = .9897643089712955, (9, 1) = 0.9832219045e-1, (9, 2) = .9831663264615924, (10, 1) = .1497685095, (10, 2) = .9636490617746843, (11, 1) = .2015558482, (11, 2) = .9387294801520493, (12, 1) = .2530970507, (12, 2) = .9100158244112896, (13, 1) = .3008823432, (13, 2) = .8808910522216901, (14, 1) = .3503612457, (14, 2) = .849020465668176, (15, 1) = .4015323975, (15, 2) = .8149616876547534, (16, 1) = .4525394427, (16, 2) = .7805321004387699, (17, 1) = .5050064583, (17, 2) = .7451659487981704, (18, 1) = .5512194342, (18, 2) = .7144189464810311, (19, 1) = .6032442995, (19, 2) = .6805846099080608, (20, 1) = .6554827838999999, (20, 2) = .6477154084838929, (21, 1) = .7058242432, (21, 2) = .6172912547042758, (22, 1) = .751539111, (22, 2) = .5908513626011606, (23, 1) = .8058985105, (23, 2) = .5609933828894761, (24, 1) = .8519480522, (24, 2) = .537103365292949, (25, 1) = .9055146166, (25, 2) = .5109730251167722, (26, 1) = .9529301025, (26, 2) = .48934264380789977, (27, 1) = 1.004952405, (27, 2) = .4672206195899612, (28, 1) = 1.05448994, (28, 2) = .447694323439513, (29, 1) = 1.106177161, (29, 2) = .4288779931493993, (30, 1) = 1.153642164, (30, 2) = .4129514005924598, (31, 1) = 1.204839583, (31, 2) = .3971631779630983, (32, 1) = 1.258019312, (32, 2) = .3822165065830296, (33, 1) = 1.304312423, (33, 2) = .37034402129340793, (34, 1) = 1.35431025, (34, 2) = .3586393085134616, (35, 1) = 1.405962898, (35, 2) = .34768571764926387, (36, 1) = 1.456494938, (36, 2) = .3380065848331283, (37, 1) = 1.505387284, (37, 2) = .3295398308515588, (38, 1) = 1.559673898, (38, 2) = .32108333381444715, (39, 1) = 1.608452836, (39, 2) = .31425304013202343, (40, 1) = 1.660534764, (40, 2) = .3076799826216422, (41, 1) = 1.707728731, (41, 2) = .3022969729901385, (42, 1) = 1.759324203, (42, 2) = .29696157282421853, (43, 1) = 1.807871521, (43, 2) = .29239926559264123, (44, 1) = 1.858617457, (44, 2) = .2880372477086302, (45, 1) = 1.908230884, (45, 2) = .2841116119401534, (46, 1) = 1.960171545, (46, 2) = .28029595882949954, (47, 1) = 2.010196575, (47, 2) = .2768461373899222, (48, 1) = 2.061354393, (48, 2) = .27348924724522344, (49, 1) = 2.112088598, (49, 2) = .270277558693484, (50, 1) = 2.158708064, (50, 2) = .2673864595429602, (51, 1) = 2.212139233, (51, 2) = .2640958370448624, (52, 1) = 2.259928707, (52, 2) = .26113391331291796, (53, 1) = 2.310882255, (53, 2) = .2579173119149723, (54, 1) = 2.359651301, (54, 2) = .2547483662764452, (55, 1) = 2.413803059, (55, 2) = .2510895411118279, (56, 1) = 2.460694503, (56, 2) = .24777460326008727, (57, 1) = 2.513916711, (57, 2) = .24381852040713184, (58, 1) = 2.562422976, (58, 2) = .24001092131847385, (59, 1) = 2.615481206, (59, 2) = .23560253046193538, (60, 1) = 2.661261486, (60, 2) = .23157854373522027, (61, 1) = 2.713399881, (61, 2) = .2267314709141136, (62, 1) = 2.763762997, (62, 2) = .2217692794975129, (63, 1) = 2.814093211, (63, 2) = .21652463432605246, (64, 1) = 2.86423827, (64, 2) = .21100719865701584, (65, 1) = 2.912411973, (65, 2) = .20542672905561007, (66, 1) = 2.964489022, (66, 2) = .19908181634599723, (67, 1) = 3.014122226, (67, 2) = .19273122242881466, (68, 1) = 3.066358835, (68, 2) = .18572827130832273, (69, 1) = 3.113645546, (69, 2) = .1791088786353742, (70, 1) = 3.165906213, (70, 2) = .17148816550788065, (71, 1) = 3.215962826, (71, 2) = .16389471156432742, (72, 1) = 3.265897599, (72, 2) = .15604077412190828, (73, 1) = 3.318054663, (73, 2) = .1475498227815901, (74, 1) = 3.366093224, (74, 2) = .1394798388986101, (75, 1) = 3.41529128, (75, 2) = .1309786499762854, (76, 1) = 3.469611781, (76, 2) = .12132972060795755, (77, 1) = 3.518794545, (77, 2) = .11237089010281272, (78, 1) = 3.569093133, (78, 2) = .10300633433915421, (79, 1) = 3.620245502, (79, 2) = 0.9329045891377659e-1, (80, 1) = 3.667264483, (80, 2) = 0.8420489837775907e-1, (81, 1) = 3.717385194, (81, 2) = 0.743747687802773e-1, (82, 1) = 3.767124383, (82, 2) = 0.644903227102123e-1, (83, 1) = 3.820329854, (83, 2) = 0.53797268981441736e-1, (84, 1) = 3.867281378, (84, 2) = 0.4427792214412591e-1, (85, 1) = 3.921453689, (85, 2) = 0.332218588346916e-1, (86, 1) = 3.970340024, (86, 2) = 0.23199860207933156e-1, (87, 1) = 4.018710497, (87, 2) = 0.13263052777071783e-1, (88, 1) = 4.070724294, (88, 2) = 0.2578528732319797e-2, (89, 1) = 4.122948498, (89, 2) = -0.8123068288340024e-2, (90, 1) = 4.170464791, (90, 2) = -0.17815041971595717e-1, (91, 1) = 4.220924984, (91, 2) = -0.28037715520325596e-1, (92, 1) = 4.2701692, (92, 2) = -0.37922412028201055e-1, (93, 1) = 4.32355045, (93, 2) = -0.48509430098023956e-1, (94, 1) = 4.369740072, (94, 2) = -0.57541621798754564e-1, (95, 1) = 4.422790533, (95, 2) = -0.6774388585776954e-1, (96, 1) = 4.472660755, (96, 2) = -0.771443416208509e-1, (97, 1) = 4.522049285, (97, 2) = -0.8625025045997109e-1, (98, 1) = 4.571477104, (98, 2) = -0.9513932016489765e-1, (99, 1) = 4.621890351, (99, 2) = -.10395335078625968, (100, 1) = 4.675327548, (100, 2) = -.11299439465630967, (101, 1) = 4.724324225, (101, 2) = -.12099067641058553, (102, 1) = 4.772690237, (102, 2) = -.12859020163143162, (103, 1) = 4.824392707, (103, 2) = -.13637180089883225, (104, 1) = 4.875982625, (104, 2) = -.1437645939419782, (105, 1) = 4.9222876410000005, (105, 2) = -.15006814225801277, (106, 1) = 4.977139271, (106, 2) = -.1571103673827192, (107, 1) = 5.0230365720000005, (107, 2) = -.162634943157268, (108, 1) = 5.076718618, (108, 2) = -.16865511511423628, (109, 1) = 5.127952935, (109, 2) = -.17394229748547915, (110, 1) = 5.173699075, (110, 2) = -.17827357270338226, (111, 1) = 5.225145392, (111, 2) = -.18269419123443337, (112, 1) = 5.276932734, (112, 2) = -.18665162170834415, (113, 1) = 5.328473935, (113, 2) = -.19008951882794115, (114, 1) = 5.376259226, (114, 2) = -.19282293615544432, (115, 1) = 5.425738131, (115, 2) = -.19518638113504627, (116, 1) = 5.476909281, (116, 2) = -.19712523513845326, (117, 1) = 5.527916326, (117, 2) = -.19854168567656105, (118, 1) = 5.580383342, (118, 2) = -.1994573539335686, (119, 1) = 5.6265963160000005, (119, 2) = -.19980733286229063, (120, 1) = 5.678621186, (120, 2) = -.19968888137874743, (121, 1) = 5.730859668, (121, 2) = -.19902436656574793, (122, 1) = 5.781201125, (122, 2) = -.19786854930188952, (123, 1) = 5.826915995, (123, 2) = -.19638323502374158, (124, 1) = 5.881275397, (124, 2) = -.19408185989974025, (125, 1) = 5.927324935, (125, 2) = -.19168227087545578, (126, 1) = 5.980891502, (126, 2) = -.1883788719724395, (127, 1) = 6.028306985, (127, 2) = -.18500262050621727, (128, 1) = 6.080329291, (128, 2) = -.18081928034412156, (129, 1) = 6.1298668240000005, (129, 2) = -.17637997652956947, (130, 1) = 6.181554045, (130, 2) = -.1712860929784234, (131, 1) = 6.22901905, (131, 2) = -.16620434537531703, (132, 1) = 6.280216467, (132, 2) = -.16030301604736102, (133, 1) = 6.333396196, (133, 2) = -.1537279694652175, (134, 1) = 6.3796893059999995, (134, 2) = -.14764933295078814, (135, 1) = 6.429687135, (135, 2) = -.14072882725894093, (136, 1) = 6.481339783999999, (136, 2) = -.1332096410843731, (137, 1) = 6.5318718239999995, (137, 2) = -.1255091805508351, (138, 1) = 6.580764171, (138, 2) = -.11775303398796816, (139, 1) = 6.635050784, (139, 2) = -.10881188922983188, (140, 1) = 6.683829718, (140, 2) = -.10050333385192152, (141, 1) = 6.735911648, (141, 2) = -0.9136846946952544e-1, (142, 1) = 6.7831056180000004, (142, 2) = -0.8287601360476815e-1, (143, 1) = 6.834701085, (143, 2) = -0.7338079463831108e-1, (144, 1) = 6.883248407, (144, 2) = -0.6426752930106008e-1, (145, 1) = 6.933994342, (145, 2) = -0.5457981986352952e-1, (146, 1) = 6.983607769, (146, 2) = -0.4497210671917301e-1, (147, 1) = 7.035548432, (147, 2) = -0.34795368300990774e-1, (148, 1) = 7.085573457, (148, 2) = -0.24904769648086533e-1, (149, 1) = 7.136731276, (149, 2) = -0.14725817335212398e-1, (150, 1) = 7.187465482, (150, 2) = -0.4592902045661834e-2, (151, 1) = 7.23408495, (151, 2) = 0.4729336749628799e-2, (152, 1) = 7.287516115, (152, 2) = 0.15399927761080205e-1, (153, 1) = 7.335305592999999, (153, 2) = 0.24907588481860372e-1, (154, 1) = 7.38625914, (154, 2) = 0.3498164755155765e-1, (155, 1) = 7.435028186, (155, 2) = 0.44539182442694454e-1, (156, 1) = 7.489179945, (156, 2) = 0.5502661014851547e-1, (157, 1) = 7.536071387, (157, 2) = 0.63978781044417e-1, (158, 1) = 7.589293597999999, (158, 2) = 0.7396815929256038e-1, (159, 1) = 7.637799858999999, (159, 2) = 0.8289070619684706e-1, (160, 1) = 7.69085809, (160, 2) = 0.9242658399328424e-1, (161, 1) = 7.736638372, (161, 2) = .10044638090872322, (162, 1) = 7.788776764, (162, 2) = .10932274320412882, (163, 1) = 7.839139878999999, (163, 2) = .11761504749951865, (164, 1) = 7.889470095, (164, 2) = .12560400349534273, (165, 1) = 7.939615156, (165, 2) = .1332472723040891, (166, 1) = 7.987788859, (166, 2) = .14027482676952052, (167, 1) = 8.039865904, (167, 2) = .14750524637030596, (168, 1) = 8.08949911, (168, 2) = .15402442340541764, (169, 1) = 8.141735718, (169, 2) = .16047555781891515, (170, 1) = 8.189022432, (170, 2) = .16593833817692605, (171, 1) = 8.241283095, (171, 2) = .1715437182002867, (172, 1) = 8.291339707999999, (172, 2) = .1764737069587624, (173, 1) = 8.341274482, (173, 2) = .1809512403702546, (174, 1) = 8.393431548, (174, 2) = .18514622611628614, (175, 1) = 8.441470110000001, (175, 2) = .18856473778706384, (176, 1) = 8.490668165999999, (176, 2) = .19161476547659032, (177, 1) = 8.544988663000002, (177, 2) = .19444346405794258, (178, 1) = 8.594171427, (178, 2) = .1965100455645416, (179, 1) = 8.64447002, (179, 2) = .19813193214712171, (180, 1) = 8.695622387, (180, 2) = .19926734780203556, (181, 1) = 8.742641367, (181, 2) = .19985126823856733, (182, 1) = 8.79276208, (182, 2) = .19998728181040865, (183, 1) = 8.842501266, (183, 2) = .19962570442247934, (184, 1) = 8.895706738, (184, 2) = .1986923973339122, (185, 1) = 8.942658261, (185, 2) = .19740160747867452, (186, 1) = 8.996830573, (186, 2) = .19537194308114905, (187, 1) = 9.045716909, (187, 2) = .19304809353219887, (188, 1) = 9.094087382, (188, 2) = .19029475377005817, (189, 1) = 9.146101181, (189, 2) = .1868375325017263, (190, 1) = 9.198325382, (190, 2) = .18285791005241095, (191, 1) = 9.245841678, (191, 2) = .17880352488262588, (192, 1) = 9.296301869, (192, 2) = .1740562621559014, (193, 1) = 9.345546085, (193, 2) = .16899609358012704, (194, 1) = 9.398927336, (194, 2) = .16304842186753424, (195, 1) = 9.445116955, (195, 2) = .15752653333484226, (196, 1) = 9.498167417, (196, 2) = .1507706050811346, (197, 1) = 9.548037638, (197, 2) = .14403247889914625, (198, 1) = 9.597426171, (198, 2) = .1370064130797137, (199, 1) = 9.64685399, (199, 2) = .12964024364708743, (200, 1) = 9.697267236, (200, 2) = .1218011519969946, (201, 1) = 9.750704432, (201, 2) = .11315440066053806, (202, 1) = 9.79970111, (202, 2) = .1049416705260272, (203, 1) = 9.84806712, (203, 2) = 0.96587529667413e-1, (204, 1) = 9.899769593, (204, 2) = 0.8740778485944833e-1, (205, 1) = 9.951359507, (205, 2) = 0.7801516805416196e-1, (206, 1) = 10.0, (206, 2) = 0.6896895910281918e-1}, datatype = float[8])), COLOUR(RGB, 1.00000000, 0., 0.), TITLE("numerical"), AXESLABELS(x, ""), _AXIS[1](_GRIDLINES(DEFAULT)), _AXIS[2](_GRIDLINES(DEFAULT)), VIEW(0. .. 10., DEFAULT, _ATTRIBUTE("source" = "mathdefault")), _ATTRIBUTE("input" = [TABLE([1 = plot, 2 = [sol_numeric(x)], 3 = (x = 0 .. 10), 4 = (title = "numerical"), 5 = (color = red), 6 = (gridlines = true)]), "originalview" = [0. .. 10., -.199807332862290632 .. 1.]]))]

 

 

Download AA.mw

feel free to make improvements as needed

restart;
y := x-> a*x^3 + b*x^2 + c*x + d:
pts:=[[-1,-4],[1,0],[2,0],[3,-4]]:
eqs:=[seq(y(pts[i,1])=pts[i,2],i=1..numelems(pts))]; 
sol:=solve(eqs,{a,b,c,d}):
equation_of_curve:=eval(y(x),sol);
plots:-display(plot(equation_of_curve,x=-4..4,gridlines),plots:-pointplot(pts,color=blue,symbol=solidcircle,symbolsize=20))

 

pick say x=-1, then your function becomes   (-1)^(1/3). But -1=exp(I*Pi). Hence (-1)^(1/3) is the same as exp(I*Pi/3). Using Euler's formula, this is the same as  cos(Pi/3)+I*sin(Pi/3) = 0.5 + 0.8660254037*I   which is complex. 

That is why Maple does not plot for for negative x. 

may ways to do this. One is to use zip. But they have to be lists not sets. You can convert them

s1:=[a, b, c];
s2:=[a, b, d];
add(zip((x,y)->x+y,s1,s2))

         2*a + 2*b + c + d

Or use shorthand

add(zip(`+`,s1,s2))

      2*a + 2*b + c + d

Under Options->General. Uncheck it

 

try expanding it first so both sides have same structure?    evalb(a-a*b=expand(a*(1-b)))  now gives true.

Help says

The evalb command does not simplify expressions. It may return false for a relation that is true. In such a case, apply a simplification to the relation before using evalb.
 

In this case simplify() did not make it give true.

or you could just use is(a-a*b=a*(1-b)) gives true without the need to expand or simplify.

You can try adding some assumptions? for example

expr:=sqrt(y^2/(x^2+y^2))*sqrt(x^2+y^2)

(y^2/(x^2+y^2))^(1/2)*(x^2+y^2)^(1/2)

simplify(expr)

(y^2/(x^2+y^2))^(1/2)*(x^2+y^2)^(1/2)

simplify(expr) assuming x::real,y::real

abs(y)

simplify(expr) assuming x::real,y::real,y>0

y

 

Download t2.mw

This works for me. 

 

restart;
f := 9*x^3 - 7*x^2*y + 8*x*y^2 - 6*y^3 + 3*x^2 - 3*x*y + 4*y^2 - 3*x + 9*y - 7;
fx:=diff(f,x);
fy:= diff(f,y);

ctpts:= solve({fx=0,fy=0},{x,y});
evalf(allvalues(ctpts))

 

{x = 0.04295586238 + 0.2689937615*I, y = 0.9924517251 + 0.1221355623*I}, {x = -0.1196978953, y = -0.5678259706}, {x = -0.2777747003, y = -0.6265224321}, {x = 0.04295586238 - 0.2689937615*I, y = 0.9924517251 - 0.1221355623*I}

 

I do not know how to add rules to the build in simplify command in Maple (It is possible to do this in Mathematica easily). May there is a way to do it in Maple in order to teach it a new "rule".  The standard simplify(expr,ln) did not do it.

For now you can do

expr:=(ln(-z*I + b) - ln(z*I + b));
I*simplify(log(exp(expr)))

I calculated 6 critical points :how to show them in the plot? 

restart;
f:=(x,y)->x^4-3*x^2-2*y^3+3*y+1/2*x*y; 
cp:=  solve( {diff(f(x,y),x)=0,diff(f(x,y),y)=0}, {x,y});
cp:=  evalf(allvalues(cp));
pts:= map(X->eval([x,y],X),[cp]);
pts:=map(X->[op(X),f(X[1],X[2])],pts);
plots:-display([plot3d(f),plots:-pointplot3d(pts,'color'='red','symbol'='solidcircle','symbolsize'=15)])

 

Using the view point used by others, we get

plots:-display([plot3d(f(x,y),x=-2..2,y=-2..2, view=-6..6),plots:-pointplot3d(pts,'color'='red','symbol'='solidcircle','symbolsize'=15)])

How to make table out of this list.CriticalPoints. for easy reading.?

 

<<'x'|'y'|'z'>,Matrix(pts)>

would it not be better to just use collect? Then the result is automatically sorted by L[n], but it is also collected, which is easier to read also.

result:= expand(((673*L[13] - 485*L[14] - 176*L[15])*h^2 - 90*(L[13] - (13*L[14])/15 - (2*L[14])/15)*x*h)/(12*h^3));
collect(result,indets(result,'indexed'))

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