Kitonum

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MaplePrimes Activity


These are replies submitted by Kitonum

@vv  Great idea!  Vote up.

@anthonyfl  I have been working with Maple for about 18 years.

@vv  Thanks for the helpful comment. As you saw, I wrote  "... sometimes ...". Undoubtedly, for examples with  floor , your method is better.

@mehran rajabi  Maple cannot cope with the symbolic solution of this system, but it can be solved numerically:


 

restart;
eq := diff(F1(zeta), zeta, zeta)-b^2*F1(zeta)+2*exp(-b*zeta)*G1(zeta)+(exp(2*b*zeta)-2*exp(b*zeta)+1)*exp(-2*b*zeta)*(exp(b*zeta)*exp(-2*b*zeta)/(3*b)-(2*(exp(b*zeta)-1))*exp(-2*b*zeta)/(3*b))/(3*b^3)-(exp(b*zeta)-1)^2*(exp(-2*b*zeta))^2/(9*b^4)+(1/3)*(exp(b*zeta)-1)*exp(-2*b*zeta) = 0, diff(G1(zeta), zeta, zeta)-b^2*G1(zeta)-(exp(2*b*zeta)-2*exp(b*zeta)+1)*exp(-2*b*zeta)*exp(-b*zeta)/(3*b^2)-(2*(exp(b*zeta)-1))*exp(-2*b*zeta)*exp(-b*zeta)/(3*b^2)+b^2*exp(-b*zeta) = 0, 2*F1(zeta)+diff(H1(zeta), zeta) = 0;
ics := F1(0) = 0, G1(0) = 0, H1(0) = 0, F1(10) = 0, G1(10) = 0;

diff(diff(F1(zeta), zeta), zeta)-b^2*F1(zeta)+2*exp(-b*zeta)*G1(zeta)+(1/3)*(exp(2*b*zeta)-2*exp(b*zeta)+1)*exp(-2*b*zeta)*((1/3)*exp(b*zeta)*exp(-2*b*zeta)/b-(2/3)*(exp(b*zeta)-1)*exp(-2*b*zeta)/b)/b^3-(1/9)*(exp(b*zeta)-1)^2*(exp(-2*b*zeta))^2/b^4+(1/3)*(exp(b*zeta)-1)*exp(-2*b*zeta) = 0, diff(diff(G1(zeta), zeta), zeta)-b^2*G1(zeta)-(1/3)*(exp(2*b*zeta)-2*exp(b*zeta)+1)*exp(-2*b*zeta)*exp(-b*zeta)/b^2-(2/3)*(exp(b*zeta)-1)*exp(-2*b*zeta)*exp(-b*zeta)/b^2+b^2*exp(-b*zeta) = 0, 2*F1(zeta)+diff(H1(zeta), zeta) = 0

 

F1(0) = 0, G1(0) = 0, H1(0) = 0, F1(10) = 0, G1(10) = 0

(1)

sol:=dsolve({eval(eq,b=1),ics}, {F1(zeta),G1(zeta),H1(zeta)}, numeric);

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(23, {(1) = .0, (2) = .44928358946598074, (3) = .8992280016236485, (4) = 1.3498361609654799, (5) = 1.8012662223501124, (6) = 2.2538176451082137, (7) = 2.7075058473204168, (8) = 3.1622104441879415, (9) = 3.617523715379814, (10) = 4.073416898400966, (11) = 4.529828534320989, (12) = 4.986426542395182, (13) = 5.443162925516589, (14) = 5.90002876052367, (15) = 6.3569429608286505, (16) = 6.813886254976485, (17) = 7.270857655114633, (18) = 7.727839396874414, (19) = 8.184824918712069, (20) = 8.641783164869185, (21) = 9.097073709220012, (22) = 9.549798354479439, (23) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(23, 5, {(1, 1) = .0, (1, 2) = .1351851752492863, (1, 3) = .0, (1, 4) = .41666665836616046, (1, 5) = .0, (2, 1) = 0.5115494468017586e-1, (2, 2) = 0.8113419738163506e-1, (2, 3) = .11132234411959376, (2, 4) = .12302251075777063, (2, 5) = -0.24914671295543627e-1, (3, 1) = 0.7233554601458965e-1, (3, 2) = 0.17357015828046368e-1, (3, 3) = .13610713779065636, (3, 4) = 0.5134157483476928e-2, (3, 5) = -0.8264444410819323e-1, (4, 1) = 0.7135659319136944e-1, (4, 2) = -0.1696184290536502e-1, (4, 3) = .12674020370180883, (4, 4) = -0.38860099645228664e-1, (4, 5) = -.14854879844833171, (5, 1) = 0.6041349462457967e-1, (5, 2) = -0.28755621998151695e-1, (5, 3) = .10581472844225323, (5, 4) = -0.50409952802245465e-1, (5, 5) = -.20842786708768668, (6, 1) = 0.4709409559748275e-1, (6, 2) = -0.28879081547784926e-1, (6, 3) = 0.8320842921389804e-1, (6, 4) = -0.4811289459656999e-1, (6, 5) = -.25708080263529137, (7, 1) = 0.3492083729507625e-1, (7, 2) = -0.24403957661635056e-1, (7, 3) = 0.6296637788667604e-1, (7, 4) = -0.40707532483008464e-1, (7, 5) = -.2941345144098128, (8, 1) = 0.25070003281839223e-1, (8, 2) = -0.1893111003883e-1, (8, 3) = 0.4638147698328233e-1, (8, 4) = -0.32264795733010464e-1, (8, 5) = -.3212232294743046, (9, 1) = 0.17611571909885645e-1, (9, 2) = -0.13977250930407952e-1, (9, 3) = 0.33493374348802465e-1, (9, 4) = -0.24542586233020944e-1, (9, 5) = -.3404853250515704, (10, 1) = 0.12184701255497917e-1, (10, 2) = -0.10002753559946396e-1, (10, 3) = 0.23817195842104507e-1, (10, 4) = -0.18144557058951072e-1, (10, 5) = -.35393158488637366, (11, 1) = 0.8337091720945352e-2, (11, 2) = -0.70108099469820655e-2, (11, 3) = 0.16729570595585577e-1, (11, 4) = -0.13136581521343518e-1, (11, 5) = -.36319419500666317, (12, 1) = 0.5658426549190852e-2, (12, 2) = -0.4843973820379962e-2, (12, 3) = 0.11636029945898978e-1, (12, 4) = -0.9361364480710756e-2, (12, 5) = -.369509342937797, (13, 1) = 0.3816482825940519e-2, (13, 2) = -0.3312650434613768e-2, (13, 3) = 0.8027270170587932e-2, (13, 4) = -0.6588553177501801e-2, (13, 5) = -.3737837363058767, (14, 1) = 0.25611722459435832e-2, (14, 2) = -0.22483099413305057e-2, (14, 3) = 0.5499046102432881e-2, (14, 4) = -0.4591001213267668e-2, (14, 5) = -.37666052051945037, (15, 1) = 0.17114348068358774e-2, (15, 2) = -0.15174667598063293e-2, (15, 3) = 0.3743981941592335e-2, (15, 4) = -0.3173781454315336e-2, (15, 5) = -.37858736316938824, (16, 1) = 0.11389945207849871e-2, (16, 2) = -0.10202477258979441e-2, (16, 3) = 0.25342610892095207e-2, (16, 4) = -0.21807885842735457e-2, (16, 5) = -.37987258609442215, (17, 1) = 0.7545084866810752e-3, (17, 2) = -0.6846799203792152e-3, (17, 3) = 0.17046420673436833e-2, (17, 4) = -0.1492807199890507e-2, (17, 5) = -.3807262127850646, (18, 1) = 0.4963920372649282e-3, (18, 2) = -0.46017779695480676e-3, (18, 3) = 0.11369868841425213e-2, (18, 4) = -0.10217803121256395e-2, (18, 5) = -.38129005756286605, (19, 1) = 0.3223713762156566e-3, (19, 2) = -0.3118738646949354e-3, (19, 3) = 0.74746077956267e-3, (19, 4) = -0.7044025597402917e-3, (19, 5) = -.3816590721701828, (20, 1) = 0.20336866967754657e-3, (20, 2) = -0.21626740918513138e-3, (20, 3) = 0.4765918146673492e-3, (20, 4) = -0.4965285098485759e-3, (20, 5) = -.38189599488365217, (21, 1) = 0.11931969219112595e-3, (21, 2) = -0.15820939128644842e-3, (21, 3) = 0.2821548893513022e-3, (21, 4) = -0.36905288775930067e-3, (21, 5) = -.3820409112174494, (22, 1) = 0.554102699130244e-4, (22, 2) = -0.12824646354115483e-3, (22, 3) = 0.13198487000106905e-3, (22, 4) = -0.3036077757130274e-3, (22, 5) = -.3821189946686551, (23, 1) = .0, (23, 2) = -0.1216257983196006e-3, (23, 3) = .0, (23, 4) = -0.2913162149422897e-3, (23, 5) = -.3821437169151561}, datatype = float[8], order = C_order); YP := Matrix(23, 5, {(1, 1) = .1351851752492863, (1, 2) = .0, (1, 3) = .41666665836616046, (1, 4) = -1.0, (1, 5) = -.0, (2, 1) = 0.8113419738163506e-1, (2, 2) = -.1645279189060742, (2, 3) = .12302251075777063, (2, 4) = -.40066707748254227, (2, 5) = -.10230988936035172, (3, 1) = 0.17357015828046368e-1, (3, 2) = -.10943416036596883, (3, 3) = 0.5134157483476928e-2, (3, 4) = -.15760241049089635, (3, 5) = -.1446710920291793, (4, 1) = -0.1696184290536502e-1, (4, 2) = -0.46676744936817796e-1, (4, 3) = -0.38860099645228664e-1, (4, 4) = -0.5192526821103144e-1, (4, 5) = -.1427131863827389, (5, 1) = -0.28755621998151695e-1, (5, 2) = -0.9793671716924128e-2, (5, 3) = -0.50409952802245465e-1, (5, 4) = -0.5744900746345538e-2, (5, 5) = -.12082698924915934, (6, 1) = -0.28879081547784926e-1, (6, 2) = 0.6660263410530297e-2, (6, 3) = -0.4811289459656999e-1, (6, 4) = 0.12824170631730872e-1, (6, 5) = -0.941881911949655e-1, (7, 1) = -0.24403957661635056e-1, (7, 2) = 0.11794594639625879e-1, (7, 3) = -0.40707532483008464e-1, (7, 4) = 0.18398806500833406e-1, (7, 5) = -0.698416745901525e-1, (8, 1) = -0.1893111003883e-1, (8, 2) = 0.11760959952295542e-1, (8, 3) = -0.32264795733010464e-1, (8, 4) = 0.1813481396479044e-1, (8, 5) = -0.50140006563678445e-1, (9, 1) = -0.13977250930407952e-1, (9, 2) = 0.9852970906926514e-2, (9, 3) = -0.24542586233020944e-1, (9, 4) = 0.15587535951612403e-1, (9, 5) = -0.3522314381977129e-1, (10, 1) = -0.10002753559946396e-1, (10, 2) = 0.7593608620784867e-2, (10, 3) = -0.18144557058951072e-1, (10, 4) = 0.1246946171648126e-1, (10, 5) = -0.24369402510995834e-1, (11, 1) = -0.70108099469820655e-2, (11, 2) = 0.5580617459638005e-2, (11, 3) = -0.13136581521343518e-1, (11, 4) = 0.9540802895153576e-2, (11, 5) = -0.16674183441890703e-1, (12, 1) = -0.4843973820379962e-2, (12, 2) = 0.39817997532887684e-2, (12, 3) = -0.9361364480710756e-2, (12, 4) = 0.7082571907025149e-2, (12, 5) = -0.11316853098381704e-1, (13, 1) = -0.3312650434613768e-2, (13, 2) = 0.2785777036021733e-2, (13, 3) = -0.6588553177501801e-2, (13, 4) = 0.5143390194185994e-2, (13, 5) = -0.7632965651881038e-2, (14, 1) = -0.22483099413305057e-2, (14, 2) = 0.19223032845477558e-2, (14, 3) = -0.4591001213267668e-2, (14, 4) = 0.36727952288941592e-2, (14, 5) = -0.51223444918871664e-2, (15, 1) = -0.15174667598063293e-2, (15, 2) = 0.13129671199059636e-2, (15, 3) = -0.3173781454315336e-2, (15, 4) = 0.2587539173186767e-2, (15, 5) = -0.34228696136717547e-2, (16, 1) = -0.10202477258979441e-2, (16, 2) = 0.8893352015347192e-3, (16, 3) = -0.21807885842735457e-2, (16, 4) = 0.18019834005339398e-2, (16, 5) = -0.22779890415699743e-2, (17, 1) = -0.6846799203792152e-3, (17, 2) = 0.5975784507371285e-3, (17, 3) = -0.1492807199890507e-2, (17, 4) = 0.12409651380636609e-2, (17, 5) = -0.15090169733621504e-2, (18, 1) = -0.46017779695480676e-3, (18, 2) = 0.3975251515277088e-3, (18, 3) = -0.10217803121256395e-2, (18, 4) = 0.8433904504169269e-3, (18, 5) = -0.9927840745298565e-3, (19, 1) = -0.3118738646949354e-3, (19, 2) = 0.2599871319744332e-3, (19, 3) = -0.7044025597402917e-3, (19, 4) = 0.5615586091124345e-3, (19, 5) = -0.6447427524313132e-3, (20, 1) = -0.21626740918513138e-3, (20, 2) = 0.1639621962441588e-3, (20, 3) = -0.4965285098485759e-3, (20, 4) = 0.3588773029741943e-3, (20, 5) = -0.40673733935509313e-3, (21, 1) = -0.15820939128644842e-3, (21, 2) = 0.94369148619604e-4, (21, 3) = -0.36905288775930067e-3, (21, 4) = 0.20749285308993136e-3, (21, 5) = -0.2386393843822519e-3, (22, 1) = -0.12824646354115483e-3, (22, 2) = 0.3956577750191933e-4, (22, 3) = -0.3036077757130274e-3, (22, 4) = 0.8450778859380169e-4, (22, 5) = -0.1108205398260488e-3, (23, 1) = -0.1216257983196006e-3, (23, 2) = -0.10088873249360564e-4, (23, 3) = -0.2913162149422897e-3, (23, 4) = -0.3026661987284866e-4, (23, 5) = -.0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(23, {(1) = .0, (2) = .44928358946598074, (3) = .8992280016236485, (4) = 1.3498361609654799, (5) = 1.8012662223501124, (6) = 2.2538176451082137, (7) = 2.7075058473204168, (8) = 3.1622104441879415, (9) = 3.617523715379814, (10) = 4.073416898400966, (11) = 4.529828534320989, (12) = 4.986426542395182, (13) = 5.443162925516589, (14) = 5.90002876052367, (15) = 6.3569429608286505, (16) = 6.813886254976485, (17) = 7.270857655114633, (18) = 7.727839396874414, (19) = 8.184824918712069, (20) = 8.641783164869185, (21) = 9.097073709220012, (22) = 9.549798354479439, (23) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(23, 5, {(1, 1) = .0, (1, 2) = -0.5060266839403578e-8, (1, 3) = .0, (1, 4) = -0.5595449761709814e-8, (1, 5) = .0, (2, 1) = -0.4414648603101034e-8, (2, 2) = 0.5237230439637039e-8, (2, 3) = 0.24227823406843136e-8, (2, 4) = -0.3896659498317099e-8, (2, 5) = -0.1830740038095415e-7, (3, 1) = -0.13533808568033192e-8, (3, 2) = 0.20141702480360933e-8, (3, 3) = 0.20179978179724083e-8, (3, 4) = -0.24069379272293536e-8, (3, 5) = -0.14219658207266639e-7, (4, 1) = 0.337331282284249e-9, (4, 2) = -0.68892695799165e-10, (4, 3) = 0.1305133772877301e-8, (4, 4) = -0.1408689414357604e-8, (4, 5) = -0.11353788189169731e-7, (5, 1) = 0.7780950890751212e-9, (5, 2) = -0.6880292639584532e-9, (5, 3) = 0.7758259856104964e-9, (5, 4) = -0.8039695713767156e-9, (5, 5) = -0.10606964433064684e-7, (6, 1) = 0.7062321448788342e-9, (6, 2) = -0.679287934336782e-9, (6, 3) = 0.448310657957495e-9, (6, 4) = -0.45626590029080564e-9, (6, 5) = -0.10778608065549263e-7, (7, 1) = 0.511133376662903e-9, (7, 2) = -0.5038713184705324e-9, (7, 3) = 0.2601727951753781e-9, (7, 4) = -0.2626161291261405e-9, (7, 5) = -0.11168877664051357e-7, (8, 1) = 0.33464351734378353e-9, (8, 2) = -0.3329048397765606e-9, (8, 3) = 0.15569285919298006e-9, (8, 4) = -0.15656106356462702e-9, (8, 5) = -0.11517201941357773e-7, (9, 1) = 0.20863327364243254e-9, (9, 2) = -0.20826607659080967e-9, (9, 3) = 0.9808757002461656e-10, (9, 4) = -0.9846207919438929e-10, (9, 5) = -0.1176552236640131e-7, (10, 1) = 0.12745430400741654e-9, (10, 2) = -0.12737686541825966e-9, (10, 3) = 0.6557519233836531e-10, (10, 4) = -0.6576689298206469e-10, (10, 5) = -0.11925736660809614e-7, (11, 1) = 0.7773030931510619e-10, (11, 2) = -0.7770210481776407e-10, (11, 3) = 0.4623142673833509e-10, (11, 4) = -0.4634130844562985e-10, (11, 5) = -0.12024113981320469e-7, (12, 1) = 0.4793880506691524e-10, (12, 2) = -0.47920081606321304e-10, (12, 3) = 0.3384161881495305e-10, (12, 4) = -0.339098382448478e-10, (12, 5) = -0.12083213151157077e-7, (13, 1) = 0.3010887618409992e-10, (13, 2) = -0.30097400538997424e-10, (13, 3) = 0.25259653273266184e-10, (13, 4) = -0.25306573823900935e-10, (13, 5) = -0.12118669606512674e-7, (14, 1) = 0.19296189453237174e-10, (14, 2) = -0.1929364196429287e-10, (14, 3) = 0.18944755023838608e-10, (14, 4) = -0.1898405470589748e-10, (14, 5) = -0.12140212012100835e-7, (15, 1) = 0.12593525445588906e-10, (15, 2) = -0.12601937695329738e-10, (15, 3) = 0.14135516940578834e-10, (15, 4) = -0.14179273959243492e-10, (15, 5) = -0.12153577902399673e-7, (16, 1) = 0.8329285428099472e-11, (16, 2) = -0.8352481787026178e-11, (16, 3) = 0.10426765405818495e-10, (16, 4) = -0.10488513341902094e-10, (16, 5) = -0.12162075013745392e-7, (17, 1) = 0.5546883414937215e-11, (17, 2) = -0.55922347729653605e-11, (17, 3) = 0.7570774463024126e-11, (17, 4) = -0.7668286628881844e-11, (17, 5) = -0.12167597772930108e-7, (18, 1) = 0.3690750561552212e-11, (18, 2) = -0.3771039349477756e-11, (18, 3) = 0.5388426387445673e-11, (18, 4) = -0.5547066209268148e-11, (18, 5) = -0.12171242390376102e-7, (19, 1) = 0.2427709366136143e-11, (19, 2) = -0.2563746778570831e-11, (19, 3) = 0.373310185312118e-11, (19, 4) = -0.3990516528592753e-11, (19, 5) = -0.12173658534101514e-7, (20, 1) = 0.15486146251726389e-11, (20, 2) = -0.17734116930070722e-11, (20, 3) = 0.24772238266996045e-11, (20, 4) = -0.2890670417236702e-11, (20, 5) = -0.12175239757029905e-7, (21, 1) = 0.9154864023028152e-12, (21, 2) = -0.12804994267799692e-11, (21, 3) = 0.15081801558644428e-11, (21, 4) = -0.2165620235996891e-11, (21, 5) = -0.12176226070623022e-7, (22, 1) = 0.4268778197861308e-12, (22, 2) = -0.10125184044592964e-11, (22, 3) = 0.7188473624212691e-12, (22, 4) = -0.17584063374567492e-11, (22, 5) = -0.12176762317804481e-7, (23, 1) = .0, (23, 2) = -0.9338425049396765e-12, (23, 3) = .0, (23, 4) = -0.16457719352978926e-11, (23, 5) = -0.12176919844781482e-7}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[23] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(1.830740038095415e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 23, [F1(zeta), diff(F1(zeta), zeta), G1(zeta), diff(G1(zeta), zeta), H1(zeta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(23, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(23, 5, X, Y, outpoint, yout, L, V) end if; [zeta = outpoint, seq('[F1(zeta), diff(F1(zeta), zeta), G1(zeta), diff(G1(zeta), zeta), H1(zeta)]'[i] = yout[i], i = 1 .. 5)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[23] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(1.830740038095415e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 23, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(23, 5, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(23, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(0..0, {}), (3) = [zeta, F1(zeta), diff(F1(zeta), zeta), G1(zeta), diff(G1(zeta), zeta), H1(zeta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [zeta = res[1], seq('[F1(zeta), diff(F1(zeta), zeta), G1(zeta), diff(G1(zeta), zeta), H1(zeta)]'[i] = res[i+1], i = 1 .. 5)] catch: error  end try end proc

(2)

plots:-odeplot(sol,[[zeta,F1(zeta)],[zeta,G1(zeta)],[zeta,H1(zeta)]], zeta=0..10, color=[red,blue,green], size=[500,500]);

 

 


 

Download numeric.mw

@mehran rajabi  Add the line

sol:=simplify(sol) assuming b>0;

Try the option  explicit  in the last line:

T:=solve({f1,f2,f3}, [x,y1,y2], explicit);

 

@spinoza  I did not understand the meaning of your question.

@Carl Love  Your plot  does not prove anything, because it is built on a finite set of points, and the break point is somewhere between them. Here is another plot  on a very small interval, inside which there is a break point (the zero of the denominator):

Digits:=20:
fsolve(denom(x(t)));
plot(x(t), t=-0.00077376199177721..-0.00077376199177719, -5000..5000);

      

 

@666 jvbasha 


 

restart;
ContoursWithLabels := proc (Expr, Range1::(range(realcons)), Range2::(range(realcons)), Number::posint := 8, S::(set(realcons)) := {}, GraphicOptions::list := [color = black, axes = box], Coloring::`=` := NULL)
local r1, r2, L, f, L1, h, S1, P, P1, r, M, C, T, p, p1, m, n, A, B, E;
uses plots, plottools;
f := unapply(Expr, x, y);
if S = {} then r1 := rand(convert(Range1, float)); r2 := rand(convert(Range2, float));
L := [seq([r1(), r2()], i = 1 .. 205)];
L1 := convert(sort(select(a->type(a, realcons), [seq(f(op(t)), t = L)]), (a, b) ->is(abs(a) < abs(b))), set);
h := (L1[-6]-L1[1])/Number;
S1 := [seq(L1[1]+(1/2)*h+h*(n-1), n = 1 .. Number)] else
S1 := convert(S, list)  fi;
print(Contours = evalf[2](S1));
r := k->rand(20 .. k-20); M := []; T := [];
for C in S1 do
P := implicitplot(Expr = C, x = Range1, y = Range2, op(GraphicOptions), gridrefine = 3);
P1 := [getdata(P)];
for p in P1 do
p1 := convert(p[3], listlist); n := nops(p1);
if n < 500 then m := `if`(40 < n, (r(n))(), round((1/2)*n)); M := `if`(40 < n, [op(M), p1[1 .. m-11], p1[m+11 .. n]], [op(M), p1]); T := [op(T), [op(p1[m]), evalf[2](C)]] else
if 500 <= n then h := floor((1/2)*n); m := (r(h))(); M := [op(M), p1[1 .. m-11], p1[m+11 .. m+h-11], p1[m+h+11 .. n]]; T := [op(T), [op(p1[m]), evalf[2](C)], [op(p1[m+h]), evalf[2](C)]]
fi; fi; od; od;
A := plot(M, op(GraphicOptions));
B := plots:-textplot(T);
if Coloring = NULL then E := NULL else E := ([plots:-densityplot])(Expr, x = Range1, y = Range2, op(GraphicOptions), op(rhs(Coloring)))  fi;
display(E, A, B);
end proc:

# Your new example

A3 := .25*y*(-6*x^2+6*x-2.477250468*x*(x-1)^2-2.477250468*x^2*(x-1)-1.476663599*x*(x-1)^3-2.214995399*x^2*(x-1)^2+.3837076420*x*(x-1)^4+.7674152840*x^2*(x-1)^3+1.049305257*x*(x-1)^5+2.623263142*x^2*(x-1)^4+1.470504325*x*(x-1)^6+4.411512974*x^2*(x-1)^5+2.062933702*x*(x-1)^7+7.220267957*x^2*(x-1)^6+1.610136961*x*(x-1)^8+6.440547843*x^2*(x-1)^7+.6577852166*x*(x-1)^9+2.960033475*x^2*(x-1)^8);




ContoursWithLabels(A3, 0 .. 1, 0 .. 10, {seq(0.1..5,0.2)}, [color = black, thickness = 2, axes = box, size=[450,450], labels = ["eta", "r"],labeldirections = [horizontal, vertical], labelfont = ['TIMES', 'BOLDOBLIQUE', 16]], Coloring = [colorstyle = HUE,style = surface]);

.25*y*(-6*x^2+6*x-2.477250468*x*(x-1)^2-2.477250468*x^2*(x-1)-1.476663599*x*(x-1)^3-2.214995399*x^2*(x-1)^2+.3837076420*x*(x-1)^4+.7674152840*x^2*(x-1)^3+1.049305257*x*(x-1)^5+2.623263142*x^2*(x-1)^4+1.470504325*x*(x-1)^6+4.411512974*x^2*(x-1)^5+2.062933702*x*(x-1)^7+7.220267957*x^2*(x-1)^6+1.610136961*x*(x-1)^8+6.440547843*x^2*(x-1)^7+.6577852166*x*(x-1)^9+2.960033475*x^2*(x-1)^8)

 

Contours = [.1, .3, .5, .7, .9, 1.1, 1.3, 1.5, 1.7, 1.9, 2.1, 2.3, 2.5, 2.7, 2.9, 3.1, 3.3, 3.5, 3.7, 3.9, 4.1, 4.3, 4.5, 4.7, 4.9]

 

 

 


 

Download ContoursWithLabels11.mw

@radaar  For example, when you define a procedure using  arrow-notation:

x:=10: t:=20:
f:=x->x^2:
g:=t->t^2:
f(3); g(3);

f  and  g  are  the same function.

The solution to similar and much more complex examples is automated in this post
https://www.mapleprimes.com/posts/145922-Perimeter-Area-And-Visualization-Of-A-Plane-Figure-

@SanzharMukatay  This is correct, but a little cumbersome. For example, if you set the law of motion in a list, the components of which represent the corresponding coordinates, then you can immediately differentiate this list and get speed components in the form of a list too. The same goes for acceleration:

xy:=[3*t,4*t^2+1]:
v_xy:=diff(XY,t);
a_xy:=diff(v_xy,t);

                                               v_xy := [3, 8 t]
                                                a_xy := [0, 8]

@Axel Vogt  Probably, vv deliberately swapped the numerator with the denominator in order to obtain the desired result for OP. I actually did the same in my answer.

@AHSAN  You can use the same data, only each sublist needs to be reversed:

 

Download help_new1.mw

@Rouben Rostamian  Thank you. I dont know. The case  assuming integer is more complicated because we must consider the case separately when one parameter is  0 .

int(cos(m*t)*cos(0*t), t=-Pi..Pi, allsolutions) assuming integer;
convert(%, piecewise, m);

 

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