[next] [prev] [prev-tail] [tail] [up]

2.286   ODE No. 286

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

(2y(x)−3x+1)2y′(x)−(3y(x)−2x−4)2=0 ✓ Mathematica : cpu = 0.239643 (sec), leaf count = 3501

{{y(x)→Root[1024x10+38400x9+506880x8+2246400x7−5261760x6−50349600x5+71033760x4+409406400x3−1247114880x2+295245c15x+1275458400x+1024#110+(19200−21760x)#19+(190080x2−288000x+74880)#18+(−873120x3+1504800x2−84960x−496800)#17+(2235540x4−2559600x3−6300360x2+9795600x−2953260)#16+177147c15+(−3122577x5−3208725x4+35619030x3−43079850x2+6246315x+7174575)#15+(2235540x6+14206950x5−55677150x4−2902500x3+155568600x2−154390050x+39869010)#14+(−873120x7−11592000x6−3051720x5+219051000x4−473785200x3+276922800x2+85118040x−90541800)#13+(190080x8+3988800x7+17972640x6−70534800x5−266036400x4+1264183200x3−1778293440x2+1015642800x−184232880)#12+(−21760x9−633600x8−5592960x7−4838400x6+114715440x5+45586800x4−1246764960x3+2598156000x2−2139935760x−295245c15+637729200)#1−459165024&,1]},{y(x)→Root[1024x10+38400x9+506880x8+2246400x7−5261760x6−50349600x5+71033760x4+409406400x3−1247114880x2+295245c15x+1275458400x+1024#110+(19200−21760x)#19+(190080x2−288000x+74880)#18+(−873120x3+1504800x2−84960x−496800)#17+(2235540x4−2559600x3−6300360x2+9795600x−2953260)#16+177147c15+(−3122577x5−3208725x4+35619030x3−43079850x2+6246315x+7174575)#15+(2235540x6+14206950x5−55677150x4−2902500x3+155568600x2−154390050x+39869010)#14+(−873120x7−11592000x6−3051720x5+219051000x4−473785200x3+276922800x2+85118040x−90541800)#13+(190080x8+3988800x7+17972640x6−70534800x5−266036400x4+1264183200x3−1778293440x2+1015642800x−184232880)#12+(−21760x9−633600x8−5592960x7−4838400x6+114715440x5+45586800x4−1246764960x3+2598156000x2−2139935760x−295245c15+637729200)#1−459165024&,2]},{y(x)→Root[1024x10+38400x9+506880x8+2246400x7−5261760x6−50349600x5+71033760x4+409406400x3−1247114880x2+295245c15x+1275458400x+1024#110+(19200−21760x)#19+(190080x2−288000x+74880)#18+(−873120x3+1504800x2−84960x−496800)#17+(2235540x4−2559600x3−6300360x2+9795600x−2953260)#16+177147c15+(−3122577x5−3208725x4+35619030x3−43079850x2+6246315x+7174575)#15+(2235540x6+14206950x5−55677150x4−2902500x3+155568600x2−154390050x+39869010)#14+(−873120x7−11592000x6−3051720x5+219051000x4−473785200x3+276922800x2+85118040x−90541800)#13+(190080x8+3988800x7+17972640x6−70534800x5−266036400x4+1264183200x3−1778293440x2+1015642800x−184232880)#12+(−21760x9−633600x8−5592960x7−4838400x6+114715440x5+45586800x4−1246764960x3+2598156000x2−2139935760x−295245c15+637729200)#1−459165024&,3]},{y(x)→Root[1024x10+38400x9+506880x8+2246400x7−5261760x6−50349600x5+71033760x4+409406400x3−1247114880x2+295245c15x+1275458400x+1024#110+(19200−21760x)#19+(190080x2−288000x+74880)#18+(−873120x3+1504800x2−84960x−496800)#17+(2235540x4−2559600x3−6300360x2+9795600x−2953260)#16+177147c15+(−3122577x5−3208725x4+35619030x3−43079850x2+6246315x+7174575)#15+(2235540x6+14206950x5−55677150x4−2902500x3+155568600x2−154390050x+39869010)#14+(−873120x7−11592000x6−3051720x5+219051000x4−473785200x3+276922800x2+85118040x−90541800)#13+(190080x8+3988800x7+17972640x6−70534800x5−266036400x4+1264183200x3−1778293440x2+1015642800x−184232880)#12+(−21760x9−633600x8−5592960x7−4838400x6+114715440x5+45586800x4−1246764960x3+2598156000x2−2139935760x−295245c15+637729200)#1−459165024&,4]},{y(x)→Root[1024x10+38400x9+506880x8+2246400x7−5261760x6−50349600x5+71033760x4+409406400x3−1247114880x2+295245c15x+1275458400x+1024#110+(19200−21760x)#19+(190080x2−288000x+74880)#18+(−873120x3+1504800x2−84960x−496800)#17+(2235540x4−2559600x3−6300360x2+9795600x−2953260)#16+177147c15+(−3122577x5−3208725x4+35619030x3−43079850x2+6246315x+7174575)#15+(2235540x6+14206950x5−55677150x4−2902500x3+155568600x2−154390050x+39869010)#14+(−873120x7−11592000x6−3051720x5+219051000x4−473785200x3+276922800x2+85118040x−90541800)#13+(190080x8+3988800x7+17972640x6−70534800x5−266036400x4+1264183200x3−1778293440x2+1015642800x−184232880)#12+(−21760x9−633600x8−5592960x7−4838400x6+114715440x5+45586800x4−1246764960x3+2598156000x2−2139935760x−295245c15+637729200)#1−459165024&,5]},{y(x)→Root[1024x10+38400x9+506880x8+2246400x7−5261760x6−50349600x5+71033760x4+409406400x3−1247114880x2+295245c15x+1275458400x+1024#110+(19200−21760x)#19+(190080x2−288000x+74880)#18+(−873120x3+1504800x2−84960x−496800)#17+(2235540x4−2559600x3−6300360x2+9795600x−2953260)#16+177147c15+(−3122577x5−3208725x4+35619030x3−43079850x2+6246315x+7174575)#15+(2235540x6+14206950x5−55677150x4−2902500x3+155568600x2−154390050x+39869010)#14+(−873120x7−11592000x6−3051720x5+219051000x4−473785200x3+276922800x2+85118040x−90541800)#13+(190080x8+3988800x7+17972640x6−70534800x5−266036400x4+1264183200x3−1778293440x2+1015642800x−184232880)#12+(−21760x9−633600x8−5592960x7−4838400x6+114715440x5+45586800x4−1246764960x3+2598156000x2−2139935760x−295245c15+637729200)#1−459165024&,6]},{y(x)→Root[1024x10+38400x9+506880x8+2246400x7−5261760x6−50349600x5+71033760x4+409406400x3−1247114880x2+295245c15x+1275458400x+1024#110+(19200−21760x)#19+(190080x2−288000x+74880)#18+(−873120x3+1504800x2−84960x−496800)#17+(2235540x4−2559600x3−6300360x2+9795600x−2953260)#16+177147c15+(−3122577x5−3208725x4+35619030x3−43079850x2+6246315x+7174575)#15+(2235540x6+14206950x5−55677150x4−2902500x3+155568600x2−154390050x+39869010)#14+(−873120x7−11592000x6−3051720x5+219051000x4−473785200x3+276922800x2+85118040x−90541800)#13+(190080x8+3988800x7+17972640x6−70534800x5−266036400x4+1264183200x3−1778293440x2+1015642800x−184232880)#12+(−21760x9−633600x8−5592960x7−4838400x6+114715440x5+45586800x4−1246764960x3+2598156000x2−2139935760x−295245c15+637729200)#1−459165024&,7]},{y(x)→Root[1024x10+38400x9+506880x8+2246400x7−5261760x6−50349600x5+71033760x4+409406400x3−1247114880x2+295245c15x+1275458400x+1024#110+(19200−21760x)#19+(190080x2−288000x+74880)#18+(−873120x3+1504800x2−84960x−496800)#17+(2235540x4−2559600x3−6300360x2+9795600x−2953260)#16+177147c15+(−3122577x5−3208725x4+35619030x3−43079850x2+6246315x+7174575)#15+(2235540x6+14206950x5−55677150x4−2902500x3+155568600x2−154390050x+39869010)#14+(−873120x7−11592000x6−3051720x5+219051000x4−473785200x3+276922800x2+85118040x−90541800)#13+(190080x8+3988800x7+17972640x6−70534800x5−266036400x4+1264183200x3−1778293440x2+1015642800x−184232880)#12+(−21760x9−633600x8−5592960x7−4838400x6+114715440x5+45586800x4−1246764960x3+2598156000x2−2139935760x−295245c15+637729200)#1−459165024&,8]},{y(x)→Root[1024x10+38400x9+506880x8+2246400x7−5261760x6−50349600x5+71033760x4+409406400x3−1247114880x2+295245c15x+1275458400x+1024#110+(19200−21760x)#19+(190080x2−288000x+74880)#18+(−873120x3+1504800x2−84960x−496800)#17+(2235540x4−2559600x3−6300360x2+9795600x−2953260)#16+177147c15+(−3122577x5−3208725x4+35619030x3−43079850x2+6246315x+7174575)#15+(2235540x6+14206950x5−55677150x4−2902500x3+155568600x2−154390050x+39869010)#14+(−873120x7−11592000x6−3051720x5+219051000x4−473785200x3+276922800x2+85118040x−90541800)#13+(190080x8+3988800x7+17972640x6−70534800x5−266036400x4+1264183200x3−1778293440x2+1015642800x−184232880)#12+(−21760x9−633600x8−5592960x7−4838400x6+114715440x5+45586800x4−1246764960x3+2598156000x2−2139935760x−295245c15+637729200)#1−459165024&,9]},{y(x)→Root[1024x10+38400x9+506880x8+2246400x7−5261760x6−50349600x5+71033760x4+409406400x3−1247114880x2+295245c15x+1275458400x+1024#110+(19200−21760x)#19+(190080x2−288000x+74880)#18+(−873120x3+1504800x2−84960x−496800)#17+(2235540x4−2559600x3−6300360x2+9795600x−2953260)#16+177147c15+(−3122577x5−3208725x4+35619030x3−43079850x2+6246315x+7174575)#15+(2235540x6+14206950x5−55677150x4−2902500x3+155568600x2−154390050x+39869010)#14+(−873120x7−11592000x6−3051720x5+219051000x4−473785200x3+276922800x2+85118040x−90541800)#13+(190080x8+3988800x7+17972640x6−70534800x5−266036400x4+1264183200x3−1778293440x2+1015642800x−184232880)#12+(−21760x9−633600x8−5592960x7−4838400x6+114715440x5+45586800x4−1246764960x3+2598156000x2−2139935760x−295245c15+637729200)#1−459165024&,10]}} ✓ Maple : cpu = 1.16 (sec), leaf count = 1337

{y(x)=(5x+3)(RootOf((115330078125_C1x9−2283535546875_C1x8+20095112812500_C1x7−103154912437500_C1x6+340411211043750_C1x5−748904664296250_C1x4+1098393507634500_C1x3−1035628164341100_C1x2+569595490387605_C1x−139234453205859_C1)_Z90+(−576650390625_C1x9+11417677734375_C1x8−100475564062500_C1x7+515774562187500_C1x6−1702056055218750_C1x5+3744523321481250_C1x4−5491967538172500_C1x3+5178140821705500_C1x2−2847977451938025_C1x+696172266029295_C1+1)_Z81+(897011718750_C1x9−17760832031250_C1x8+156295321875000_C1x7−802315985625000_C1x6+2647642752562500_C1x5−5824814055637500_C1x4+8543060614935000_C1x3−8054885722653000_C1x2+4430187147459150_C1x−1082934636045570_C1)_Z72+(−128144531250_C1x9+2537261718750_C1x8−22327903125000_C1x7+114616569375000_C1x6−378234678937500_C1x5+832116293662500_C1x4−1220437230705000_C1x3+1150697960379000_C1x2−632883878208450_C1x+154704948006510_C1)_Z63+(−733271484375_C1x9+14518775390625_C1x8−127765223437500_C1x7+655861480312500_C1x6−2164342885031250_C1x5+4761554347068750_C1x4−6983613042367500_C1x3+6584549439946500_C1x2−3621502191970575_C1x+885256091370585_C1)_Z54+(226388671875_C1x9−4482495703125_C1x8+39445962187500_C1x7−202489272562500_C1x6+668214599456250_C1x5−1470072118803750_C1x4+2156105774245500_C1x3−2032899730002900_C1x2+1118094851501595_C1x−273312074811501_C1)_Z45+(325898437500_C1x9−6452789062500_C1x8+56784543750000_C1x7−291493991250000_C1x6+961930171125000_C1x5−2116246376475000_C1x4+3103828018830000_C1x3−2926466417754000_C1x2+1609556529764700_C1x−393447151720260_C1)_Z36+(−25312500000_C1x9+501187500000_C1x8−4410450000000_C1x7+22640310000000_C1x6−74713023000000_C1x5+164368650600000_C1x4−241074020880000_C1x3+227298362544000_C1x2−125014099399200_C1x+30559002075360_C1)_Z27+(−78750000000_C1x9+1559250000000_C1x8−13721400000000_C1x7+70436520000000_C1x6−232440516000000_C1x5+511369135200000_C1x4−750008064960000_C1x3+707150461248000_C1x2−388932753686400_C1x+95072450901120_C1)_Z18+(−22500000000_C1x9+445500000000_C1x8−3920400000000_C1x7+20124720000000_C1x6−66411576000000_C1x5+146105467200000_C1x4−214288018560000_C1x3+202042988928000_C1x2−111123643910400_C1x+27163557400320_C1)_Z9−2000000000_C1x9+39600000000_C1x8−348480000000_C1x7+1788864000000_C1x6−5903251200000_C1x5+12987152640000_C1x4−19047823872000_C1x3+17959376793600_C1x2−9877657236480_C1x+2414538435584_C1))9−5x+115(RootOf((115330078125_C1x9−2283535546875_C1x8+20095112812500_C1x7−103154912437500_C1x6+340411211043750_C1x5−748904664296250_C1x4+1098393507634500_C1x3−1035628164341100_C1x2+569595490387605_C1x−139234453205859_C1)_Z90+(−576650390625_C1x9+11417677734375_C1x8−100475564062500_C1x7+515774562187500_C1x6−1702056055218750_C1x5+3744523321481250_C1x4−5491967538172500_C1x3+5178140821705500_C1x2−2847977451938025_C1x+696172266029295_C1+1)_Z81+(897011718750_C1x9−17760832031250_C1x8+156295321875000_C1x7−802315985625000_C1x6+2647642752562500_C1x5−5824814055637500_C1x4+8543060614935000_C1x3−8054885722653000_C1x2+4430187147459150_C1x−1082934636045570_C1)_Z72+(−128144531250_C1x9+2537261718750_C1x8−22327903125000_C1x7+114616569375000_C1x6−378234678937500_C1x5+832116293662500_C1x4−1220437230705000_C1x3+1150697960379000_C1x2−632883878208450_C1x+154704948006510_C1)_Z63+(−733271484375_C1x9+14518775390625_C1x8−127765223437500_C1x7+655861480312500_C1x6−2164342885031250_C1x5+4761554347068750_C1x4−6983613042367500_C1x3+6584549439946500_C1x2−3621502191970575_C1x+885256091370585_C1)_Z54+(226388671875_C1x9−4482495703125_C1x8+39445962187500_C1x7−202489272562500_C1x6+668214599456250_C1x5−1470072118803750_C1x4+2156105774245500_C1x3−2032899730002900_C1x2+1118094851501595_C1x−273312074811501_C1)_Z45+(325898437500_C1x9−6452789062500_C1x8+56784543750000_C1x7−291493991250000_C1x6+961930171125000_C1x5−2116246376475000_C1x4+3103828018830000_C1x3−2926466417754000_C1x2+1609556529764700_C1x−393447151720260_C1)_Z36+(−25312500000_C1x9+501187500000_C1x8−4410450000000_C1x7+22640310000000_C1x6−74713023000000_C1x5+164368650600000_C1x4−241074020880000_C1x3+227298362544000_C1x2−125014099399200_C1x+30559002075360_C1)_Z27+(−78750000000_C1x9+1559250000000_C1x8−13721400000000_C1x7+70436520000000_C1x6−232440516000000_C1x5+511369135200000_C1x4−750008064960000_C1x3+707150461248000_C1x2−388932753686400_C1x+95072450901120_C1)_Z18+(−22500000000_C1x9+445500000000_C1x8−3920400000000_C1x7+20124720000000_C1x6−66411576000000_C1x5+146105467200000_C1x4−214288018560000_C1x3+202042988928000_C1x2−111123643910400_C1x+27163557400320_C1)_Z9−2000000000_C1x9+39600000000_C1x8−348480000000_C1x7+1788864000000_C1x6−5903251200000_C1x5+12987152640000_C1x4−19047823872000_C1x3+17959376793600_C1x2−9877657236480_C1x+2414538435584_C1))9}

[next] [prev] [prev-tail] [front] [up]