2.286   ODE No. 286

$(2 y(x)-3 x+1)^2 y'(x)-(3 y(x)-2 x-4)^2=0$ Mathematica : cpu = 0.243073 (sec), leaf count = 3501

$\left \{\left \{y(x)\to \text {Root}\left [1024 x^{10}+38400 x^9+506880 x^8+2246400 x^7-5261760 x^6-50349600 x^5+71033760 x^4+409406400 x^3-1247114880 x^2+295245 c_1{}^5 x+1275458400 x+1024 \text {\#1}^{10}+(19200-21760 x) \text {\#1}^9+\left (190080 x^2-288000 x+74880\right ) \text {\#1}^8+\left (-873120 x^3+1504800 x^2-84960 x-496800\right ) \text {\#1}^7+\left (2235540 x^4-2559600 x^3-6300360 x^2+9795600 x-2953260\right ) \text {\#1}^6+177147 c_1{}^5+\left (-3122577 x^5-3208725 x^4+35619030 x^3-43079850 x^2+6246315 x+7174575\right ) \text {\#1}^5+\left (2235540 x^6+14206950 x^5-55677150 x^4-2902500 x^3+155568600 x^2-154390050 x+39869010\right ) \text {\#1}^4+\left (-873120 x^7-11592000 x^6-3051720 x^5+219051000 x^4-473785200 x^3+276922800 x^2+85118040 x-90541800\right ) \text {\#1}^3+\left (190080 x^8+3988800 x^7+17972640 x^6-70534800 x^5-266036400 x^4+1264183200 x^3-1778293440 x^2+1015642800 x-184232880\right ) \text {\#1}^2+\left (-21760 x^9-633600 x^8-5592960 x^7-4838400 x^6+114715440 x^5+45586800 x^4-1246764960 x^3+2598156000 x^2-2139935760 x-295245 c_1{}^5+637729200\right ) \text {\#1}-459165024\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [1024 x^{10}+38400 x^9+506880 x^8+2246400 x^7-5261760 x^6-50349600 x^5+71033760 x^4+409406400 x^3-1247114880 x^2+295245 c_1{}^5 x+1275458400 x+1024 \text {\#1}^{10}+(19200-21760 x) \text {\#1}^9+\left (190080 x^2-288000 x+74880\right ) \text {\#1}^8+\left (-873120 x^3+1504800 x^2-84960 x-496800\right ) \text {\#1}^7+\left (2235540 x^4-2559600 x^3-6300360 x^2+9795600 x-2953260\right ) \text {\#1}^6+177147 c_1{}^5+\left (-3122577 x^5-3208725 x^4+35619030 x^3-43079850 x^2+6246315 x+7174575\right ) \text {\#1}^5+\left (2235540 x^6+14206950 x^5-55677150 x^4-2902500 x^3+155568600 x^2-154390050 x+39869010\right ) \text {\#1}^4+\left (-873120 x^7-11592000 x^6-3051720 x^5+219051000 x^4-473785200 x^3+276922800 x^2+85118040 x-90541800\right ) \text {\#1}^3+\left (190080 x^8+3988800 x^7+17972640 x^6-70534800 x^5-266036400 x^4+1264183200 x^3-1778293440 x^2+1015642800 x-184232880\right ) \text {\#1}^2+\left (-21760 x^9-633600 x^8-5592960 x^7-4838400 x^6+114715440 x^5+45586800 x^4-1246764960 x^3+2598156000 x^2-2139935760 x-295245 c_1{}^5+637729200\right ) \text {\#1}-459165024\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [1024 x^{10}+38400 x^9+506880 x^8+2246400 x^7-5261760 x^6-50349600 x^5+71033760 x^4+409406400 x^3-1247114880 x^2+295245 c_1{}^5 x+1275458400 x+1024 \text {\#1}^{10}+(19200-21760 x) \text {\#1}^9+\left (190080 x^2-288000 x+74880\right ) \text {\#1}^8+\left (-873120 x^3+1504800 x^2-84960 x-496800\right ) \text {\#1}^7+\left (2235540 x^4-2559600 x^3-6300360 x^2+9795600 x-2953260\right ) \text {\#1}^6+177147 c_1{}^5+\left (-3122577 x^5-3208725 x^4+35619030 x^3-43079850 x^2+6246315 x+7174575\right ) \text {\#1}^5+\left (2235540 x^6+14206950 x^5-55677150 x^4-2902500 x^3+155568600 x^2-154390050 x+39869010\right ) \text {\#1}^4+\left (-873120 x^7-11592000 x^6-3051720 x^5+219051000 x^4-473785200 x^3+276922800 x^2+85118040 x-90541800\right ) \text {\#1}^3+\left (190080 x^8+3988800 x^7+17972640 x^6-70534800 x^5-266036400 x^4+1264183200 x^3-1778293440 x^2+1015642800 x-184232880\right ) \text {\#1}^2+\left (-21760 x^9-633600 x^8-5592960 x^7-4838400 x^6+114715440 x^5+45586800 x^4-1246764960 x^3+2598156000 x^2-2139935760 x-295245 c_1{}^5+637729200\right ) \text {\#1}-459165024\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [1024 x^{10}+38400 x^9+506880 x^8+2246400 x^7-5261760 x^6-50349600 x^5+71033760 x^4+409406400 x^3-1247114880 x^2+295245 c_1{}^5 x+1275458400 x+1024 \text {\#1}^{10}+(19200-21760 x) \text {\#1}^9+\left (190080 x^2-288000 x+74880\right ) \text {\#1}^8+\left (-873120 x^3+1504800 x^2-84960 x-496800\right ) \text {\#1}^7+\left (2235540 x^4-2559600 x^3-6300360 x^2+9795600 x-2953260\right ) \text {\#1}^6+177147 c_1{}^5+\left (-3122577 x^5-3208725 x^4+35619030 x^3-43079850 x^2+6246315 x+7174575\right ) \text {\#1}^5+\left (2235540 x^6+14206950 x^5-55677150 x^4-2902500 x^3+155568600 x^2-154390050 x+39869010\right ) \text {\#1}^4+\left (-873120 x^7-11592000 x^6-3051720 x^5+219051000 x^4-473785200 x^3+276922800 x^2+85118040 x-90541800\right ) \text {\#1}^3+\left (190080 x^8+3988800 x^7+17972640 x^6-70534800 x^5-266036400 x^4+1264183200 x^3-1778293440 x^2+1015642800 x-184232880\right ) \text {\#1}^2+\left (-21760 x^9-633600 x^8-5592960 x^7-4838400 x^6+114715440 x^5+45586800 x^4-1246764960 x^3+2598156000 x^2-2139935760 x-295245 c_1{}^5+637729200\right ) \text {\#1}-459165024\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [1024 x^{10}+38400 x^9+506880 x^8+2246400 x^7-5261760 x^6-50349600 x^5+71033760 x^4+409406400 x^3-1247114880 x^2+295245 c_1{}^5 x+1275458400 x+1024 \text {\#1}^{10}+(19200-21760 x) \text {\#1}^9+\left (190080 x^2-288000 x+74880\right ) \text {\#1}^8+\left (-873120 x^3+1504800 x^2-84960 x-496800\right ) \text {\#1}^7+\left (2235540 x^4-2559600 x^3-6300360 x^2+9795600 x-2953260\right ) \text {\#1}^6+177147 c_1{}^5+\left (-3122577 x^5-3208725 x^4+35619030 x^3-43079850 x^2+6246315 x+7174575\right ) \text {\#1}^5+\left (2235540 x^6+14206950 x^5-55677150 x^4-2902500 x^3+155568600 x^2-154390050 x+39869010\right ) \text {\#1}^4+\left (-873120 x^7-11592000 x^6-3051720 x^5+219051000 x^4-473785200 x^3+276922800 x^2+85118040 x-90541800\right ) \text {\#1}^3+\left (190080 x^8+3988800 x^7+17972640 x^6-70534800 x^5-266036400 x^4+1264183200 x^3-1778293440 x^2+1015642800 x-184232880\right ) \text {\#1}^2+\left (-21760 x^9-633600 x^8-5592960 x^7-4838400 x^6+114715440 x^5+45586800 x^4-1246764960 x^3+2598156000 x^2-2139935760 x-295245 c_1{}^5+637729200\right ) \text {\#1}-459165024\& ,5\right ]\right \},\left \{y(x)\to \text {Root}\left [1024 x^{10}+38400 x^9+506880 x^8+2246400 x^7-5261760 x^6-50349600 x^5+71033760 x^4+409406400 x^3-1247114880 x^2+295245 c_1{}^5 x+1275458400 x+1024 \text {\#1}^{10}+(19200-21760 x) \text {\#1}^9+\left (190080 x^2-288000 x+74880\right ) \text {\#1}^8+\left (-873120 x^3+1504800 x^2-84960 x-496800\right ) \text {\#1}^7+\left (2235540 x^4-2559600 x^3-6300360 x^2+9795600 x-2953260\right ) \text {\#1}^6+177147 c_1{}^5+\left (-3122577 x^5-3208725 x^4+35619030 x^3-43079850 x^2+6246315 x+7174575\right ) \text {\#1}^5+\left (2235540 x^6+14206950 x^5-55677150 x^4-2902500 x^3+155568600 x^2-154390050 x+39869010\right ) \text {\#1}^4+\left (-873120 x^7-11592000 x^6-3051720 x^5+219051000 x^4-473785200 x^3+276922800 x^2+85118040 x-90541800\right ) \text {\#1}^3+\left (190080 x^8+3988800 x^7+17972640 x^6-70534800 x^5-266036400 x^4+1264183200 x^3-1778293440 x^2+1015642800 x-184232880\right ) \text {\#1}^2+\left (-21760 x^9-633600 x^8-5592960 x^7-4838400 x^6+114715440 x^5+45586800 x^4-1246764960 x^3+2598156000 x^2-2139935760 x-295245 c_1{}^5+637729200\right ) \text {\#1}-459165024\& ,6\right ]\right \},\left \{y(x)\to \text {Root}\left [1024 x^{10}+38400 x^9+506880 x^8+2246400 x^7-5261760 x^6-50349600 x^5+71033760 x^4+409406400 x^3-1247114880 x^2+295245 c_1{}^5 x+1275458400 x+1024 \text {\#1}^{10}+(19200-21760 x) \text {\#1}^9+\left (190080 x^2-288000 x+74880\right ) \text {\#1}^8+\left (-873120 x^3+1504800 x^2-84960 x-496800\right ) \text {\#1}^7+\left (2235540 x^4-2559600 x^3-6300360 x^2+9795600 x-2953260\right ) \text {\#1}^6+177147 c_1{}^5+\left (-3122577 x^5-3208725 x^4+35619030 x^3-43079850 x^2+6246315 x+7174575\right ) \text {\#1}^5+\left (2235540 x^6+14206950 x^5-55677150 x^4-2902500 x^3+155568600 x^2-154390050 x+39869010\right ) \text {\#1}^4+\left (-873120 x^7-11592000 x^6-3051720 x^5+219051000 x^4-473785200 x^3+276922800 x^2+85118040 x-90541800\right ) \text {\#1}^3+\left (190080 x^8+3988800 x^7+17972640 x^6-70534800 x^5-266036400 x^4+1264183200 x^3-1778293440 x^2+1015642800 x-184232880\right ) \text {\#1}^2+\left (-21760 x^9-633600 x^8-5592960 x^7-4838400 x^6+114715440 x^5+45586800 x^4-1246764960 x^3+2598156000 x^2-2139935760 x-295245 c_1{}^5+637729200\right ) \text {\#1}-459165024\& ,7\right ]\right \},\left \{y(x)\to \text {Root}\left [1024 x^{10}+38400 x^9+506880 x^8+2246400 x^7-5261760 x^6-50349600 x^5+71033760 x^4+409406400 x^3-1247114880 x^2+295245 c_1{}^5 x+1275458400 x+1024 \text {\#1}^{10}+(19200-21760 x) \text {\#1}^9+\left (190080 x^2-288000 x+74880\right ) \text {\#1}^8+\left (-873120 x^3+1504800 x^2-84960 x-496800\right ) \text {\#1}^7+\left (2235540 x^4-2559600 x^3-6300360 x^2+9795600 x-2953260\right ) \text {\#1}^6+177147 c_1{}^5+\left (-3122577 x^5-3208725 x^4+35619030 x^3-43079850 x^2+6246315 x+7174575\right ) \text {\#1}^5+\left (2235540 x^6+14206950 x^5-55677150 x^4-2902500 x^3+155568600 x^2-154390050 x+39869010\right ) \text {\#1}^4+\left (-873120 x^7-11592000 x^6-3051720 x^5+219051000 x^4-473785200 x^3+276922800 x^2+85118040 x-90541800\right ) \text {\#1}^3+\left (190080 x^8+3988800 x^7+17972640 x^6-70534800 x^5-266036400 x^4+1264183200 x^3-1778293440 x^2+1015642800 x-184232880\right ) \text {\#1}^2+\left (-21760 x^9-633600 x^8-5592960 x^7-4838400 x^6+114715440 x^5+45586800 x^4-1246764960 x^3+2598156000 x^2-2139935760 x-295245 c_1{}^5+637729200\right ) \text {\#1}-459165024\& ,8\right ]\right \},\left \{y(x)\to \text {Root}\left [1024 x^{10}+38400 x^9+506880 x^8+2246400 x^7-5261760 x^6-50349600 x^5+71033760 x^4+409406400 x^3-1247114880 x^2+295245 c_1{}^5 x+1275458400 x+1024 \text {\#1}^{10}+(19200-21760 x) \text {\#1}^9+\left (190080 x^2-288000 x+74880\right ) \text {\#1}^8+\left (-873120 x^3+1504800 x^2-84960 x-496800\right ) \text {\#1}^7+\left (2235540 x^4-2559600 x^3-6300360 x^2+9795600 x-2953260\right ) \text {\#1}^6+177147 c_1{}^5+\left (-3122577 x^5-3208725 x^4+35619030 x^3-43079850 x^2+6246315 x+7174575\right ) \text {\#1}^5+\left (2235540 x^6+14206950 x^5-55677150 x^4-2902500 x^3+155568600 x^2-154390050 x+39869010\right ) \text {\#1}^4+\left (-873120 x^7-11592000 x^6-3051720 x^5+219051000 x^4-473785200 x^3+276922800 x^2+85118040 x-90541800\right ) \text {\#1}^3+\left (190080 x^8+3988800 x^7+17972640 x^6-70534800 x^5-266036400 x^4+1264183200 x^3-1778293440 x^2+1015642800 x-184232880\right ) \text {\#1}^2+\left (-21760 x^9-633600 x^8-5592960 x^7-4838400 x^6+114715440 x^5+45586800 x^4-1246764960 x^3+2598156000 x^2-2139935760 x-295245 c_1{}^5+637729200\right ) \text {\#1}-459165024\& ,9\right ]\right \},\left \{y(x)\to \text {Root}\left [1024 x^{10}+38400 x^9+506880 x^8+2246400 x^7-5261760 x^6-50349600 x^5+71033760 x^4+409406400 x^3-1247114880 x^2+295245 c_1{}^5 x+1275458400 x+1024 \text {\#1}^{10}+(19200-21760 x) \text {\#1}^9+\left (190080 x^2-288000 x+74880\right ) \text {\#1}^8+\left (-873120 x^3+1504800 x^2-84960 x-496800\right ) \text {\#1}^7+\left (2235540 x^4-2559600 x^3-6300360 x^2+9795600 x-2953260\right ) \text {\#1}^6+177147 c_1{}^5+\left (-3122577 x^5-3208725 x^4+35619030 x^3-43079850 x^2+6246315 x+7174575\right ) \text {\#1}^5+\left (2235540 x^6+14206950 x^5-55677150 x^4-2902500 x^3+155568600 x^2-154390050 x+39869010\right ) \text {\#1}^4+\left (-873120 x^7-11592000 x^6-3051720 x^5+219051000 x^4-473785200 x^3+276922800 x^2+85118040 x-90541800\right ) \text {\#1}^3+\left (190080 x^8+3988800 x^7+17972640 x^6-70534800 x^5-266036400 x^4+1264183200 x^3-1778293440 x^2+1015642800 x-184232880\right ) \text {\#1}^2+\left (-21760 x^9-633600 x^8-5592960 x^7-4838400 x^6+114715440 x^5+45586800 x^4-1246764960 x^3+2598156000 x^2-2139935760 x-295245 c_1{}^5+637729200\right ) \text {\#1}-459165024\& ,10\right ]\right \}\right \}$ Maple : cpu = 1.18 (sec), leaf count = 1337

$\left \{ y \left ( x \right ) ={\frac { \left ( 5\,x+3 \right ) \left ( {\it RootOf} \left ( \left ( 115330078125\,{\it \_C1}\,{x}^{9}-2283535546875\,{\it \_C1}\,{x}^{8}+20095112812500\,{\it \_C1}\,{x}^{7}-103154912437500\,{\it \_C1}\,{x}^{6}+340411211043750\,{\it \_C1}\,{x}^{5}-748904664296250\,{\it \_C1}\,{x}^{4}+1098393507634500\,{\it \_C1}\,{x}^{3}-1035628164341100\,{\it \_C1}\,{x}^{2}+569595490387605\,{\it \_C1}\,x-139234453205859\,{\it \_C1} \right ) {{\it \_Z}}^{90}+ \left ( -576650390625\,{\it \_C1}\,{x}^{9}+11417677734375\,{\it \_C1}\,{x}^{8}-100475564062500\,{\it \_C1}\,{x}^{7}+515774562187500\,{\it \_C1}\,{x}^{6}-1702056055218750\,{\it \_C1}\,{x}^{5}+3744523321481250\,{\it \_C1}\,{x}^{4}-5491967538172500\,{\it \_C1}\,{x}^{3}+5178140821705500\,{\it \_C1}\,{x}^{2}-2847977451938025\,{\it \_C1}\,x+696172266029295\,{\it \_C1}+1 \right ) {{\it \_Z}}^{81}+ \left ( 897011718750\,{\it \_C1}\,{x}^{9}-17760832031250\,{\it \_C1}\,{x}^{8}+156295321875000\,{\it 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{{\it \_Z}}^{18}+ \left ( -22500000000\,{\it \_C1}\,{x}^{9}+445500000000\,{\it \_C1}\,{x}^{8}-3920400000000\,{\it \_C1}\,{x}^{7}+20124720000000\,{\it \_C1}\,{x}^{6}-66411576000000\,{\it \_C1}\,{x}^{5}+146105467200000\,{\it \_C1}\,{x}^{4}-214288018560000\,{\it \_C1}\,{x}^{3}+202042988928000\,{\it \_C1}\,{x}^{2}-111123643910400\,{\it \_C1}\,x+27163557400320\,{\it \_C1} \right ) {{\it \_Z}}^{9}-2000000000\,{\it \_C1}\,{x}^{9}+39600000000\,{\it \_C1}\,{x}^{8}-348480000000\,{\it \_C1}\,{x}^{7}+1788864000000\,{\it \_C1}\,{x}^{6}-5903251200000\,{\it \_C1}\,{x}^{5}+12987152640000\,{\it \_C1}\,{x}^{4}-19047823872000\,{\it \_C1}\,{x}^{3}+17959376793600\,{\it \_C1}\,{x}^{2}-9877657236480\,{\it \_C1}\,x+2414538435584\,{\it \_C1} \right ) \right ) ^{9}}} \right \}$