\[ (2 y(x)-3 x+1)^2 y'(x)-(3 y(x)-2 x-4)^2=0 \] ✓ Mathematica : cpu = 0.258203 (sec), leaf count = 3501
DSolve[-(-4 - 2*x + 3*y[x])^2 + (1 - 3*x + 2*y[x])^2*Derivative[1][y][x] == 0,y[x],x]
\[\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 = 1.237 (sec), leaf count = 1337
dsolve((2*y(x)-3*x+1)^2*diff(y(x),x)-(3*y(x)-2*x-4)^2 = 0,y(x))
\[y \left (x \right ) = \frac {\left (5 x +3\right ) \RootOf \left (\left (115330078125 c_{1} x^{9}-2283535546875 c_{1} x^{8}+20095112812500 c_{1} x^{7}-103154912437500 x^{6} c_{1}+340411211043750 c_{1} x^{5}-748904664296250 c_{1} x^{4}+1098393507634500 x^{3} c_{1}-1035628164341100 x^{2} c_{1}+569595490387605 c_{1} x -139234453205859 c_{1}\right ) \textit {\_Z}^{90}+\left (-576650390625 c_{1} x^{9}+11417677734375 c_{1} x^{8}-100475564062500 c_{1} x^{7}+515774562187500 x^{6} c_{1}-1702056055218750 c_{1} x^{5}+3744523321481250 c_{1} x^{4}-5491967538172500 x^{3} c_{1}+5178140821705500 x^{2} c_{1}-2847977451938025 c_{1} x +696172266029295 c_{1}+1\right ) \textit {\_Z}^{81}+\left (897011718750 c_{1} x^{9}-17760832031250 c_{1} x^{8}+156295321875000 c_{1} x^{7}-802315985625000 x^{6} c_{1}+2647642752562500 c_{1} x^{5}-5824814055637500 c_{1} x^{4}+8543060614935000 x^{3} c_{1}-8054885722653000 x^{2} c_{1}+4430187147459150 c_{1} x -1082934636045570 c_{1}\right ) \textit {\_Z}^{72}+\left (-128144531250 c_{1} x^{9}+2537261718750 c_{1} x^{8}-22327903125000 c_{1} x^{7}+114616569375000 x^{6} c_{1}-378234678937500 c_{1} x^{5}+832116293662500 c_{1} x^{4}-1220437230705000 x^{3} c_{1}+1150697960379000 x^{2} c_{1}-632883878208450 c_{1} x +154704948006510 c_{1}\right ) \textit {\_Z}^{63}+\left (-733271484375 c_{1} x^{9}+14518775390625 c_{1} x^{8}-127765223437500 c_{1} x^{7}+655861480312500 x^{6} c_{1}-2164342885031250 c_{1} x^{5}+4761554347068750 c_{1} x^{4}-6983613042367500 x^{3} c_{1}+6584549439946500 x^{2} c_{1}-3621502191970575 c_{1} x +885256091370585 c_{1}\right ) \textit {\_Z}^{54}+\left (226388671875 c_{1} x^{9}-4482495703125 c_{1} x^{8}+39445962187500 c_{1} x^{7}-202489272562500 x^{6} c_{1}+668214599456250 c_{1} x^{5}-1470072118803750 c_{1} x^{4}+2156105774245500 x^{3} c_{1}-2032899730002900 x^{2} c_{1}+1118094851501595 c_{1} x -273312074811501 c_{1}\right ) \textit {\_Z}^{45}+\left (325898437500 c_{1} x^{9}-6452789062500 c_{1} x^{8}+56784543750000 c_{1} x^{7}-291493991250000 x^{6} c_{1}+961930171125000 c_{1} x^{5}-2116246376475000 c_{1} x^{4}+3103828018830000 x^{3} c_{1}-2926466417754000 x^{2} c_{1}+1609556529764700 c_{1} x -393447151720260 c_{1}\right ) \textit {\_Z}^{36}+\left (-25312500000 c_{1} x^{9}+501187500000 c_{1} x^{8}-4410450000000 c_{1} x^{7}+22640310000000 x^{6} c_{1}-74713023000000 c_{1} x^{5}+164368650600000 c_{1} x^{4}-241074020880000 x^{3} c_{1}+227298362544000 x^{2} c_{1}-125014099399200 c_{1} x +30559002075360 c_{1}\right ) \textit {\_Z}^{27}+\left (-78750000000 c_{1} x^{9}+1559250000000 c_{1} x^{8}-13721400000000 c_{1} x^{7}+70436520000000 x^{6} c_{1}-232440516000000 c_{1} x^{5}+511369135200000 c_{1} x^{4}-750008064960000 x^{3} c_{1}+707150461248000 x^{2} c_{1}-388932753686400 c_{1} x +95072450901120 c_{1}\right ) \textit {\_Z}^{18}+\left (-22500000000 c_{1} x^{9}+445500000000 c_{1} x^{8}-3920400000000 c_{1} x^{7}+20124720000000 x^{6} c_{1}-66411576000000 c_{1} x^{5}+146105467200000 c_{1} x^{4}-214288018560000 x^{3} c_{1}+202042988928000 x^{2} c_{1}-111123643910400 c_{1} x +27163557400320 c_{1}\right ) \textit {\_Z}^{9}-2000000000 c_{1} x^{9}+39600000000 c_{1} x^{8}-348480000000 c_{1} x^{7}+1788864000000 x^{6} c_{1}-5903251200000 c_{1} x^{5}+12987152640000 c_{1} x^{4}-19047823872000 x^{3} c_{1}+17959376793600 x^{2} c_{1}-9877657236480 c_{1} x +2414538435584 c_{1}\right )^{9}-5 x +11}{5 \RootOf \left (\left (115330078125 c_{1} x^{9}-2283535546875 c_{1} x^{8}+20095112812500 c_{1} x^{7}-103154912437500 x^{6} c_{1}+340411211043750 c_{1} x^{5}-748904664296250 c_{1} x^{4}+1098393507634500 x^{3} c_{1}-1035628164341100 x^{2} c_{1}+569595490387605 c_{1} x -139234453205859 c_{1}\right ) \textit {\_Z}^{90}+\left (-576650390625 c_{1} x^{9}+11417677734375 c_{1} x^{8}-100475564062500 c_{1} x^{7}+515774562187500 x^{6} c_{1}-1702056055218750 c_{1} x^{5}+3744523321481250 c_{1} x^{4}-5491967538172500 x^{3} c_{1}+5178140821705500 x^{2} c_{1}-2847977451938025 c_{1} x +696172266029295 c_{1}+1\right ) \textit {\_Z}^{81}+\left (897011718750 c_{1} x^{9}-17760832031250 c_{1} x^{8}+156295321875000 c_{1} x^{7}-802315985625000 x^{6} c_{1}+2647642752562500 c_{1} x^{5}-5824814055637500 c_{1} x^{4}+8543060614935000 x^{3} c_{1}-8054885722653000 x^{2} c_{1}+4430187147459150 c_{1} x -1082934636045570 c_{1}\right ) \textit {\_Z}^{72}+\left (-128144531250 c_{1} x^{9}+2537261718750 c_{1} x^{8}-22327903125000 c_{1} x^{7}+114616569375000 x^{6} c_{1}-378234678937500 c_{1} x^{5}+832116293662500 c_{1} x^{4}-1220437230705000 x^{3} c_{1}+1150697960379000 x^{2} c_{1}-632883878208450 c_{1} x +154704948006510 c_{1}\right ) \textit {\_Z}^{63}+\left (-733271484375 c_{1} x^{9}+14518775390625 c_{1} x^{8}-127765223437500 c_{1} x^{7}+655861480312500 x^{6} c_{1}-2164342885031250 c_{1} x^{5}+4761554347068750 c_{1} x^{4}-6983613042367500 x^{3} c_{1}+6584549439946500 x^{2} c_{1}-3621502191970575 c_{1} x +885256091370585 c_{1}\right ) \textit {\_Z}^{54}+\left (226388671875 c_{1} x^{9}-4482495703125 c_{1} x^{8}+39445962187500 c_{1} x^{7}-202489272562500 x^{6} c_{1}+668214599456250 c_{1} x^{5}-1470072118803750 c_{1} x^{4}+2156105774245500 x^{3} c_{1}-2032899730002900 x^{2} c_{1}+1118094851501595 c_{1} x -273312074811501 c_{1}\right ) \textit {\_Z}^{45}+\left (325898437500 c_{1} x^{9}-6452789062500 c_{1} x^{8}+56784543750000 c_{1} x^{7}-291493991250000 x^{6} c_{1}+961930171125000 c_{1} x^{5}-2116246376475000 c_{1} x^{4}+3103828018830000 x^{3} c_{1}-2926466417754000 x^{2} c_{1}+1609556529764700 c_{1} x -393447151720260 c_{1}\right ) \textit {\_Z}^{36}+\left (-25312500000 c_{1} x^{9}+501187500000 c_{1} x^{8}-4410450000000 c_{1} x^{7}+22640310000000 x^{6} c_{1}-74713023000000 c_{1} x^{5}+164368650600000 c_{1} x^{4}-241074020880000 x^{3} c_{1}+227298362544000 x^{2} c_{1}-125014099399200 c_{1} x +30559002075360 c_{1}\right ) \textit {\_Z}^{27}+\left (-78750000000 c_{1} x^{9}+1559250000000 c_{1} x^{8}-13721400000000 c_{1} x^{7}+70436520000000 x^{6} c_{1}-232440516000000 c_{1} x^{5}+511369135200000 c_{1} x^{4}-750008064960000 x^{3} c_{1}+707150461248000 x^{2} c_{1}-388932753686400 c_{1} x +95072450901120 c_{1}\right ) \textit {\_Z}^{18}+\left (-22500000000 c_{1} x^{9}+445500000000 c_{1} x^{8}-3920400000000 c_{1} x^{7}+20124720000000 x^{6} c_{1}-66411576000000 c_{1} x^{5}+146105467200000 c_{1} x^{4}-214288018560000 x^{3} c_{1}+202042988928000 x^{2} c_{1}-111123643910400 c_{1} x +27163557400320 c_{1}\right ) \textit {\_Z}^{9}-2000000000 c_{1} x^{9}+39600000000 c_{1} x^{8}-348480000000 c_{1} x^{7}+1788864000000 x^{6} c_{1}-5903251200000 c_{1} x^{5}+12987152640000 c_{1} x^{4}-19047823872000 x^{3} c_{1}+17959376793600 x^{2} c_{1}-9877657236480 c_{1} x +2414538435584 c_{1}\right )^{9}}\]