\[ \boxed { \left ( 2\,y \left ( x \right ) -3\,x+1 \right ) ^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( 3\,y \left ( x \right ) -2\,x-4 \right ) ^{2}=0} \]
Mathematica: cpu = 0.183523 (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 = 0 (sec), leaf count = 0 \[ \text {hanged} \]