##### 4.13.33 $$(2 y(x)-3 x+1)^2 y'(x)=(-3 y(x)+2 x+4)^2$$

ODE
$(2 y(x)-3 x+1)^2 y'(x)=(-3 y(x)+2 x+4)^2$ ODE Classiﬁcation

[[_homogeneous, class C], _rational]

Book solution method
Equation linear in the variables, $$y'(x)=f\left ( \frac {X_1}{X_2} \right )$$

Mathematica
cpu = 0.529317 (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 = 1.389 (sec), leaf count = 1335

$\text {Expression too large to display}$ Mathematica raw input

DSolve[(1 - 3*x + 2*y[x])^2*y'[x] == (4 + 2*x - 3*y[x])^2,y[x],x]

Mathematica raw output

{{y[x] -> Root[-459165024 + 1275458400*x - 1247114880*x^2 + 409406400*x^3 + 7103
3760*x^4 - 50349600*x^5 - 5261760*x^6 + 2246400*x^7 + 506880*x^8 + 38400*x^9 + 1
024*x^10 + 177147*C[1]^5 + 295245*x*C[1]^5 + (637729200 - 2139935760*x + 2598156
000*x^2 - 1246764960*x^3 + 45586800*x^4 + 114715440*x^5 - 4838400*x^6 - 5592960*
x^7 - 633600*x^8 - 21760*x^9 - 295245*C[1]^5)*#1 + (-184232880 + 1015642800*x -
1778293440*x^2 + 1264183200*x^3 - 266036400*x^4 - 70534800*x^5 + 17972640*x^6 +
3988800*x^7 + 190080*x^8)*#1^2 + (-90541800 + 85118040*x + 276922800*x^2 - 47378
5200*x^3 + 219051000*x^4 - 3051720*x^5 - 11592000*x^6 - 873120*x^7)*#1^3 + (3986
9010 - 154390050*x + 155568600*x^2 - 2902500*x^3 - 55677150*x^4 + 14206950*x^5 +
 2235540*x^6)*#1^4 + (7174575 + 6246315*x - 43079850*x^2 + 35619030*x^3 - 320872
5*x^4 - 3122577*x^5)*#1^5 + (-2953260 + 9795600*x - 6300360*x^2 - 2559600*x^3 +
2235540*x^4)*#1^6 + (-496800 - 84960*x + 1504800*x^2 - 873120*x^3)*#1^7 + (74880
 - 288000*x + 190080*x^2)*#1^8 + (19200 - 21760*x)*#1^9 + 1024*#1^10 & , 1]}, {y
[x] -> Root[-459165024 + 1275458400*x - 1247114880*x^2 + 409406400*x^3 + 7103376
0*x^4 - 50349600*x^5 - 5261760*x^6 + 2246400*x^7 + 506880*x^8 + 38400*x^9 + 1024
*x^10 + 177147*C[1]^5 + 295245*x*C[1]^5 + (637729200 - 2139935760*x + 2598156000
*x^2 - 1246764960*x^3 + 45586800*x^4 + 114715440*x^5 - 4838400*x^6 - 5592960*x^7
 - 633600*x^8 - 21760*x^9 - 295245*C[1]^5)*#1 + (-184232880 + 1015642800*x - 177
8293440*x^2 + 1264183200*x^3 - 266036400*x^4 - 70534800*x^5 + 17972640*x^6 + 398
8800*x^7 + 190080*x^8)*#1^2 + (-90541800 + 85118040*x + 276922800*x^2 - 47378520
0*x^3 + 219051000*x^4 - 3051720*x^5 - 11592000*x^6 - 873120*x^7)*#1^3 + (3986901
0 - 154390050*x + 155568600*x^2 - 2902500*x^3 - 55677150*x^4 + 14206950*x^5 + 22
35540*x^6)*#1^4 + (7174575 + 6246315*x - 43079850*x^2 + 35619030*x^3 - 3208725*x
^4 - 3122577*x^5)*#1^5 + (-2953260 + 9795600*x - 6300360*x^2 - 2559600*x^3 + 223
5540*x^4)*#1^6 + (-496800 - 84960*x + 1504800*x^2 - 873120*x^3)*#1^7 + (74880 -
288000*x + 190080*x^2)*#1^8 + (19200 - 21760*x)*#1^9 + 1024*#1^10 & , 2]}, {y[x]
 -> Root[-459165024 + 1275458400*x - 1247114880*x^2 + 409406400*x^3 + 71033760*x
^4 - 50349600*x^5 - 5261760*x^6 + 2246400*x^7 + 506880*x^8 + 38400*x^9 + 1024*x^
10 + 177147*C[1]^5 + 295245*x*C[1]^5 + (637729200 - 2139935760*x + 2598156000*x^
2 - 1246764960*x^3 + 45586800*x^4 + 114715440*x^5 - 4838400*x^6 - 5592960*x^7 -
633600*x^8 - 21760*x^9 - 295245*C[1]^5)*#1 + (-184232880 + 1015642800*x - 177829
3440*x^2 + 1264183200*x^3 - 266036400*x^4 - 70534800*x^5 + 17972640*x^6 + 398880
0*x^7 + 190080*x^8)*#1^2 + (-90541800 + 85118040*x + 276922800*x^2 - 473785200*x
^3 + 219051000*x^4 - 3051720*x^5 - 11592000*x^6 - 873120*x^7)*#1^3 + (39869010 -
 154390050*x + 155568600*x^2 - 2902500*x^3 - 55677150*x^4 + 14206950*x^5 + 22355
40*x^6)*#1^4 + (7174575 + 6246315*x - 43079850*x^2 + 35619030*x^3 - 3208725*x^4
- 3122577*x^5)*#1^5 + (-2953260 + 9795600*x - 6300360*x^2 - 2559600*x^3 + 223554
0*x^4)*#1^6 + (-496800 - 84960*x + 1504800*x^2 - 873120*x^3)*#1^7 + (74880 - 288
000*x + 190080*x^2)*#1^8 + (19200 - 21760*x)*#1^9 + 1024*#1^10 & , 3]}, {y[x] ->
 Root[-459165024 + 1275458400*x - 1247114880*x^2 + 409406400*x^3 + 71033760*x^4
- 50349600*x^5 - 5261760*x^6 + 2246400*x^7 + 506880*x^8 + 38400*x^9 + 1024*x^10
+ 177147*C[1]^5 + 295245*x*C[1]^5 + (637729200 - 2139935760*x + 2598156000*x^2 -
 1246764960*x^3 + 45586800*x^4 + 114715440*x^5 - 4838400*x^6 - 5592960*x^7 - 633
600*x^8 - 21760*x^9 - 295245*C[1]^5)*#1 + (-184232880 + 1015642800*x - 177829344
0*x^2 + 1264183200*x^3 - 266036400*x^4 - 70534800*x^5 + 17972640*x^6 + 3988800*x
^7 + 190080*x^8)*#1^2 + (-90541800 + 85118040*x + 276922800*x^2 - 473785200*x^3
+ 219051000*x^4 - 3051720*x^5 - 11592000*x^6 - 873120*x^7)*#1^3 + (39869010 - 15
4390050*x + 155568600*x^2 - 2902500*x^3 - 55677150*x^4 + 14206950*x^5 + 2235540*
x^6)*#1^4 + (7174575 + 6246315*x - 43079850*x^2 + 35619030*x^3 - 3208725*x^4 - 3
122577*x^5)*#1^5 + (-2953260 + 9795600*x - 6300360*x^2 - 2559600*x^3 + 2235540*x
^4)*#1^6 + (-496800 - 84960*x + 1504800*x^2 - 873120*x^3)*#1^7 + (74880 - 288000
*x + 190080*x^2)*#1^8 + (19200 - 21760*x)*#1^9 + 1024*#1^10 & , 4]}, {y[x] -> Ro
ot[-459165024 + 1275458400*x - 1247114880*x^2 + 409406400*x^3 + 71033760*x^4 - 5
0349600*x^5 - 5261760*x^6 + 2246400*x^7 + 506880*x^8 + 38400*x^9 + 1024*x^10 + 1
77147*C[1]^5 + 295245*x*C[1]^5 + (637729200 - 2139935760*x + 2598156000*x^2 - 12
46764960*x^3 + 45586800*x^4 + 114715440*x^5 - 4838400*x^6 - 5592960*x^7 - 633600
*x^8 - 21760*x^9 - 295245*C[1]^5)*#1 + (-184232880 + 1015642800*x - 1778293440*x
^2 + 1264183200*x^3 - 266036400*x^4 - 70534800*x^5 + 17972640*x^6 + 3988800*x^7
+ 190080*x^8)*#1^2 + (-90541800 + 85118040*x + 276922800*x^2 - 473785200*x^3 + 2
19051000*x^4 - 3051720*x^5 - 11592000*x^6 - 873120*x^7)*#1^3 + (39869010 - 15439
0050*x + 155568600*x^2 - 2902500*x^3 - 55677150*x^4 + 14206950*x^5 + 2235540*x^6
)*#1^4 + (7174575 + 6246315*x - 43079850*x^2 + 35619030*x^3 - 3208725*x^4 - 3122
577*x^5)*#1^5 + (-2953260 + 9795600*x - 6300360*x^2 - 2559600*x^3 + 2235540*x^4)
*#1^6 + (-496800 - 84960*x + 1504800*x^2 - 873120*x^3)*#1^7 + (74880 - 288000*x
+ 190080*x^2)*#1^8 + (19200 - 21760*x)*#1^9 + 1024*#1^10 & , 5]}, {y[x] -> Root[
-459165024 + 1275458400*x - 1247114880*x^2 + 409406400*x^3 + 71033760*x^4 - 5034
9600*x^5 - 5261760*x^6 + 2246400*x^7 + 506880*x^8 + 38400*x^9 + 1024*x^10 + 1771
47*C[1]^5 + 295245*x*C[1]^5 + (637729200 - 2139935760*x + 2598156000*x^2 - 12467
64960*x^3 + 45586800*x^4 + 114715440*x^5 - 4838400*x^6 - 5592960*x^7 - 633600*x^
8 - 21760*x^9 - 295245*C[1]^5)*#1 + (-184232880 + 1015642800*x - 1778293440*x^2
+ 1264183200*x^3 - 266036400*x^4 - 70534800*x^5 + 17972640*x^6 + 3988800*x^7 + 1
90080*x^8)*#1^2 + (-90541800 + 85118040*x + 276922800*x^2 - 473785200*x^3 + 2190
51000*x^4 - 3051720*x^5 - 11592000*x^6 - 873120*x^7)*#1^3 + (39869010 - 15439005
0*x + 155568600*x^2 - 2902500*x^3 - 55677150*x^4 + 14206950*x^5 + 2235540*x^6)*#
1^4 + (7174575 + 6246315*x - 43079850*x^2 + 35619030*x^3 - 3208725*x^4 - 3122577
*x^5)*#1^5 + (-2953260 + 9795600*x - 6300360*x^2 - 2559600*x^3 + 2235540*x^4)*#1
^6 + (-496800 - 84960*x + 1504800*x^2 - 873120*x^3)*#1^7 + (74880 - 288000*x + 1
90080*x^2)*#1^8 + (19200 - 21760*x)*#1^9 + 1024*#1^10 & , 6]}, {y[x] -> Root[-45
9165024 + 1275458400*x - 1247114880*x^2 + 409406400*x^3 + 71033760*x^4 - 5034960
0*x^5 - 5261760*x^6 + 2246400*x^7 + 506880*x^8 + 38400*x^9 + 1024*x^10 + 177147*
C[1]^5 + 295245*x*C[1]^5 + (637729200 - 2139935760*x + 2598156000*x^2 - 12467649
60*x^3 + 45586800*x^4 + 114715440*x^5 - 4838400*x^6 - 5592960*x^7 - 633600*x^8 -
 21760*x^9 - 295245*C[1]^5)*#1 + (-184232880 + 1015642800*x - 1778293440*x^2 + 1
264183200*x^3 - 266036400*x^4 - 70534800*x^5 + 17972640*x^6 + 3988800*x^7 + 1900
80*x^8)*#1^2 + (-90541800 + 85118040*x + 276922800*x^2 - 473785200*x^3 + 2190510
00*x^4 - 3051720*x^5 - 11592000*x^6 - 873120*x^7)*#1^3 + (39869010 - 154390050*x
 + 155568600*x^2 - 2902500*x^3 - 55677150*x^4 + 14206950*x^5 + 2235540*x^6)*#1^4
 + (7174575 + 6246315*x - 43079850*x^2 + 35619030*x^3 - 3208725*x^4 - 3122577*x^
5)*#1^5 + (-2953260 + 9795600*x - 6300360*x^2 - 2559600*x^3 + 2235540*x^4)*#1^6
+ (-496800 - 84960*x + 1504800*x^2 - 873120*x^3)*#1^7 + (74880 - 288000*x + 1900
80*x^2)*#1^8 + (19200 - 21760*x)*#1^9 + 1024*#1^10 & , 7]}, {y[x] -> Root[-45916
5024 + 1275458400*x - 1247114880*x^2 + 409406400*x^3 + 71033760*x^4 - 50349600*x
^5 - 5261760*x^6 + 2246400*x^7 + 506880*x^8 + 38400*x^9 + 1024*x^10 + 177147*C[1
]^5 + 295245*x*C[1]^5 + (637729200 - 2139935760*x + 2598156000*x^2 - 1246764960*
x^3 + 45586800*x^4 + 114715440*x^5 - 4838400*x^6 - 5592960*x^7 - 633600*x^8 - 21
760*x^9 - 295245*C[1]^5)*#1 + (-184232880 + 1015642800*x - 1778293440*x^2 + 1264
183200*x^3 - 266036400*x^4 - 70534800*x^5 + 17972640*x^6 + 3988800*x^7 + 190080*
x^8)*#1^2 + (-90541800 + 85118040*x + 276922800*x^2 - 473785200*x^3 + 219051000*
x^4 - 3051720*x^5 - 11592000*x^6 - 873120*x^7)*#1^3 + (39869010 - 154390050*x +
155568600*x^2 - 2902500*x^3 - 55677150*x^4 + 14206950*x^5 + 2235540*x^6)*#1^4 +
(7174575 + 6246315*x - 43079850*x^2 + 35619030*x^3 - 3208725*x^4 - 3122577*x^5)*
#1^5 + (-2953260 + 9795600*x - 6300360*x^2 - 2559600*x^3 + 2235540*x^4)*#1^6 + (
-496800 - 84960*x + 1504800*x^2 - 873120*x^3)*#1^7 + (74880 - 288000*x + 190080*
x^2)*#1^8 + (19200 - 21760*x)*#1^9 + 1024*#1^10 & , 8]}, {y[x] -> Root[-45916502
4 + 1275458400*x - 1247114880*x^2 + 409406400*x^3 + 71033760*x^4 - 50349600*x^5
- 5261760*x^6 + 2246400*x^7 + 506880*x^8 + 38400*x^9 + 1024*x^10 + 177147*C[1]^5
 + 295245*x*C[1]^5 + (637729200 - 2139935760*x + 2598156000*x^2 - 1246764960*x^3
 + 45586800*x^4 + 114715440*x^5 - 4838400*x^6 - 5592960*x^7 - 633600*x^8 - 21760
*x^9 - 295245*C[1]^5)*#1 + (-184232880 + 1015642800*x - 1778293440*x^2 + 1264183
200*x^3 - 266036400*x^4 - 70534800*x^5 + 17972640*x^6 + 3988800*x^7 + 190080*x^8
)*#1^2 + (-90541800 + 85118040*x + 276922800*x^2 - 473785200*x^3 + 219051000*x^4
 - 3051720*x^5 - 11592000*x^6 - 873120*x^7)*#1^3 + (39869010 - 154390050*x + 155
568600*x^2 - 2902500*x^3 - 55677150*x^4 + 14206950*x^5 + 2235540*x^6)*#1^4 + (71
74575 + 6246315*x - 43079850*x^2 + 35619030*x^3 - 3208725*x^4 - 3122577*x^5)*#1^
5 + (-2953260 + 9795600*x - 6300360*x^2 - 2559600*x^3 + 2235540*x^4)*#1^6 + (-49
6800 - 84960*x + 1504800*x^2 - 873120*x^3)*#1^7 + (74880 - 288000*x + 190080*x^2
)*#1^8 + (19200 - 21760*x)*#1^9 + 1024*#1^10 & , 9]}, {y[x] -> Root[-459165024 +
 1275458400*x - 1247114880*x^2 + 409406400*x^3 + 71033760*x^4 - 50349600*x^5 - 5
261760*x^6 + 2246400*x^7 + 506880*x^8 + 38400*x^9 + 1024*x^10 + 177147*C[1]^5 +
295245*x*C[1]^5 + (637729200 - 2139935760*x + 2598156000*x^2 - 1246764960*x^3 +
45586800*x^4 + 114715440*x^5 - 4838400*x^6 - 5592960*x^7 - 633600*x^8 - 21760*x^
9 - 295245*C[1]^5)*#1 + (-184232880 + 1015642800*x - 1778293440*x^2 + 1264183200
*x^3 - 266036400*x^4 - 70534800*x^5 + 17972640*x^6 + 3988800*x^7 + 190080*x^8)*#
1^2 + (-90541800 + 85118040*x + 276922800*x^2 - 473785200*x^3 + 219051000*x^4 -
3051720*x^5 - 11592000*x^6 - 873120*x^7)*#1^3 + (39869010 - 154390050*x + 155568
600*x^2 - 2902500*x^3 - 55677150*x^4 + 14206950*x^5 + 2235540*x^6)*#1^4 + (71745
75 + 6246315*x - 43079850*x^2 + 35619030*x^3 - 3208725*x^4 - 3122577*x^5)*#1^5 +
 (-2953260 + 9795600*x - 6300360*x^2 - 2559600*x^3 + 2235540*x^4)*#1^6 + (-49680
0 - 84960*x + 1504800*x^2 - 873120*x^3)*#1^7 + (74880 - 288000*x + 190080*x^2)*#
1^8 + (19200 - 21760*x)*#1^9 + 1024*#1^10 & , 10]}}

Maple raw input

dsolve((1-3*x+2*y(x))^2*diff(y(x),x) = (4+2*x-3*y(x))^2, y(x))

Maple raw output

[y(x) = 14/5+1/5*(-11+5*x)*(RootOf((115330078125*_C1*x^9-2283535546875*_C1*x^8+2
0095112812500*_C1*x^7-103154912437500*_C1*x^6+340411211043750*_C1*x^5-7489046642
96250*_C1*x^4+1098393507634500*_C1*x^3-1035628164341100*_C1*x^2+569595490387605*
_C1*x-139234453205859*_C1)*_Z^90+(-576650390625*_C1*x^9+11417677734375*_C1*x^8-1
00475564062500*_C1*x^7+515774562187500*_C1*x^6-1702056055218750*_C1*x^5+37445233
21481250*_C1*x^4-5491967538172500*_C1*x^3+5178140821705500*_C1*x^2-2847977451938
025*_C1*x+696172266029295*_C1+1)*_Z^81+(897011718750*_C1*x^9-17760832031250*_C1*
x^8+156295321875000*_C1*x^7-802315985625000*_C1*x^6+2647642752562500*_C1*x^5-582
4814055637500*_C1*x^4+8543060614935000*_C1*x^3-8054885722653000*_C1*x^2+44301871
47459150*_C1*x-1082934636045570*_C1)*_Z^72+(-128144531250*_C1*x^9+2537261718750*
_C1*x^8-22327903125000*_C1*x^7+114616569375000*_C1*x^6-378234678937500*_C1*x^5+8
32116293662500*_C1*x^4-1220437230705000*_C1*x^3+1150697960379000*_C1*x^2-6328838
78208450*_C1*x+154704948006510*_C1)*_Z^63+(-733271484375*_C1*x^9+14518775390625*
_C1*x^8-127765223437500*_C1*x^7+655861480312500*_C1*x^6-2164342885031250*_C1*x^5
+4761554347068750*_C1*x^4-6983613042367500*_C1*x^3+6584549439946500*_C1*x^2-3621
502191970575*_C1*x+885256091370585*_C1)*_Z^54+(226388671875*_C1*x^9-448249570312
5*_C1*x^8+39445962187500*_C1*x^7-202489272562500*_C1*x^6+668214599456250*_C1*x^5
-1470072118803750*_C1*x^4+2156105774245500*_C1*x^3-2032899730002900*_C1*x^2+1118
094851501595*_C1*x-273312074811501*_C1)*_Z^45+(325898437500*_C1*x^9-645278906250
0*_C1*x^8+56784543750000*_C1*x^7-291493991250000*_C1*x^6+961930171125000*_C1*x^5
-2116246376475000*_C1*x^4+3103828018830000*_C1*x^3-2926466417754000*_C1*x^2+1609
556529764700*_C1*x-393447151720260*_C1)*_Z^36+(-25312500000*_C1*x^9+501187500000
*_C1*x^8-4410450000000*_C1*x^7+22640310000000*_C1*x^6-74713023000000*_C1*x^5+164
368650600000*_C1*x^4-241074020880000*_C1*x^3+227298362544000*_C1*x^2-12501409939
9200*_C1*x+30559002075360*_C1)*_Z^27+(-78750000000*_C1*x^9+1559250000000*_C1*x^8
-13721400000000*_C1*x^7+70436520000000*_C1*x^6-232440516000000*_C1*x^5+511369135
200000*_C1*x^4-750008064960000*_C1*x^3+707150461248000*_C1*x^2-388932753686400*_
C1*x+95072450901120*_C1)*_Z^18+(-22500000000*_C1*x^9+445500000000*_C1*x^8-392040
0000000*_C1*x^7+20124720000000*_C1*x^6-66411576000000*_C1*x^5+146105467200000*_C
1*x^4-214288018560000*_C1*x^3+202042988928000*_C1*x^2-111123643910400*_C1*x+2716
3557400320*_C1)*_Z^9-2000000000*_C1*x^9+39600000000*_C1*x^8-348480000000*_C1*x^7
+1788864000000*_C1*x^6-5903251200000*_C1*x^5+12987152640000*_C1*x^4-190478238720
00*_C1*x^3+17959376793600*x^2*_C1-9877657236480*x*_C1+2414538435584*_C1)^9-1)/Ro
otOf((115330078125*_C1*x^9-2283535546875*_C1*x^8+20095112812500*_C1*x^7-10315491
2437500*_C1*x^6+340411211043750*_C1*x^5-748904664296250*_C1*x^4+1098393507634500
*_C1*x^3-1035628164341100*_C1*x^2+569595490387605*_C1*x-139234453205859*_C1)*_Z^
90+(-576650390625*_C1*x^9+11417677734375*_C1*x^8-100475564062500*_C1*x^7+5157745
62187500*_C1*x^6-1702056055218750*_C1*x^5+3744523321481250*_C1*x^4-5491967538172
500*_C1*x^3+5178140821705500*_C1*x^2-2847977451938025*_C1*x+696172266029295*_C1+
1)*_Z^81+(897011718750*_C1*x^9-17760832031250*_C1*x^8+156295321875000*_C1*x^7-80
2315985625000*_C1*x^6+2647642752562500*_C1*x^5-5824814055637500*_C1*x^4+85430606
14935000*_C1*x^3-8054885722653000*_C1*x^2+4430187147459150*_C1*x-108293463604557
0*_C1)*_Z^72+(-128144531250*_C1*x^9+2537261718750*_C1*x^8-22327903125000*_C1*x^7
+114616569375000*_C1*x^6-378234678937500*_C1*x^5+832116293662500*_C1*x^4-1220437
230705000*_C1*x^3+1150697960379000*_C1*x^2-632883878208450*_C1*x+154704948006510
*_C1)*_Z^63+(-733271484375*_C1*x^9+14518775390625*_C1*x^8-127765223437500*_C1*x^
7+655861480312500*_C1*x^6-2164342885031250*_C1*x^5+4761554347068750*_C1*x^4-6983
613042367500*_C1*x^3+6584549439946500*_C1*x^2-3621502191970575*_C1*x+88525609137
0585*_C1)*_Z^54+(226388671875*_C1*x^9-4482495703125*_C1*x^8+39445962187500*_C1*x
^7-202489272562500*_C1*x^6+668214599456250*_C1*x^5-1470072118803750*_C1*x^4+2156
105774245500*_C1*x^3-2032899730002900*_C1*x^2+1118094851501595*_C1*x-27331207481
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