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 = 0.177474 (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 = 0.042 (sec), leaf count = 75

\[ \left \{ -{\frac {5}{9}\ln \left ({\frac {45-20\,y \relax (x ) +5\,x}{-11+5\,x}} \right ) }+{\frac {1}{9}\ln \left ({\frac {3-5\,y \relax (x ) +5\,x}{-11+5\,x}} \right ) }-{\frac {5}{9}\ln \left ({\frac {-30-5\,y \relax (x ) +20\,x}{-11+5\,x}} \right ) }-\ln \left (-11+5\,x \right ) -{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

-5/9*ln((45-20*y(x)+5*x)/(-11+5*x))+1/9*ln((3-5*y(x)+5*x)/(-11+5*x))-5/9*ln((-30
-5*y(x)+20*x)/(-11+5*x))-ln(-11+5*x)-_C1 = 0