##### 4.10.7 $$(-y(x)-4 x+6) y'(x)=2 x-y(x)$$

ODE
$(-y(x)-4 x+6) y'(x)=2 x-y(x)$ ODE Classiﬁcation

[[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]

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

Mathematica
cpu = 0.299679 (sec), leaf count = 2563

$\left \{\left \{y(x)\to -4 x+\frac {1}{\text {Root}\left [\left (11664 e^{\frac {12 c_1}{25}} x^6-69984 e^{\frac {12 c_1}{25}} x^5+174960 e^{\frac {12 c_1}{25}} x^4+11664 x^4-233280 e^{\frac {12 c_1}{25}} x^3-46656 x^3+174960 e^{\frac {12 c_1}{25}} x^2+69984 x^2-69984 e^{\frac {12 c_1}{25}} x-46656 x+11664 e^{\frac {12 c_1}{25}}+11664\right ) \text {\#1}^6+\left (-23328 e^{\frac {12 c_1}{25}} x^5+116640 e^{\frac {12 c_1}{25}} x^4-233280 e^{\frac {12 c_1}{25}} x^3-23328 x^3+233280 e^{\frac {12 c_1}{25}} x^2+69984 x^2-116640 e^{\frac {12 c_1}{25}} x-69984 x+23328 e^{\frac {12 c_1}{25}}+23328\right ) \text {\#1}^5+\left (19440 e^{\frac {12 c_1}{25}} x^4-77760 e^{\frac {12 c_1}{25}} x^3+116640 e^{\frac {12 c_1}{25}} x^2+17496 x^2-77760 e^{\frac {12 c_1}{25}} x-34992 x+19440 e^{\frac {12 c_1}{25}}+17496\right ) \text {\#1}^4+\left (-8640 e^{\frac {12 c_1}{25}} x^3+25920 e^{\frac {12 c_1}{25}} x^2-25920 e^{\frac {12 c_1}{25}} x-5832 x+8640 e^{\frac {12 c_1}{25}}+5832\right ) \text {\#1}^3+\left (2160 e^{\frac {12 c_1}{25}} x^2-4320 e^{\frac {12 c_1}{25}} x+2160 e^{\frac {12 c_1}{25}}+729\right ) \text {\#1}^2+\left (288 e^{\frac {12 c_1}{25}}-288 e^{\frac {12 c_1}{25}} x\right ) \text {\#1}+16 e^{\frac {12 c_1}{25}}\& ,1\right ]}+6\right \},\left \{y(x)\to -4 x+\frac {1}{\text {Root}\left [\left (11664 e^{\frac {12 c_1}{25}} x^6-69984 e^{\frac {12 c_1}{25}} x^5+174960 e^{\frac {12 c_1}{25}} x^4+11664 x^4-233280 e^{\frac {12 c_1}{25}} x^3-46656 x^3+174960 e^{\frac {12 c_1}{25}} x^2+69984 x^2-69984 e^{\frac {12 c_1}{25}} x-46656 x+11664 e^{\frac {12 c_1}{25}}+11664\right ) \text {\#1}^6+\left (-23328 e^{\frac {12 c_1}{25}} x^5+116640 e^{\frac {12 c_1}{25}} x^4-233280 e^{\frac {12 c_1}{25}} x^3-23328 x^3+233280 e^{\frac {12 c_1}{25}} x^2+69984 x^2-116640 e^{\frac {12 c_1}{25}} x-69984 x+23328 e^{\frac {12 c_1}{25}}+23328\right ) \text {\#1}^5+\left (19440 e^{\frac {12 c_1}{25}} x^4-77760 e^{\frac {12 c_1}{25}} x^3+116640 e^{\frac {12 c_1}{25}} x^2+17496 x^2-77760 e^{\frac {12 c_1}{25}} x-34992 x+19440 e^{\frac {12 c_1}{25}}+17496\right ) \text {\#1}^4+\left (-8640 e^{\frac {12 c_1}{25}} x^3+25920 e^{\frac {12 c_1}{25}} x^2-25920 e^{\frac {12 c_1}{25}} x-5832 x+8640 e^{\frac {12 c_1}{25}}+5832\right ) \text {\#1}^3+\left (2160 e^{\frac {12 c_1}{25}} x^2-4320 e^{\frac {12 c_1}{25}} x+2160 e^{\frac {12 c_1}{25}}+729\right ) \text {\#1}^2+\left (288 e^{\frac {12 c_1}{25}}-288 e^{\frac {12 c_1}{25}} x\right ) \text {\#1}+16 e^{\frac {12 c_1}{25}}\& ,2\right ]}+6\right \},\left \{y(x)\to -4 x+\frac {1}{\text {Root}\left [\left (11664 e^{\frac {12 c_1}{25}} x^6-69984 e^{\frac {12 c_1}{25}} x^5+174960 e^{\frac {12 c_1}{25}} x^4+11664 x^4-233280 e^{\frac {12 c_1}{25}} x^3-46656 x^3+174960 e^{\frac {12 c_1}{25}} x^2+69984 x^2-69984 e^{\frac {12 c_1}{25}} x-46656 x+11664 e^{\frac {12 c_1}{25}}+11664\right ) \text {\#1}^6+\left (-23328 e^{\frac {12 c_1}{25}} x^5+116640 e^{\frac {12 c_1}{25}} x^4-233280 e^{\frac {12 c_1}{25}} x^3-23328 x^3+233280 e^{\frac {12 c_1}{25}} x^2+69984 x^2-116640 e^{\frac {12 c_1}{25}} x-69984 x+23328 e^{\frac {12 c_1}{25}}+23328\right ) \text {\#1}^5+\left (19440 e^{\frac {12 c_1}{25}} x^4-77760 e^{\frac {12 c_1}{25}} x^3+116640 e^{\frac {12 c_1}{25}} x^2+17496 x^2-77760 e^{\frac {12 c_1}{25}} x-34992 x+19440 e^{\frac {12 c_1}{25}}+17496\right ) \text {\#1}^4+\left (-8640 e^{\frac {12 c_1}{25}} x^3+25920 e^{\frac {12 c_1}{25}} x^2-25920 e^{\frac {12 c_1}{25}} x-5832 x+8640 e^{\frac {12 c_1}{25}}+5832\right ) \text {\#1}^3+\left (2160 e^{\frac {12 c_1}{25}} x^2-4320 e^{\frac {12 c_1}{25}} x+2160 e^{\frac {12 c_1}{25}}+729\right ) \text {\#1}^2+\left (288 e^{\frac {12 c_1}{25}}-288 e^{\frac {12 c_1}{25}} x\right ) \text {\#1}+16 e^{\frac {12 c_1}{25}}\& ,3\right ]}+6\right \},\left \{y(x)\to -4 x+\frac {1}{\text {Root}\left [\left (11664 e^{\frac {12 c_1}{25}} x^6-69984 e^{\frac {12 c_1}{25}} x^5+174960 e^{\frac {12 c_1}{25}} x^4+11664 x^4-233280 e^{\frac {12 c_1}{25}} x^3-46656 x^3+174960 e^{\frac {12 c_1}{25}} x^2+69984 x^2-69984 e^{\frac {12 c_1}{25}} x-46656 x+11664 e^{\frac {12 c_1}{25}}+11664\right ) \text {\#1}^6+\left (-23328 e^{\frac {12 c_1}{25}} x^5+116640 e^{\frac {12 c_1}{25}} x^4-233280 e^{\frac {12 c_1}{25}} x^3-23328 x^3+233280 e^{\frac {12 c_1}{25}} x^2+69984 x^2-116640 e^{\frac {12 c_1}{25}} x-69984 x+23328 e^{\frac {12 c_1}{25}}+23328\right ) \text {\#1}^5+\left (19440 e^{\frac {12 c_1}{25}} x^4-77760 e^{\frac {12 c_1}{25}} x^3+116640 e^{\frac {12 c_1}{25}} x^2+17496 x^2-77760 e^{\frac {12 c_1}{25}} x-34992 x+19440 e^{\frac {12 c_1}{25}}+17496\right ) \text {\#1}^4+\left (-8640 e^{\frac {12 c_1}{25}} x^3+25920 e^{\frac {12 c_1}{25}} x^2-25920 e^{\frac {12 c_1}{25}} x-5832 x+8640 e^{\frac {12 c_1}{25}}+5832\right ) \text {\#1}^3+\left (2160 e^{\frac {12 c_1}{25}} x^2-4320 e^{\frac {12 c_1}{25}} x+2160 e^{\frac {12 c_1}{25}}+729\right ) \text {\#1}^2+\left (288 e^{\frac {12 c_1}{25}}-288 e^{\frac {12 c_1}{25}} x\right ) \text {\#1}+16 e^{\frac {12 c_1}{25}}\& ,4\right ]}+6\right \},\left \{y(x)\to -4 x+\frac {1}{\text {Root}\left [\left (11664 e^{\frac {12 c_1}{25}} x^6-69984 e^{\frac {12 c_1}{25}} x^5+174960 e^{\frac {12 c_1}{25}} x^4+11664 x^4-233280 e^{\frac {12 c_1}{25}} x^3-46656 x^3+174960 e^{\frac {12 c_1}{25}} x^2+69984 x^2-69984 e^{\frac {12 c_1}{25}} x-46656 x+11664 e^{\frac {12 c_1}{25}}+11664\right ) \text {\#1}^6+\left (-23328 e^{\frac {12 c_1}{25}} x^5+116640 e^{\frac {12 c_1}{25}} x^4-233280 e^{\frac {12 c_1}{25}} x^3-23328 x^3+233280 e^{\frac {12 c_1}{25}} x^2+69984 x^2-116640 e^{\frac {12 c_1}{25}} x-69984 x+23328 e^{\frac {12 c_1}{25}}+23328\right ) \text {\#1}^5+\left (19440 e^{\frac {12 c_1}{25}} x^4-77760 e^{\frac {12 c_1}{25}} x^3+116640 e^{\frac {12 c_1}{25}} x^2+17496 x^2-77760 e^{\frac {12 c_1}{25}} x-34992 x+19440 e^{\frac {12 c_1}{25}}+17496\right ) \text {\#1}^4+\left (-8640 e^{\frac {12 c_1}{25}} x^3+25920 e^{\frac {12 c_1}{25}} x^2-25920 e^{\frac {12 c_1}{25}} x-5832 x+8640 e^{\frac {12 c_1}{25}}+5832\right ) \text {\#1}^3+\left (2160 e^{\frac {12 c_1}{25}} x^2-4320 e^{\frac {12 c_1}{25}} x+2160 e^{\frac {12 c_1}{25}}+729\right ) \text {\#1}^2+\left (288 e^{\frac {12 c_1}{25}}-288 e^{\frac {12 c_1}{25}} x\right ) \text {\#1}+16 e^{\frac {12 c_1}{25}}\& ,5\right ]}+6\right \},\left \{y(x)\to -4 x+\frac {1}{\text {Root}\left [\left (11664 e^{\frac {12 c_1}{25}} x^6-69984 e^{\frac {12 c_1}{25}} x^5+174960 e^{\frac {12 c_1}{25}} x^4+11664 x^4-233280 e^{\frac {12 c_1}{25}} x^3-46656 x^3+174960 e^{\frac {12 c_1}{25}} x^2+69984 x^2-69984 e^{\frac {12 c_1}{25}} x-46656 x+11664 e^{\frac {12 c_1}{25}}+11664\right ) \text {\#1}^6+\left (-23328 e^{\frac {12 c_1}{25}} x^5+116640 e^{\frac {12 c_1}{25}} x^4-233280 e^{\frac {12 c_1}{25}} x^3-23328 x^3+233280 e^{\frac {12 c_1}{25}} x^2+69984 x^2-116640 e^{\frac {12 c_1}{25}} x-69984 x+23328 e^{\frac {12 c_1}{25}}+23328\right ) \text {\#1}^5+\left (19440 e^{\frac {12 c_1}{25}} x^4-77760 e^{\frac {12 c_1}{25}} x^3+116640 e^{\frac {12 c_1}{25}} x^2+17496 x^2-77760 e^{\frac {12 c_1}{25}} x-34992 x+19440 e^{\frac {12 c_1}{25}}+17496\right ) \text {\#1}^4+\left (-8640 e^{\frac {12 c_1}{25}} x^3+25920 e^{\frac {12 c_1}{25}} x^2-25920 e^{\frac {12 c_1}{25}} x-5832 x+8640 e^{\frac {12 c_1}{25}}+5832\right ) \text {\#1}^3+\left (2160 e^{\frac {12 c_1}{25}} x^2-4320 e^{\frac {12 c_1}{25}} x+2160 e^{\frac {12 c_1}{25}}+729\right ) \text {\#1}^2+\left (288 e^{\frac {12 c_1}{25}}-288 e^{\frac {12 c_1}{25}} x\right ) \text {\#1}+16 e^{\frac {12 c_1}{25}}\& ,6\right ]}+6\right \}\right \}$

Maple
cpu = 0.073 (sec), leaf count = 254

$\left [y \left (x \right ) = 2+\frac {\left (12 \sqrt {3}\, \left (x -1\right ) \sqrt {\frac {\left (x -1\right ) \left (27 \textit {\_C1} \left (x -1\right )-4\right )}{\textit {\_C1}}}\, \textit {\_C1}^{2}+108 \left (x -1\right )^{2} \textit {\_C1}^{2}-72 \textit {\_C1} \left (x -1\right )+8\right )^{\frac {1}{3}}}{12 \textit {\_C1}}-\frac {6 \textit {\_C1} \left (x -1\right )-1}{3 \textit {\_C1} \left (12 \sqrt {3}\, \left (x -1\right ) \sqrt {\frac {\left (x -1\right ) \left (27 \textit {\_C1} \left (x -1\right )-4\right )}{\textit {\_C1}}}\, \textit {\_C1}^{2}+108 \left (x -1\right )^{2} \textit {\_C1}^{2}-72 \textit {\_C1} \left (x -1\right )+8\right )^{\frac {1}{3}}}-\frac {3 \textit {\_C1} \left (x -1\right )+1}{3 \textit {\_C1}}-\frac {i \sqrt {3}\, \left (\frac {\left (12 \sqrt {3}\, \left (x -1\right ) \sqrt {\frac {\left (x -1\right ) \left (27 \textit {\_C1} \left (x -1\right )-4\right )}{\textit {\_C1}}}\, \textit {\_C1}^{2}+108 \left (x -1\right )^{2} \textit {\_C1}^{2}-72 \textit {\_C1} \left (x -1\right )+8\right )^{\frac {1}{3}}}{6 \textit {\_C1}}+\frac {4 \textit {\_C1} \left (x -1\right )-\frac {2}{3}}{\textit {\_C1} \left (12 \sqrt {3}\, \left (x -1\right ) \sqrt {\frac {\left (x -1\right ) \left (27 \textit {\_C1} \left (x -1\right )-4\right )}{\textit {\_C1}}}\, \textit {\_C1}^{2}+108 \left (x -1\right )^{2} \textit {\_C1}^{2}-72 \textit {\_C1} \left (x -1\right )+8\right )^{\frac {1}{3}}}\right )}{2}\right ]$ Mathematica raw input

DSolve[(6 - 4*x - y[x])*y'[x] == 2*x - y[x],y[x],x]

Mathematica raw output

{{y[x] -> 6 - 4*x + Root[16*E^((12*C[1])/25) + (288*E^((12*C[1])/25) - 288*E^((1
2*C[1])/25)*x)*#1 + (729 + 2160*E^((12*C[1])/25) - 4320*E^((12*C[1])/25)*x + 216
0*E^((12*C[1])/25)*x^2)*#1^2 + (5832 + 8640*E^((12*C[1])/25) - 5832*x - 25920*E^
((12*C[1])/25)*x + 25920*E^((12*C[1])/25)*x^2 - 8640*E^((12*C[1])/25)*x^3)*#1^3
+ (17496 + 19440*E^((12*C[1])/25) - 34992*x - 77760*E^((12*C[1])/25)*x + 17496*x
^2 + 116640*E^((12*C[1])/25)*x^2 - 77760*E^((12*C[1])/25)*x^3 + 19440*E^((12*C[1
])/25)*x^4)*#1^4 + (23328 + 23328*E^((12*C[1])/25) - 69984*x - 116640*E^((12*C[1
])/25)*x + 69984*x^2 + 233280*E^((12*C[1])/25)*x^2 - 23328*x^3 - 233280*E^((12*C
[1])/25)*x^3 + 116640*E^((12*C[1])/25)*x^4 - 23328*E^((12*C[1])/25)*x^5)*#1^5 +
(11664 + 11664*E^((12*C[1])/25) - 46656*x - 69984*E^((12*C[1])/25)*x + 69984*x^2
 + 174960*E^((12*C[1])/25)*x^2 - 46656*x^3 - 233280*E^((12*C[1])/25)*x^3 + 11664
*x^4 + 174960*E^((12*C[1])/25)*x^4 - 69984*E^((12*C[1])/25)*x^5 + 11664*E^((12*C
[1])/25)*x^6)*#1^6 & , 1]^(-1)}, {y[x] -> 6 - 4*x + Root[16*E^((12*C[1])/25) + (
288*E^((12*C[1])/25) - 288*E^((12*C[1])/25)*x)*#1 + (729 + 2160*E^((12*C[1])/25)
 - 4320*E^((12*C[1])/25)*x + 2160*E^((12*C[1])/25)*x^2)*#1^2 + (5832 + 8640*E^((
12*C[1])/25) - 5832*x - 25920*E^((12*C[1])/25)*x + 25920*E^((12*C[1])/25)*x^2 -
8640*E^((12*C[1])/25)*x^3)*#1^3 + (17496 + 19440*E^((12*C[1])/25) - 34992*x - 77
760*E^((12*C[1])/25)*x + 17496*x^2 + 116640*E^((12*C[1])/25)*x^2 - 77760*E^((12*
C[1])/25)*x^3 + 19440*E^((12*C[1])/25)*x^4)*#1^4 + (23328 + 23328*E^((12*C[1])/2
5) - 69984*x - 116640*E^((12*C[1])/25)*x + 69984*x^2 + 233280*E^((12*C[1])/25)*x
^2 - 23328*x^3 - 233280*E^((12*C[1])/25)*x^3 + 116640*E^((12*C[1])/25)*x^4 - 233
28*E^((12*C[1])/25)*x^5)*#1^5 + (11664 + 11664*E^((12*C[1])/25) - 46656*x - 6998
4*E^((12*C[1])/25)*x + 69984*x^2 + 174960*E^((12*C[1])/25)*x^2 - 46656*x^3 - 233
280*E^((12*C[1])/25)*x^3 + 11664*x^4 + 174960*E^((12*C[1])/25)*x^4 - 69984*E^((1
2*C[1])/25)*x^5 + 11664*E^((12*C[1])/25)*x^6)*#1^6 & , 2]^(-1)}, {y[x] -> 6 - 4*
x + Root[16*E^((12*C[1])/25) + (288*E^((12*C[1])/25) - 288*E^((12*C[1])/25)*x)*#
1 + (729 + 2160*E^((12*C[1])/25) - 4320*E^((12*C[1])/25)*x + 2160*E^((12*C[1])/2
5)*x^2)*#1^2 + (5832 + 8640*E^((12*C[1])/25) - 5832*x - 25920*E^((12*C[1])/25)*x
 + 25920*E^((12*C[1])/25)*x^2 - 8640*E^((12*C[1])/25)*x^3)*#1^3 + (17496 + 19440
*E^((12*C[1])/25) - 34992*x - 77760*E^((12*C[1])/25)*x + 17496*x^2 + 116640*E^((
12*C[1])/25)*x^2 - 77760*E^((12*C[1])/25)*x^3 + 19440*E^((12*C[1])/25)*x^4)*#1^4
 + (23328 + 23328*E^((12*C[1])/25) - 69984*x - 116640*E^((12*C[1])/25)*x + 69984
*x^2 + 233280*E^((12*C[1])/25)*x^2 - 23328*x^3 - 233280*E^((12*C[1])/25)*x^3 + 1
16640*E^((12*C[1])/25)*x^4 - 23328*E^((12*C[1])/25)*x^5)*#1^5 + (11664 + 11664*E
^((12*C[1])/25) - 46656*x - 69984*E^((12*C[1])/25)*x + 69984*x^2 + 174960*E^((12
*C[1])/25)*x^2 - 46656*x^3 - 233280*E^((12*C[1])/25)*x^3 + 11664*x^4 + 174960*E^
((12*C[1])/25)*x^4 - 69984*E^((12*C[1])/25)*x^5 + 11664*E^((12*C[1])/25)*x^6)*#1
^6 & , 3]^(-1)}, {y[x] -> 6 - 4*x + Root[16*E^((12*C[1])/25) + (288*E^((12*C[1])
/25) - 288*E^((12*C[1])/25)*x)*#1 + (729 + 2160*E^((12*C[1])/25) - 4320*E^((12*C
[1])/25)*x + 2160*E^((12*C[1])/25)*x^2)*#1^2 + (5832 + 8640*E^((12*C[1])/25) - 5
832*x - 25920*E^((12*C[1])/25)*x + 25920*E^((12*C[1])/25)*x^2 - 8640*E^((12*C[1]
)/25)*x^3)*#1^3 + (17496 + 19440*E^((12*C[1])/25) - 34992*x - 77760*E^((12*C[1])
/25)*x + 17496*x^2 + 116640*E^((12*C[1])/25)*x^2 - 77760*E^((12*C[1])/25)*x^3 +
19440*E^((12*C[1])/25)*x^4)*#1^4 + (23328 + 23328*E^((12*C[1])/25) - 69984*x - 1
16640*E^((12*C[1])/25)*x + 69984*x^2 + 233280*E^((12*C[1])/25)*x^2 - 23328*x^3 -
 233280*E^((12*C[1])/25)*x^3 + 116640*E^((12*C[1])/25)*x^4 - 23328*E^((12*C[1])/
25)*x^5)*#1^5 + (11664 + 11664*E^((12*C[1])/25) - 46656*x - 69984*E^((12*C[1])/2
5)*x + 69984*x^2 + 174960*E^((12*C[1])/25)*x^2 - 46656*x^3 - 233280*E^((12*C[1])
/25)*x^3 + 11664*x^4 + 174960*E^((12*C[1])/25)*x^4 - 69984*E^((12*C[1])/25)*x^5
+ 11664*E^((12*C[1])/25)*x^6)*#1^6 & , 4]^(-1)}, {y[x] -> 6 - 4*x + Root[16*E^((
12*C[1])/25) + (288*E^((12*C[1])/25) - 288*E^((12*C[1])/25)*x)*#1 + (729 + 2160*
E^((12*C[1])/25) - 4320*E^((12*C[1])/25)*x + 2160*E^((12*C[1])/25)*x^2)*#1^2 + (
5832 + 8640*E^((12*C[1])/25) - 5832*x - 25920*E^((12*C[1])/25)*x + 25920*E^((12*
C[1])/25)*x^2 - 8640*E^((12*C[1])/25)*x^3)*#1^3 + (17496 + 19440*E^((12*C[1])/25
) - 34992*x - 77760*E^((12*C[1])/25)*x + 17496*x^2 + 116640*E^((12*C[1])/25)*x^2
 - 77760*E^((12*C[1])/25)*x^3 + 19440*E^((12*C[1])/25)*x^4)*#1^4 + (23328 + 2332
8*E^((12*C[1])/25) - 69984*x - 116640*E^((12*C[1])/25)*x + 69984*x^2 + 233280*E^
((12*C[1])/25)*x^2 - 23328*x^3 - 233280*E^((12*C[1])/25)*x^3 + 116640*E^((12*C[1
])/25)*x^4 - 23328*E^((12*C[1])/25)*x^5)*#1^5 + (11664 + 11664*E^((12*C[1])/25)
- 46656*x - 69984*E^((12*C[1])/25)*x + 69984*x^2 + 174960*E^((12*C[1])/25)*x^2 -
 46656*x^3 - 233280*E^((12*C[1])/25)*x^3 + 11664*x^4 + 174960*E^((12*C[1])/25)*x
^4 - 69984*E^((12*C[1])/25)*x^5 + 11664*E^((12*C[1])/25)*x^6)*#1^6 & , 5]^(-1)},
 {y[x] -> 6 - 4*x + Root[16*E^((12*C[1])/25) + (288*E^((12*C[1])/25) - 288*E^((1
2*C[1])/25)*x)*#1 + (729 + 2160*E^((12*C[1])/25) - 4320*E^((12*C[1])/25)*x + 216
0*E^((12*C[1])/25)*x^2)*#1^2 + (5832 + 8640*E^((12*C[1])/25) - 5832*x - 25920*E^
((12*C[1])/25)*x + 25920*E^((12*C[1])/25)*x^2 - 8640*E^((12*C[1])/25)*x^3)*#1^3
+ (17496 + 19440*E^((12*C[1])/25) - 34992*x - 77760*E^((12*C[1])/25)*x + 17496*x
^2 + 116640*E^((12*C[1])/25)*x^2 - 77760*E^((12*C[1])/25)*x^3 + 19440*E^((12*C[1
])/25)*x^4)*#1^4 + (23328 + 23328*E^((12*C[1])/25) - 69984*x - 116640*E^((12*C[1
])/25)*x + 69984*x^2 + 233280*E^((12*C[1])/25)*x^2 - 23328*x^3 - 233280*E^((12*C
[1])/25)*x^3 + 116640*E^((12*C[1])/25)*x^4 - 23328*E^((12*C[1])/25)*x^5)*#1^5 +
(11664 + 11664*E^((12*C[1])/25) - 46656*x - 69984*E^((12*C[1])/25)*x + 69984*x^2
 + 174960*E^((12*C[1])/25)*x^2 - 46656*x^3 - 233280*E^((12*C[1])/25)*x^3 + 11664
*x^4 + 174960*E^((12*C[1])/25)*x^4 - 69984*E^((12*C[1])/25)*x^5 + 11664*E^((12*C
[1])/25)*x^6)*#1^6 & , 6]^(-1)}}

Maple raw input

dsolve((6-4*x-y(x))*diff(y(x),x) = 2*x-y(x), y(x))

Maple raw output

[y(x) = 2+1/12/_C1*(12*3^(1/2)*(x-1)*(1/_C1*(x-1)*(27*_C1*(x-1)-4))^(1/2)*_C1^2+
108*(x-1)^2*_C1^2-72*_C1*(x-1)+8)^(1/3)-1/3*(6*_C1*(x-1)-1)/_C1/(12*3^(1/2)*(x-1
)*(1/_C1*(x-1)*(27*_C1*(x-1)-4))^(1/2)*_C1^2+108*(x-1)^2*_C1^2-72*_C1*(x-1)+8)^(
1/3)-1/3*(3*_C1*(x-1)+1)/_C1-1/2*I*3^(1/2)*(1/6/_C1*(12*3^(1/2)*(x-1)*(1/_C1*(x-
1)*(27*_C1*(x-1)-4))^(1/2)*_C1^2+108*(x-1)^2*_C1^2-72*_C1*(x-1)+8)^(1/3)+2/3*(6*
_C1*(x-1)-1)/_C1/(12*3^(1/2)*(x-1)*(1/_C1*(x-1)*(27*_C1*(x-1)-4))^(1/2)*_C1^2+10
8*(x-1)^2*_C1^2-72*_C1*(x-1)+8)^(1/3))]