##### 4.10.20 $$(2 y(x)+x+1) y'(x)-4 y(x)+x+7=0$$

ODE
$(2 y(x)+x+1) y'(x)-4 y(x)+x+7=0$ 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 = 0.301585 (sec), leaf count = 2587

$\left \{\left \{y(x)\to \frac {1}{2} \left (-x+\frac {1}{\text {Root}\left [\left (11664 e^{\frac {12 c_1}{25}} x^6+209952 e^{\frac {12 c_1}{25}} x^5+1574640 e^{\frac {12 c_1}{25}} x^4+11664 x^4+6298560 e^{\frac {12 c_1}{25}} x^3+139968 x^3+14171760 e^{\frac {12 c_1}{25}} x^2+629856 x^2+17006112 e^{\frac {12 c_1}{25}} x+1259712 x+8503056 e^{\frac {12 c_1}{25}}+944784\right ) \text {\#1}^6+\left (-23328 e^{\frac {12 c_1}{25}} x^5-349920 e^{\frac {12 c_1}{25}} x^4-2099520 e^{\frac {12 c_1}{25}} x^3-23328 x^3-6298560 e^{\frac {12 c_1}{25}} x^2-209952 x^2-9447840 e^{\frac {12 c_1}{25}} x-629856 x-5668704 e^{\frac {12 c_1}{25}}-629856\right ) \text {\#1}^5+\left (19440 e^{\frac {12 c_1}{25}} x^4+233280 e^{\frac {12 c_1}{25}} x^3+1049760 e^{\frac {12 c_1}{25}} x^2+17496 x^2+2099520 e^{\frac {12 c_1}{25}} x+104976 x+1574640 e^{\frac {12 c_1}{25}}+157464\right ) \text {\#1}^4+\left (-8640 e^{\frac {12 c_1}{25}} x^3-77760 e^{\frac {12 c_1}{25}} x^2-233280 e^{\frac {12 c_1}{25}} x-5832 x-233280 e^{\frac {12 c_1}{25}}-17496\right ) \text {\#1}^3+\left (2160 e^{\frac {12 c_1}{25}} x^2+12960 e^{\frac {12 c_1}{25}} x+19440 e^{\frac {12 c_1}{25}}+729\right ) \text {\#1}^2+\left (-288 e^{\frac {12 c_1}{25}} x-864 e^{\frac {12 c_1}{25}}\right ) \text {\#1}+16 e^{\frac {12 c_1}{25}}\& ,1\right ]}-1\right )\right \},\left \{y(x)\to \frac {1}{2} \left (-x+\frac {1}{\text {Root}\left [\left (11664 e^{\frac {12 c_1}{25}} x^6+209952 e^{\frac {12 c_1}{25}} x^5+1574640 e^{\frac {12 c_1}{25}} x^4+11664 x^4+6298560 e^{\frac {12 c_1}{25}} x^3+139968 x^3+14171760 e^{\frac {12 c_1}{25}} x^2+629856 x^2+17006112 e^{\frac {12 c_1}{25}} x+1259712 x+8503056 e^{\frac {12 c_1}{25}}+944784\right ) \text {\#1}^6+\left (-23328 e^{\frac {12 c_1}{25}} x^5-349920 e^{\frac {12 c_1}{25}} x^4-2099520 e^{\frac {12 c_1}{25}} x^3-23328 x^3-6298560 e^{\frac {12 c_1}{25}} x^2-209952 x^2-9447840 e^{\frac {12 c_1}{25}} x-629856 x-5668704 e^{\frac {12 c_1}{25}}-629856\right ) \text {\#1}^5+\left (19440 e^{\frac {12 c_1}{25}} x^4+233280 e^{\frac {12 c_1}{25}} x^3+1049760 e^{\frac {12 c_1}{25}} x^2+17496 x^2+2099520 e^{\frac {12 c_1}{25}} x+104976 x+1574640 e^{\frac {12 c_1}{25}}+157464\right ) \text {\#1}^4+\left (-8640 e^{\frac {12 c_1}{25}} x^3-77760 e^{\frac {12 c_1}{25}} x^2-233280 e^{\frac {12 c_1}{25}} x-5832 x-233280 e^{\frac {12 c_1}{25}}-17496\right ) \text {\#1}^3+\left (2160 e^{\frac {12 c_1}{25}} x^2+12960 e^{\frac {12 c_1}{25}} x+19440 e^{\frac {12 c_1}{25}}+729\right ) \text {\#1}^2+\left (-288 e^{\frac {12 c_1}{25}} x-864 e^{\frac {12 c_1}{25}}\right ) \text {\#1}+16 e^{\frac {12 c_1}{25}}\& ,2\right ]}-1\right )\right \},\left \{y(x)\to \frac {1}{2} \left (-x+\frac {1}{\text {Root}\left [\left (11664 e^{\frac {12 c_1}{25}} x^6+209952 e^{\frac {12 c_1}{25}} x^5+1574640 e^{\frac {12 c_1}{25}} x^4+11664 x^4+6298560 e^{\frac {12 c_1}{25}} x^3+139968 x^3+14171760 e^{\frac {12 c_1}{25}} x^2+629856 x^2+17006112 e^{\frac {12 c_1}{25}} x+1259712 x+8503056 e^{\frac {12 c_1}{25}}+944784\right ) \text {\#1}^6+\left (-23328 e^{\frac {12 c_1}{25}} x^5-349920 e^{\frac {12 c_1}{25}} x^4-2099520 e^{\frac {12 c_1}{25}} x^3-23328 x^3-6298560 e^{\frac {12 c_1}{25}} x^2-209952 x^2-9447840 e^{\frac {12 c_1}{25}} x-629856 x-5668704 e^{\frac {12 c_1}{25}}-629856\right ) \text {\#1}^5+\left (19440 e^{\frac {12 c_1}{25}} x^4+233280 e^{\frac {12 c_1}{25}} x^3+1049760 e^{\frac {12 c_1}{25}} x^2+17496 x^2+2099520 e^{\frac {12 c_1}{25}} x+104976 x+1574640 e^{\frac {12 c_1}{25}}+157464\right ) \text {\#1}^4+\left (-8640 e^{\frac {12 c_1}{25}} x^3-77760 e^{\frac {12 c_1}{25}} x^2-233280 e^{\frac {12 c_1}{25}} x-5832 x-233280 e^{\frac {12 c_1}{25}}-17496\right ) \text {\#1}^3+\left (2160 e^{\frac {12 c_1}{25}} x^2+12960 e^{\frac {12 c_1}{25}} x+19440 e^{\frac {12 c_1}{25}}+729\right ) \text {\#1}^2+\left (-288 e^{\frac {12 c_1}{25}} x-864 e^{\frac {12 c_1}{25}}\right ) \text {\#1}+16 e^{\frac {12 c_1}{25}}\& ,3\right ]}-1\right )\right \},\left \{y(x)\to \frac {1}{2} \left (-x+\frac {1}{\text {Root}\left [\left (11664 e^{\frac {12 c_1}{25}} x^6+209952 e^{\frac {12 c_1}{25}} x^5+1574640 e^{\frac {12 c_1}{25}} x^4+11664 x^4+6298560 e^{\frac {12 c_1}{25}} x^3+139968 x^3+14171760 e^{\frac {12 c_1}{25}} x^2+629856 x^2+17006112 e^{\frac {12 c_1}{25}} x+1259712 x+8503056 e^{\frac {12 c_1}{25}}+944784\right ) \text {\#1}^6+\left (-23328 e^{\frac {12 c_1}{25}} x^5-349920 e^{\frac {12 c_1}{25}} x^4-2099520 e^{\frac {12 c_1}{25}} x^3-23328 x^3-6298560 e^{\frac {12 c_1}{25}} x^2-209952 x^2-9447840 e^{\frac {12 c_1}{25}} x-629856 x-5668704 e^{\frac {12 c_1}{25}}-629856\right ) \text {\#1}^5+\left (19440 e^{\frac {12 c_1}{25}} x^4+233280 e^{\frac {12 c_1}{25}} x^3+1049760 e^{\frac {12 c_1}{25}} x^2+17496 x^2+2099520 e^{\frac {12 c_1}{25}} x+104976 x+1574640 e^{\frac {12 c_1}{25}}+157464\right ) \text {\#1}^4+\left (-8640 e^{\frac {12 c_1}{25}} x^3-77760 e^{\frac {12 c_1}{25}} x^2-233280 e^{\frac {12 c_1}{25}} x-5832 x-233280 e^{\frac {12 c_1}{25}}-17496\right ) \text {\#1}^3+\left (2160 e^{\frac {12 c_1}{25}} x^2+12960 e^{\frac {12 c_1}{25}} x+19440 e^{\frac {12 c_1}{25}}+729\right ) \text {\#1}^2+\left (-288 e^{\frac {12 c_1}{25}} x-864 e^{\frac {12 c_1}{25}}\right ) \text {\#1}+16 e^{\frac {12 c_1}{25}}\& ,4\right ]}-1\right )\right \},\left \{y(x)\to \frac {1}{2} \left (-x+\frac {1}{\text {Root}\left [\left (11664 e^{\frac {12 c_1}{25}} x^6+209952 e^{\frac {12 c_1}{25}} x^5+1574640 e^{\frac {12 c_1}{25}} x^4+11664 x^4+6298560 e^{\frac {12 c_1}{25}} x^3+139968 x^3+14171760 e^{\frac {12 c_1}{25}} x^2+629856 x^2+17006112 e^{\frac {12 c_1}{25}} x+1259712 x+8503056 e^{\frac {12 c_1}{25}}+944784\right ) \text {\#1}^6+\left (-23328 e^{\frac {12 c_1}{25}} x^5-349920 e^{\frac {12 c_1}{25}} x^4-2099520 e^{\frac {12 c_1}{25}} x^3-23328 x^3-6298560 e^{\frac {12 c_1}{25}} x^2-209952 x^2-9447840 e^{\frac {12 c_1}{25}} x-629856 x-5668704 e^{\frac {12 c_1}{25}}-629856\right ) \text {\#1}^5+\left (19440 e^{\frac {12 c_1}{25}} x^4+233280 e^{\frac {12 c_1}{25}} x^3+1049760 e^{\frac {12 c_1}{25}} x^2+17496 x^2+2099520 e^{\frac {12 c_1}{25}} x+104976 x+1574640 e^{\frac {12 c_1}{25}}+157464\right ) \text {\#1}^4+\left (-8640 e^{\frac {12 c_1}{25}} x^3-77760 e^{\frac {12 c_1}{25}} x^2-233280 e^{\frac {12 c_1}{25}} x-5832 x-233280 e^{\frac {12 c_1}{25}}-17496\right ) \text {\#1}^3+\left (2160 e^{\frac {12 c_1}{25}} x^2+12960 e^{\frac {12 c_1}{25}} x+19440 e^{\frac {12 c_1}{25}}+729\right ) \text {\#1}^2+\left (-288 e^{\frac {12 c_1}{25}} x-864 e^{\frac {12 c_1}{25}}\right ) \text {\#1}+16 e^{\frac {12 c_1}{25}}\& ,5\right ]}-1\right )\right \},\left \{y(x)\to \frac {1}{2} \left (-x+\frac {1}{\text {Root}\left [\left (11664 e^{\frac {12 c_1}{25}} x^6+209952 e^{\frac {12 c_1}{25}} x^5+1574640 e^{\frac {12 c_1}{25}} x^4+11664 x^4+6298560 e^{\frac {12 c_1}{25}} x^3+139968 x^3+14171760 e^{\frac {12 c_1}{25}} x^2+629856 x^2+17006112 e^{\frac {12 c_1}{25}} x+1259712 x+8503056 e^{\frac {12 c_1}{25}}+944784\right ) \text {\#1}^6+\left (-23328 e^{\frac {12 c_1}{25}} x^5-349920 e^{\frac {12 c_1}{25}} x^4-2099520 e^{\frac {12 c_1}{25}} x^3-23328 x^3-6298560 e^{\frac {12 c_1}{25}} x^2-209952 x^2-9447840 e^{\frac {12 c_1}{25}} x-629856 x-5668704 e^{\frac {12 c_1}{25}}-629856\right ) \text {\#1}^5+\left (19440 e^{\frac {12 c_1}{25}} x^4+233280 e^{\frac {12 c_1}{25}} x^3+1049760 e^{\frac {12 c_1}{25}} x^2+17496 x^2+2099520 e^{\frac {12 c_1}{25}} x+104976 x+1574640 e^{\frac {12 c_1}{25}}+157464\right ) \text {\#1}^4+\left (-8640 e^{\frac {12 c_1}{25}} x^3-77760 e^{\frac {12 c_1}{25}} x^2-233280 e^{\frac {12 c_1}{25}} x-5832 x-233280 e^{\frac {12 c_1}{25}}-17496\right ) \text {\#1}^3+\left (2160 e^{\frac {12 c_1}{25}} x^2+12960 e^{\frac {12 c_1}{25}} x+19440 e^{\frac {12 c_1}{25}}+729\right ) \text {\#1}^2+\left (-288 e^{\frac {12 c_1}{25}} x-864 e^{\frac {12 c_1}{25}}\right ) \text {\#1}+16 e^{\frac {12 c_1}{25}}\& ,6\right ]}-1\right )\right \}\right \}$

Maple
cpu = 0.071 (sec), leaf count = 254

$\left [y \left (x \right ) = 1+\frac {\left (12 \sqrt {3}\, \left (3+x \right ) \sqrt {\frac {\left (3+x \right ) \left (27 \left (3+x \right ) \textit {\_C1} -32\right )}{\textit {\_C1}}}\, \textit {\_C1}^{2}+108 \left (3+x \right )^{2} \textit {\_C1}^{2}-576 \left (3+x \right ) \textit {\_C1} +512\right )^{\frac {1}{3}}}{12 \textit {\_C1}}-\frac {4 \left (3 \left (3+x \right ) \textit {\_C1} -4\right )}{3 \textit {\_C1} \left (12 \sqrt {3}\, \left (3+x \right ) \sqrt {\frac {\left (3+x \right ) \left (27 \left (3+x \right ) \textit {\_C1} -32\right )}{\textit {\_C1}}}\, \textit {\_C1}^{2}+108 \left (3+x \right )^{2} \textit {\_C1}^{2}-576 \left (3+x \right ) \textit {\_C1} +512\right )^{\frac {1}{3}}}+\frac {3 \left (3+x \right ) \textit {\_C1} -4}{3 \textit {\_C1}}-\frac {i \sqrt {3}\, \left (\frac {\left (12 \sqrt {3}\, \left (3+x \right ) \sqrt {\frac {\left (3+x \right ) \left (27 \left (3+x \right ) \textit {\_C1} -32\right )}{\textit {\_C1}}}\, \textit {\_C1}^{2}+108 \left (3+x \right )^{2} \textit {\_C1}^{2}-576 \left (3+x \right ) \textit {\_C1} +512\right )^{\frac {1}{3}}}{6 \textit {\_C1}}+\frac {8 \left (3+x \right ) \textit {\_C1} -\frac {32}{3}}{\textit {\_C1} \left (12 \sqrt {3}\, \left (3+x \right ) \sqrt {\frac {\left (3+x \right ) \left (27 \left (3+x \right ) \textit {\_C1} -32\right )}{\textit {\_C1}}}\, \textit {\_C1}^{2}+108 \left (3+x \right )^{2} \textit {\_C1}^{2}-576 \left (3+x \right ) \textit {\_C1} +512\right )^{\frac {1}{3}}}\right )}{2}\right ]$ Mathematica raw input

DSolve[7 + x - 4*y[x] + (1 + x + 2*y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (-1 - x + Root[16*E^((12*C[1])/25) + (-864*E^((12*C[1])/25) - 288*E^((
12*C[1])/25)*x)*#1 + (729 + 19440*E^((12*C[1])/25) + 12960*E^((12*C[1])/25)*x +
2160*E^((12*C[1])/25)*x^2)*#1^2 + (-17496 - 233280*E^((12*C[1])/25) - 5832*x - 2
33280*E^((12*C[1])/25)*x - 77760*E^((12*C[1])/25)*x^2 - 8640*E^((12*C[1])/25)*x^
3)*#1^3 + (157464 + 1574640*E^((12*C[1])/25) + 104976*x + 2099520*E^((12*C[1])/2
5)*x + 17496*x^2 + 1049760*E^((12*C[1])/25)*x^2 + 233280*E^((12*C[1])/25)*x^3 +
19440*E^((12*C[1])/25)*x^4)*#1^4 + (-629856 - 5668704*E^((12*C[1])/25) - 629856*
x - 9447840*E^((12*C[1])/25)*x - 209952*x^2 - 6298560*E^((12*C[1])/25)*x^2 - 233
28*x^3 - 2099520*E^((12*C[1])/25)*x^3 - 349920*E^((12*C[1])/25)*x^4 - 23328*E^((
12*C[1])/25)*x^5)*#1^5 + (944784 + 8503056*E^((12*C[1])/25) + 1259712*x + 170061
12*E^((12*C[1])/25)*x + 629856*x^2 + 14171760*E^((12*C[1])/25)*x^2 + 139968*x^3
+ 6298560*E^((12*C[1])/25)*x^3 + 11664*x^4 + 1574640*E^((12*C[1])/25)*x^4 + 2099
52*E^((12*C[1])/25)*x^5 + 11664*E^((12*C[1])/25)*x^6)*#1^6 & , 1]^(-1))/2}, {y[x
] -> (-1 - x + Root[16*E^((12*C[1])/25) + (-864*E^((12*C[1])/25) - 288*E^((12*C[
1])/25)*x)*#1 + (729 + 19440*E^((12*C[1])/25) + 12960*E^((12*C[1])/25)*x + 2160*
E^((12*C[1])/25)*x^2)*#1^2 + (-17496 - 233280*E^((12*C[1])/25) - 5832*x - 233280
*E^((12*C[1])/25)*x - 77760*E^((12*C[1])/25)*x^2 - 8640*E^((12*C[1])/25)*x^3)*#1
^3 + (157464 + 1574640*E^((12*C[1])/25) + 104976*x + 2099520*E^((12*C[1])/25)*x
+ 17496*x^2 + 1049760*E^((12*C[1])/25)*x^2 + 233280*E^((12*C[1])/25)*x^3 + 19440
*E^((12*C[1])/25)*x^4)*#1^4 + (-629856 - 5668704*E^((12*C[1])/25) - 629856*x - 9
447840*E^((12*C[1])/25)*x - 209952*x^2 - 6298560*E^((12*C[1])/25)*x^2 - 23328*x^
3 - 2099520*E^((12*C[1])/25)*x^3 - 349920*E^((12*C[1])/25)*x^4 - 23328*E^((12*C[
1])/25)*x^5)*#1^5 + (944784 + 8503056*E^((12*C[1])/25) + 1259712*x + 17006112*E^
((12*C[1])/25)*x + 629856*x^2 + 14171760*E^((12*C[1])/25)*x^2 + 139968*x^3 + 629
8560*E^((12*C[1])/25)*x^3 + 11664*x^4 + 1574640*E^((12*C[1])/25)*x^4 + 209952*E^
((12*C[1])/25)*x^5 + 11664*E^((12*C[1])/25)*x^6)*#1^6 & , 2]^(-1))/2}, {y[x] ->
(-1 - x + Root[16*E^((12*C[1])/25) + (-864*E^((12*C[1])/25) - 288*E^((12*C[1])/2
5)*x)*#1 + (729 + 19440*E^((12*C[1])/25) + 12960*E^((12*C[1])/25)*x + 2160*E^((1
2*C[1])/25)*x^2)*#1^2 + (-17496 - 233280*E^((12*C[1])/25) - 5832*x - 233280*E^((
12*C[1])/25)*x - 77760*E^((12*C[1])/25)*x^2 - 8640*E^((12*C[1])/25)*x^3)*#1^3 +
(157464 + 1574640*E^((12*C[1])/25) + 104976*x + 2099520*E^((12*C[1])/25)*x + 174
96*x^2 + 1049760*E^((12*C[1])/25)*x^2 + 233280*E^((12*C[1])/25)*x^3 + 19440*E^((
12*C[1])/25)*x^4)*#1^4 + (-629856 - 5668704*E^((12*C[1])/25) - 629856*x - 944784
0*E^((12*C[1])/25)*x - 209952*x^2 - 6298560*E^((12*C[1])/25)*x^2 - 23328*x^3 - 2
099520*E^((12*C[1])/25)*x^3 - 349920*E^((12*C[1])/25)*x^4 - 23328*E^((12*C[1])/2
5)*x^5)*#1^5 + (944784 + 8503056*E^((12*C[1])/25) + 1259712*x + 17006112*E^((12*
C[1])/25)*x + 629856*x^2 + 14171760*E^((12*C[1])/25)*x^2 + 139968*x^3 + 6298560*
E^((12*C[1])/25)*x^3 + 11664*x^4 + 1574640*E^((12*C[1])/25)*x^4 + 209952*E^((12*
C[1])/25)*x^5 + 11664*E^((12*C[1])/25)*x^6)*#1^6 & , 3]^(-1))/2}, {y[x] -> (-1 -
 x + Root[16*E^((12*C[1])/25) + (-864*E^((12*C[1])/25) - 288*E^((12*C[1])/25)*x)
*#1 + (729 + 19440*E^((12*C[1])/25) + 12960*E^((12*C[1])/25)*x + 2160*E^((12*C[1
])/25)*x^2)*#1^2 + (-17496 - 233280*E^((12*C[1])/25) - 5832*x - 233280*E^((12*C[
1])/25)*x - 77760*E^((12*C[1])/25)*x^2 - 8640*E^((12*C[1])/25)*x^3)*#1^3 + (1574
64 + 1574640*E^((12*C[1])/25) + 104976*x + 2099520*E^((12*C[1])/25)*x + 17496*x^
2 + 1049760*E^((12*C[1])/25)*x^2 + 233280*E^((12*C[1])/25)*x^3 + 19440*E^((12*C[
1])/25)*x^4)*#1^4 + (-629856 - 5668704*E^((12*C[1])/25) - 629856*x - 9447840*E^(
(12*C[1])/25)*x - 209952*x^2 - 6298560*E^((12*C[1])/25)*x^2 - 23328*x^3 - 209952
0*E^((12*C[1])/25)*x^3 - 349920*E^((12*C[1])/25)*x^4 - 23328*E^((12*C[1])/25)*x^
5)*#1^5 + (944784 + 8503056*E^((12*C[1])/25) + 1259712*x + 17006112*E^((12*C[1])
/25)*x + 629856*x^2 + 14171760*E^((12*C[1])/25)*x^2 + 139968*x^3 + 6298560*E^((1
2*C[1])/25)*x^3 + 11664*x^4 + 1574640*E^((12*C[1])/25)*x^4 + 209952*E^((12*C[1])
/25)*x^5 + 11664*E^((12*C[1])/25)*x^6)*#1^6 & , 4]^(-1))/2}, {y[x] -> (-1 - x +
Root[16*E^((12*C[1])/25) + (-864*E^((12*C[1])/25) - 288*E^((12*C[1])/25)*x)*#1 +
 (729 + 19440*E^((12*C[1])/25) + 12960*E^((12*C[1])/25)*x + 2160*E^((12*C[1])/25
)*x^2)*#1^2 + (-17496 - 233280*E^((12*C[1])/25) - 5832*x - 233280*E^((12*C[1])/2
5)*x - 77760*E^((12*C[1])/25)*x^2 - 8640*E^((12*C[1])/25)*x^3)*#1^3 + (157464 +
1574640*E^((12*C[1])/25) + 104976*x + 2099520*E^((12*C[1])/25)*x + 17496*x^2 + 1
049760*E^((12*C[1])/25)*x^2 + 233280*E^((12*C[1])/25)*x^3 + 19440*E^((12*C[1])/2
5)*x^4)*#1^4 + (-629856 - 5668704*E^((12*C[1])/25) - 629856*x - 9447840*E^((12*C
[1])/25)*x - 209952*x^2 - 6298560*E^((12*C[1])/25)*x^2 - 23328*x^3 - 2099520*E^(
(12*C[1])/25)*x^3 - 349920*E^((12*C[1])/25)*x^4 - 23328*E^((12*C[1])/25)*x^5)*#1
^5 + (944784 + 8503056*E^((12*C[1])/25) + 1259712*x + 17006112*E^((12*C[1])/25)*
x + 629856*x^2 + 14171760*E^((12*C[1])/25)*x^2 + 139968*x^3 + 6298560*E^((12*C[1
])/25)*x^3 + 11664*x^4 + 1574640*E^((12*C[1])/25)*x^4 + 209952*E^((12*C[1])/25)*
x^5 + 11664*E^((12*C[1])/25)*x^6)*#1^6 & , 5]^(-1))/2}, {y[x] -> (-1 - x + Root[
16*E^((12*C[1])/25) + (-864*E^((12*C[1])/25) - 288*E^((12*C[1])/25)*x)*#1 + (729
 + 19440*E^((12*C[1])/25) + 12960*E^((12*C[1])/25)*x + 2160*E^((12*C[1])/25)*x^2
)*#1^2 + (-17496 - 233280*E^((12*C[1])/25) - 5832*x - 233280*E^((12*C[1])/25)*x
- 77760*E^((12*C[1])/25)*x^2 - 8640*E^((12*C[1])/25)*x^3)*#1^3 + (157464 + 15746
40*E^((12*C[1])/25) + 104976*x + 2099520*E^((12*C[1])/25)*x + 17496*x^2 + 104976
0*E^((12*C[1])/25)*x^2 + 233280*E^((12*C[1])/25)*x^3 + 19440*E^((12*C[1])/25)*x^
4)*#1^4 + (-629856 - 5668704*E^((12*C[1])/25) - 629856*x - 9447840*E^((12*C[1])/
25)*x - 209952*x^2 - 6298560*E^((12*C[1])/25)*x^2 - 23328*x^3 - 2099520*E^((12*C
[1])/25)*x^3 - 349920*E^((12*C[1])/25)*x^4 - 23328*E^((12*C[1])/25)*x^5)*#1^5 +
(944784 + 8503056*E^((12*C[1])/25) + 1259712*x + 17006112*E^((12*C[1])/25)*x + 6
29856*x^2 + 14171760*E^((12*C[1])/25)*x^2 + 139968*x^3 + 6298560*E^((12*C[1])/25
)*x^3 + 11664*x^4 + 1574640*E^((12*C[1])/25)*x^4 + 209952*E^((12*C[1])/25)*x^5 +
 11664*E^((12*C[1])/25)*x^6)*#1^6 & , 6]^(-1))/2}}

Maple raw input

dsolve((1+x+2*y(x))*diff(y(x),x)+7+x-4*y(x) = 0, y(x))

Maple raw output

[y(x) = 1+1/12/_C1*(12*3^(1/2)*(3+x)*(1/_C1*(3+x)*(27*(3+x)*_C1-32))^(1/2)*_C1^2
+108*(3+x)^2*_C1^2-576*(3+x)*_C1+512)^(1/3)-4/3*(3*(3+x)*_C1-4)/_C1/(12*3^(1/2)*
(3+x)*(1/_C1*(3+x)*(27*(3+x)*_C1-32))^(1/2)*_C1^2+108*(3+x)^2*_C1^2-576*(3+x)*_C
1+512)^(1/3)+1/3*(3*(3+x)*_C1-4)/_C1-1/2*I*3^(1/2)*(1/6/_C1*(12*3^(1/2)*(3+x)*(1
/_C1*(3+x)*(27*(3+x)*_C1-32))^(1/2)*_C1^2+108*(3+x)^2*_C1^2-576*(3+x)*_C1+512)^(
1/3)+8/3*(3*(3+x)*_C1-4)/_C1/(12*3^(1/2)*(3+x)*(1/_C1*(3+x)*(27*(3+x)*_C1-32))^(
1/2)*_C1^2+108*(3+x)^2*_C1^2-576*(3+x)*_C1+512)^(1/3))]