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 - 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 - 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 & , 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 - 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 & , 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])/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 - 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 & , 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 + (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 - 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 & , 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])/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 - 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 + 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 - 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 & , 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)*_C1+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))]