##### 4.10.44 $$\left (4 x^3+5 y(x)+x\right ) y'(x)+7 x^3+3 x^2 y(x)+4 y(x)=0$$

ODE
$\left (4 x^3+5 y(x)+x\right ) y'(x)+7 x^3+3 x^2 y(x)+4 y(x)=0$ ODE Classiﬁcation

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

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.872494 (sec), leaf count = 3591

$\left \{\left \{y(x)\to \frac {1}{5} \left (-4 x^3-x+\frac {1}{\text {Root}\left [\left (65536 x^{30}-655360 x^{28}+2949120 x^{26}-7864320 x^{24}+13762560 x^{22}-16515072 x^{20}+13762560 x^{18}-7864320 x^{16}+2949120 x^{14}-655360 x^{12}+65536 x^{10}+65536 e^{\frac {40 c_1}{9}}\right ) \text {\#1}^{10}+\left (-81920 x^{24}+655360 x^{22}-2293760 x^{20}+4587520 x^{18}-5734400 x^{16}+4587520 x^{14}-2293760 x^{12}+655360 x^{10}-81920 x^8\right ) \text {\#1}^8+\left (40960 x^{21}-286720 x^{19}+860160 x^{17}-1433600 x^{15}+1433600 x^{13}-860160 x^{11}+286720 x^9-40960 x^7\right ) \text {\#1}^7+\left (17920 x^{18}-107520 x^{16}+268800 x^{14}-358400 x^{12}+268800 x^{10}-107520 x^8+17920 x^6\right ) \text {\#1}^6+\left (-25088 x^{15}+125440 x^{13}-250880 x^{11}+250880 x^9-125440 x^7+25088 x^5\right ) \text {\#1}^5+\left (11200 x^{12}-44800 x^{10}+67200 x^8-44800 x^6+11200 x^4\right ) \text {\#1}^4+\left (-2720 x^9+8160 x^7-8160 x^5+2720 x^3\right ) \text {\#1}^3+\left (385 x^6-770 x^4+385 x^2\right ) \text {\#1}^2+\left (30 x-30 x^3\right ) \text {\#1}+1\& ,1\right ]}\right )\right \},\left \{y(x)\to \frac {1}{5} \left (-4 x^3-x+\frac {1}{\text {Root}\left [\left (65536 x^{30}-655360 x^{28}+2949120 x^{26}-7864320 x^{24}+13762560 x^{22}-16515072 x^{20}+13762560 x^{18}-7864320 x^{16}+2949120 x^{14}-655360 x^{12}+65536 x^{10}+65536 e^{\frac {40 c_1}{9}}\right ) \text {\#1}^{10}+\left (-81920 x^{24}+655360 x^{22}-2293760 x^{20}+4587520 x^{18}-5734400 x^{16}+4587520 x^{14}-2293760 x^{12}+655360 x^{10}-81920 x^8\right ) \text {\#1}^8+\left (40960 x^{21}-286720 x^{19}+860160 x^{17}-1433600 x^{15}+1433600 x^{13}-860160 x^{11}+286720 x^9-40960 x^7\right ) \text {\#1}^7+\left (17920 x^{18}-107520 x^{16}+268800 x^{14}-358400 x^{12}+268800 x^{10}-107520 x^8+17920 x^6\right ) \text {\#1}^6+\left (-25088 x^{15}+125440 x^{13}-250880 x^{11}+250880 x^9-125440 x^7+25088 x^5\right ) \text {\#1}^5+\left (11200 x^{12}-44800 x^{10}+67200 x^8-44800 x^6+11200 x^4\right ) \text {\#1}^4+\left (-2720 x^9+8160 x^7-8160 x^5+2720 x^3\right ) \text {\#1}^3+\left (385 x^6-770 x^4+385 x^2\right ) \text {\#1}^2+\left (30 x-30 x^3\right ) \text {\#1}+1\& ,2\right ]}\right )\right \},\left \{y(x)\to \frac {1}{5} \left (-4 x^3-x+\frac {1}{\text {Root}\left [\left (65536 x^{30}-655360 x^{28}+2949120 x^{26}-7864320 x^{24}+13762560 x^{22}-16515072 x^{20}+13762560 x^{18}-7864320 x^{16}+2949120 x^{14}-655360 x^{12}+65536 x^{10}+65536 e^{\frac {40 c_1}{9}}\right ) \text {\#1}^{10}+\left (-81920 x^{24}+655360 x^{22}-2293760 x^{20}+4587520 x^{18}-5734400 x^{16}+4587520 x^{14}-2293760 x^{12}+655360 x^{10}-81920 x^8\right ) \text {\#1}^8+\left (40960 x^{21}-286720 x^{19}+860160 x^{17}-1433600 x^{15}+1433600 x^{13}-860160 x^{11}+286720 x^9-40960 x^7\right ) \text {\#1}^7+\left (17920 x^{18}-107520 x^{16}+268800 x^{14}-358400 x^{12}+268800 x^{10}-107520 x^8+17920 x^6\right ) \text {\#1}^6+\left (-25088 x^{15}+125440 x^{13}-250880 x^{11}+250880 x^9-125440 x^7+25088 x^5\right ) \text {\#1}^5+\left (11200 x^{12}-44800 x^{10}+67200 x^8-44800 x^6+11200 x^4\right ) \text {\#1}^4+\left (-2720 x^9+8160 x^7-8160 x^5+2720 x^3\right ) \text {\#1}^3+\left (385 x^6-770 x^4+385 x^2\right ) \text {\#1}^2+\left (30 x-30 x^3\right ) \text {\#1}+1\& ,3\right ]}\right )\right \},\left \{y(x)\to \frac {1}{5} \left (-4 x^3-x+\frac {1}{\text {Root}\left [\left (65536 x^{30}-655360 x^{28}+2949120 x^{26}-7864320 x^{24}+13762560 x^{22}-16515072 x^{20}+13762560 x^{18}-7864320 x^{16}+2949120 x^{14}-655360 x^{12}+65536 x^{10}+65536 e^{\frac {40 c_1}{9}}\right ) \text {\#1}^{10}+\left (-81920 x^{24}+655360 x^{22}-2293760 x^{20}+4587520 x^{18}-5734400 x^{16}+4587520 x^{14}-2293760 x^{12}+655360 x^{10}-81920 x^8\right ) \text {\#1}^8+\left (40960 x^{21}-286720 x^{19}+860160 x^{17}-1433600 x^{15}+1433600 x^{13}-860160 x^{11}+286720 x^9-40960 x^7\right ) \text {\#1}^7+\left (17920 x^{18}-107520 x^{16}+268800 x^{14}-358400 x^{12}+268800 x^{10}-107520 x^8+17920 x^6\right ) \text {\#1}^6+\left (-25088 x^{15}+125440 x^{13}-250880 x^{11}+250880 x^9-125440 x^7+25088 x^5\right ) \text {\#1}^5+\left (11200 x^{12}-44800 x^{10}+67200 x^8-44800 x^6+11200 x^4\right ) \text {\#1}^4+\left (-2720 x^9+8160 x^7-8160 x^5+2720 x^3\right ) \text {\#1}^3+\left (385 x^6-770 x^4+385 x^2\right ) \text {\#1}^2+\left (30 x-30 x^3\right ) \text {\#1}+1\& ,4\right ]}\right )\right \},\left \{y(x)\to \frac {1}{5} \left (-4 x^3-x+\frac {1}{\text {Root}\left [\left (65536 x^{30}-655360 x^{28}+2949120 x^{26}-7864320 x^{24}+13762560 x^{22}-16515072 x^{20}+13762560 x^{18}-7864320 x^{16}+2949120 x^{14}-655360 x^{12}+65536 x^{10}+65536 e^{\frac {40 c_1}{9}}\right ) \text {\#1}^{10}+\left (-81920 x^{24}+655360 x^{22}-2293760 x^{20}+4587520 x^{18}-5734400 x^{16}+4587520 x^{14}-2293760 x^{12}+655360 x^{10}-81920 x^8\right ) \text {\#1}^8+\left (40960 x^{21}-286720 x^{19}+860160 x^{17}-1433600 x^{15}+1433600 x^{13}-860160 x^{11}+286720 x^9-40960 x^7\right ) \text {\#1}^7+\left (17920 x^{18}-107520 x^{16}+268800 x^{14}-358400 x^{12}+268800 x^{10}-107520 x^8+17920 x^6\right ) \text {\#1}^6+\left (-25088 x^{15}+125440 x^{13}-250880 x^{11}+250880 x^9-125440 x^7+25088 x^5\right ) \text {\#1}^5+\left (11200 x^{12}-44800 x^{10}+67200 x^8-44800 x^6+11200 x^4\right ) \text {\#1}^4+\left (-2720 x^9+8160 x^7-8160 x^5+2720 x^3\right ) \text {\#1}^3+\left (385 x^6-770 x^4+385 x^2\right ) \text {\#1}^2+\left (30 x-30 x^3\right ) \text {\#1}+1\& ,5\right ]}\right )\right \},\left \{y(x)\to \frac {1}{5} \left (-4 x^3-x+\frac {1}{\text {Root}\left [\left (65536 x^{30}-655360 x^{28}+2949120 x^{26}-7864320 x^{24}+13762560 x^{22}-16515072 x^{20}+13762560 x^{18}-7864320 x^{16}+2949120 x^{14}-655360 x^{12}+65536 x^{10}+65536 e^{\frac {40 c_1}{9}}\right ) \text {\#1}^{10}+\left (-81920 x^{24}+655360 x^{22}-2293760 x^{20}+4587520 x^{18}-5734400 x^{16}+4587520 x^{14}-2293760 x^{12}+655360 x^{10}-81920 x^8\right ) \text {\#1}^8+\left (40960 x^{21}-286720 x^{19}+860160 x^{17}-1433600 x^{15}+1433600 x^{13}-860160 x^{11}+286720 x^9-40960 x^7\right ) \text {\#1}^7+\left (17920 x^{18}-107520 x^{16}+268800 x^{14}-358400 x^{12}+268800 x^{10}-107520 x^8+17920 x^6\right ) \text {\#1}^6+\left (-25088 x^{15}+125440 x^{13}-250880 x^{11}+250880 x^9-125440 x^7+25088 x^5\right ) \text {\#1}^5+\left (11200 x^{12}-44800 x^{10}+67200 x^8-44800 x^6+11200 x^4\right ) \text {\#1}^4+\left (-2720 x^9+8160 x^7-8160 x^5+2720 x^3\right ) \text {\#1}^3+\left (385 x^6-770 x^4+385 x^2\right ) \text {\#1}^2+\left (30 x-30 x^3\right ) \text {\#1}+1\& ,6\right ]}\right )\right \},\left \{y(x)\to \frac {1}{5} \left (-4 x^3-x+\frac {1}{\text {Root}\left [\left (65536 x^{30}-655360 x^{28}+2949120 x^{26}-7864320 x^{24}+13762560 x^{22}-16515072 x^{20}+13762560 x^{18}-7864320 x^{16}+2949120 x^{14}-655360 x^{12}+65536 x^{10}+65536 e^{\frac {40 c_1}{9}}\right ) \text {\#1}^{10}+\left (-81920 x^{24}+655360 x^{22}-2293760 x^{20}+4587520 x^{18}-5734400 x^{16}+4587520 x^{14}-2293760 x^{12}+655360 x^{10}-81920 x^8\right ) \text {\#1}^8+\left (40960 x^{21}-286720 x^{19}+860160 x^{17}-1433600 x^{15}+1433600 x^{13}-860160 x^{11}+286720 x^9-40960 x^7\right ) \text {\#1}^7+\left (17920 x^{18}-107520 x^{16}+268800 x^{14}-358400 x^{12}+268800 x^{10}-107520 x^8+17920 x^6\right ) \text {\#1}^6+\left (-25088 x^{15}+125440 x^{13}-250880 x^{11}+250880 x^9-125440 x^7+25088 x^5\right ) \text {\#1}^5+\left (11200 x^{12}-44800 x^{10}+67200 x^8-44800 x^6+11200 x^4\right ) \text {\#1}^4+\left (-2720 x^9+8160 x^7-8160 x^5+2720 x^3\right ) \text {\#1}^3+\left (385 x^6-770 x^4+385 x^2\right ) \text {\#1}^2+\left (30 x-30 x^3\right ) \text {\#1}+1\& ,7\right ]}\right )\right \},\left \{y(x)\to \frac {1}{5} \left (-4 x^3-x+\frac {1}{\text {Root}\left [\left (65536 x^{30}-655360 x^{28}+2949120 x^{26}-7864320 x^{24}+13762560 x^{22}-16515072 x^{20}+13762560 x^{18}-7864320 x^{16}+2949120 x^{14}-655360 x^{12}+65536 x^{10}+65536 e^{\frac {40 c_1}{9}}\right ) \text {\#1}^{10}+\left (-81920 x^{24}+655360 x^{22}-2293760 x^{20}+4587520 x^{18}-5734400 x^{16}+4587520 x^{14}-2293760 x^{12}+655360 x^{10}-81920 x^8\right ) \text {\#1}^8+\left (40960 x^{21}-286720 x^{19}+860160 x^{17}-1433600 x^{15}+1433600 x^{13}-860160 x^{11}+286720 x^9-40960 x^7\right ) \text {\#1}^7+\left (17920 x^{18}-107520 x^{16}+268800 x^{14}-358400 x^{12}+268800 x^{10}-107520 x^8+17920 x^6\right ) \text {\#1}^6+\left (-25088 x^{15}+125440 x^{13}-250880 x^{11}+250880 x^9-125440 x^7+25088 x^5\right ) \text {\#1}^5+\left (11200 x^{12}-44800 x^{10}+67200 x^8-44800 x^6+11200 x^4\right ) \text {\#1}^4+\left (-2720 x^9+8160 x^7-8160 x^5+2720 x^3\right ) \text {\#1}^3+\left (385 x^6-770 x^4+385 x^2\right ) \text {\#1}^2+\left (30 x-30 x^3\right ) \text {\#1}+1\& ,8\right ]}\right )\right \},\left \{y(x)\to \frac {1}{5} \left (-4 x^3-x+\frac {1}{\text {Root}\left [\left (65536 x^{30}-655360 x^{28}+2949120 x^{26}-7864320 x^{24}+13762560 x^{22}-16515072 x^{20}+13762560 x^{18}-7864320 x^{16}+2949120 x^{14}-655360 x^{12}+65536 x^{10}+65536 e^{\frac {40 c_1}{9}}\right ) \text {\#1}^{10}+\left (-81920 x^{24}+655360 x^{22}-2293760 x^{20}+4587520 x^{18}-5734400 x^{16}+4587520 x^{14}-2293760 x^{12}+655360 x^{10}-81920 x^8\right ) \text {\#1}^8+\left (40960 x^{21}-286720 x^{19}+860160 x^{17}-1433600 x^{15}+1433600 x^{13}-860160 x^{11}+286720 x^9-40960 x^7\right ) \text {\#1}^7+\left (17920 x^{18}-107520 x^{16}+268800 x^{14}-358400 x^{12}+268800 x^{10}-107520 x^8+17920 x^6\right ) \text {\#1}^6+\left (-25088 x^{15}+125440 x^{13}-250880 x^{11}+250880 x^9-125440 x^7+25088 x^5\right ) \text {\#1}^5+\left (11200 x^{12}-44800 x^{10}+67200 x^8-44800 x^6+11200 x^4\right ) \text {\#1}^4+\left (-2720 x^9+8160 x^7-8160 x^5+2720 x^3\right ) \text {\#1}^3+\left (385 x^6-770 x^4+385 x^2\right ) \text {\#1}^2+\left (30 x-30 x^3\right ) \text {\#1}+1\& ,9\right ]}\right )\right \},\left \{y(x)\to \frac {1}{5} \left (-4 x^3-x+\frac {1}{\text {Root}\left [\left (65536 x^{30}-655360 x^{28}+2949120 x^{26}-7864320 x^{24}+13762560 x^{22}-16515072 x^{20}+13762560 x^{18}-7864320 x^{16}+2949120 x^{14}-655360 x^{12}+65536 x^{10}+65536 e^{\frac {40 c_1}{9}}\right ) \text {\#1}^{10}+\left (-81920 x^{24}+655360 x^{22}-2293760 x^{20}+4587520 x^{18}-5734400 x^{16}+4587520 x^{14}-2293760 x^{12}+655360 x^{10}-81920 x^8\right ) \text {\#1}^8+\left (40960 x^{21}-286720 x^{19}+860160 x^{17}-1433600 x^{15}+1433600 x^{13}-860160 x^{11}+286720 x^9-40960 x^7\right ) \text {\#1}^7+\left (17920 x^{18}-107520 x^{16}+268800 x^{14}-358400 x^{12}+268800 x^{10}-107520 x^8+17920 x^6\right ) \text {\#1}^6+\left (-25088 x^{15}+125440 x^{13}-250880 x^{11}+250880 x^9-125440 x^7+25088 x^5\right ) \text {\#1}^5+\left (11200 x^{12}-44800 x^{10}+67200 x^8-44800 x^6+11200 x^4\right ) \text {\#1}^4+\left (-2720 x^9+8160 x^7-8160 x^5+2720 x^3\right ) \text {\#1}^3+\left (385 x^6-770 x^4+385 x^2\right ) \text {\#1}^2+\left (30 x-30 x^3\right ) \text {\#1}+1\& ,10\right ]}\right )\right \}\right \}$

Maple
cpu = 1.544 (sec), leaf count = 3020

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

DSolve[7*x^3 + 4*y[x] + 3*x^2*y[x] + (x + 4*x^3 + 5*y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (-x - 4*x^3 + Root[1 + (30*x - 30*x^3)*#1 + (385*x^2 - 770*x^4 + 385*x
^6)*#1^2 + (2720*x^3 - 8160*x^5 + 8160*x^7 - 2720*x^9)*#1^3 + (11200*x^4 - 44800
*x^6 + 67200*x^8 - 44800*x^10 + 11200*x^12)*#1^4 + (25088*x^5 - 125440*x^7 + 250
880*x^9 - 250880*x^11 + 125440*x^13 - 25088*x^15)*#1^5 + (17920*x^6 - 107520*x^8
 + 268800*x^10 - 358400*x^12 + 268800*x^14 - 107520*x^16 + 17920*x^18)*#1^6 + (-
40960*x^7 + 286720*x^9 - 860160*x^11 + 1433600*x^13 - 1433600*x^15 + 860160*x^17
 - 286720*x^19 + 40960*x^21)*#1^7 + (-81920*x^8 + 655360*x^10 - 2293760*x^12 + 4
587520*x^14 - 5734400*x^16 + 4587520*x^18 - 2293760*x^20 + 655360*x^22 - 81920*x
^24)*#1^8 + (65536*E^((40*C[1])/9) + 65536*x^10 - 655360*x^12 + 2949120*x^14 - 7
864320*x^16 + 13762560*x^18 - 16515072*x^20 + 13762560*x^22 - 7864320*x^24 + 294
9120*x^26 - 655360*x^28 + 65536*x^30)*#1^10 & , 1]^(-1))/5}, {y[x] -> (-x - 4*x^
3 + Root[1 + (30*x - 30*x^3)*#1 + (385*x^2 - 770*x^4 + 385*x^6)*#1^2 + (2720*x^3
 - 8160*x^5 + 8160*x^7 - 2720*x^9)*#1^3 + (11200*x^4 - 44800*x^6 + 67200*x^8 - 4
4800*x^10 + 11200*x^12)*#1^4 + (25088*x^5 - 125440*x^7 + 250880*x^9 - 250880*x^1
1 + 125440*x^13 - 25088*x^15)*#1^5 + (17920*x^6 - 107520*x^8 + 268800*x^10 - 358
400*x^12 + 268800*x^14 - 107520*x^16 + 17920*x^18)*#1^6 + (-40960*x^7 + 286720*x
^9 - 860160*x^11 + 1433600*x^13 - 1433600*x^15 + 860160*x^17 - 286720*x^19 + 409
60*x^21)*#1^7 + (-81920*x^8 + 655360*x^10 - 2293760*x^12 + 4587520*x^14 - 573440
0*x^16 + 4587520*x^18 - 2293760*x^20 + 655360*x^22 - 81920*x^24)*#1^8 + (65536*E
^((40*C[1])/9) + 65536*x^10 - 655360*x^12 + 2949120*x^14 - 7864320*x^16 + 137625
60*x^18 - 16515072*x^20 + 13762560*x^22 - 7864320*x^24 + 2949120*x^26 - 655360*x
^28 + 65536*x^30)*#1^10 & , 2]^(-1))/5}, {y[x] -> (-x - 4*x^3 + Root[1 + (30*x -
 30*x^3)*#1 + (385*x^2 - 770*x^4 + 385*x^6)*#1^2 + (2720*x^3 - 8160*x^5 + 8160*x
^7 - 2720*x^9)*#1^3 + (11200*x^4 - 44800*x^6 + 67200*x^8 - 44800*x^10 + 11200*x^
12)*#1^4 + (25088*x^5 - 125440*x^7 + 250880*x^9 - 250880*x^11 + 125440*x^13 - 25
088*x^15)*#1^5 + (17920*x^6 - 107520*x^8 + 268800*x^10 - 358400*x^12 + 268800*x^
14 - 107520*x^16 + 17920*x^18)*#1^6 + (-40960*x^7 + 286720*x^9 - 860160*x^11 + 1
433600*x^13 - 1433600*x^15 + 860160*x^17 - 286720*x^19 + 40960*x^21)*#1^7 + (-81
920*x^8 + 655360*x^10 - 2293760*x^12 + 4587520*x^14 - 5734400*x^16 + 4587520*x^1
8 - 2293760*x^20 + 655360*x^22 - 81920*x^24)*#1^8 + (65536*E^((40*C[1])/9) + 655
36*x^10 - 655360*x^12 + 2949120*x^14 - 7864320*x^16 + 13762560*x^18 - 16515072*x
^20 + 13762560*x^22 - 7864320*x^24 + 2949120*x^26 - 655360*x^28 + 65536*x^30)*#1
^10 & , 3]^(-1))/5}, {y[x] -> (-x - 4*x^3 + Root[1 + (30*x - 30*x^3)*#1 + (385*x
^2 - 770*x^4 + 385*x^6)*#1^2 + (2720*x^3 - 8160*x^5 + 8160*x^7 - 2720*x^9)*#1^3
+ (11200*x^4 - 44800*x^6 + 67200*x^8 - 44800*x^10 + 11200*x^12)*#1^4 + (25088*x^
5 - 125440*x^7 + 250880*x^9 - 250880*x^11 + 125440*x^13 - 25088*x^15)*#1^5 + (17
920*x^6 - 107520*x^8 + 268800*x^10 - 358400*x^12 + 268800*x^14 - 107520*x^16 + 1
7920*x^18)*#1^6 + (-40960*x^7 + 286720*x^9 - 860160*x^11 + 1433600*x^13 - 143360
0*x^15 + 860160*x^17 - 286720*x^19 + 40960*x^21)*#1^7 + (-81920*x^8 + 655360*x^1
0 - 2293760*x^12 + 4587520*x^14 - 5734400*x^16 + 4587520*x^18 - 2293760*x^20 + 6
55360*x^22 - 81920*x^24)*#1^8 + (65536*E^((40*C[1])/9) + 65536*x^10 - 655360*x^1
2 + 2949120*x^14 - 7864320*x^16 + 13762560*x^18 - 16515072*x^20 + 13762560*x^22
- 7864320*x^24 + 2949120*x^26 - 655360*x^28 + 65536*x^30)*#1^10 & , 4]^(-1))/5},
 {y[x] -> (-x - 4*x^3 + Root[1 + (30*x - 30*x^3)*#1 + (385*x^2 - 770*x^4 + 385*x
^6)*#1^2 + (2720*x^3 - 8160*x^5 + 8160*x^7 - 2720*x^9)*#1^3 + (11200*x^4 - 44800
*x^6 + 67200*x^8 - 44800*x^10 + 11200*x^12)*#1^4 + (25088*x^5 - 125440*x^7 + 250
880*x^9 - 250880*x^11 + 125440*x^13 - 25088*x^15)*#1^5 + (17920*x^6 - 107520*x^8
 + 268800*x^10 - 358400*x^12 + 268800*x^14 - 107520*x^16 + 17920*x^18)*#1^6 + (-
40960*x^7 + 286720*x^9 - 860160*x^11 + 1433600*x^13 - 1433600*x^15 + 860160*x^17
 - 286720*x^19 + 40960*x^21)*#1^7 + (-81920*x^8 + 655360*x^10 - 2293760*x^12 + 4
587520*x^14 - 5734400*x^16 + 4587520*x^18 - 2293760*x^20 + 655360*x^22 - 81920*x
^24)*#1^8 + (65536*E^((40*C[1])/9) + 65536*x^10 - 655360*x^12 + 2949120*x^14 - 7
864320*x^16 + 13762560*x^18 - 16515072*x^20 + 13762560*x^22 - 7864320*x^24 + 294
9120*x^26 - 655360*x^28 + 65536*x^30)*#1^10 & , 5]^(-1))/5}, {y[x] -> (-x - 4*x^
3 + Root[1 + (30*x - 30*x^3)*#1 + (385*x^2 - 770*x^4 + 385*x^6)*#1^2 + (2720*x^3
 - 8160*x^5 + 8160*x^7 - 2720*x^9)*#1^3 + (11200*x^4 - 44800*x^6 + 67200*x^8 - 4
4800*x^10 + 11200*x^12)*#1^4 + (25088*x^5 - 125440*x^7 + 250880*x^9 - 250880*x^1
1 + 125440*x^13 - 25088*x^15)*#1^5 + (17920*x^6 - 107520*x^8 + 268800*x^10 - 358
400*x^12 + 268800*x^14 - 107520*x^16 + 17920*x^18)*#1^6 + (-40960*x^7 + 286720*x
^9 - 860160*x^11 + 1433600*x^13 - 1433600*x^15 + 860160*x^17 - 286720*x^19 + 409
60*x^21)*#1^7 + (-81920*x^8 + 655360*x^10 - 2293760*x^12 + 4587520*x^14 - 573440
0*x^16 + 4587520*x^18 - 2293760*x^20 + 655360*x^22 - 81920*x^24)*#1^8 + (65536*E
^((40*C[1])/9) + 65536*x^10 - 655360*x^12 + 2949120*x^14 - 7864320*x^16 + 137625
60*x^18 - 16515072*x^20 + 13762560*x^22 - 7864320*x^24 + 2949120*x^26 - 655360*x
^28 + 65536*x^30)*#1^10 & , 6]^(-1))/5}, {y[x] -> (-x - 4*x^3 + Root[1 + (30*x -
 30*x^3)*#1 + (385*x^2 - 770*x^4 + 385*x^6)*#1^2 + (2720*x^3 - 8160*x^5 + 8160*x
^7 - 2720*x^9)*#1^3 + (11200*x^4 - 44800*x^6 + 67200*x^8 - 44800*x^10 + 11200*x^
12)*#1^4 + (25088*x^5 - 125440*x^7 + 250880*x^9 - 250880*x^11 + 125440*x^13 - 25
088*x^15)*#1^5 + (17920*x^6 - 107520*x^8 + 268800*x^10 - 358400*x^12 + 268800*x^
14 - 107520*x^16 + 17920*x^18)*#1^6 + (-40960*x^7 + 286720*x^9 - 860160*x^11 + 1
433600*x^13 - 1433600*x^15 + 860160*x^17 - 286720*x^19 + 40960*x^21)*#1^7 + (-81
920*x^8 + 655360*x^10 - 2293760*x^12 + 4587520*x^14 - 5734400*x^16 + 4587520*x^1
8 - 2293760*x^20 + 655360*x^22 - 81920*x^24)*#1^8 + (65536*E^((40*C[1])/9) + 655
36*x^10 - 655360*x^12 + 2949120*x^14 - 7864320*x^16 + 13762560*x^18 - 16515072*x
^20 + 13762560*x^22 - 7864320*x^24 + 2949120*x^26 - 655360*x^28 + 65536*x^30)*#1
^10 & , 7]^(-1))/5}, {y[x] -> (-x - 4*x^3 + Root[1 + (30*x - 30*x^3)*#1 + (385*x
^2 - 770*x^4 + 385*x^6)*#1^2 + (2720*x^3 - 8160*x^5 + 8160*x^7 - 2720*x^9)*#1^3
+ (11200*x^4 - 44800*x^6 + 67200*x^8 - 44800*x^10 + 11200*x^12)*#1^4 + (25088*x^
5 - 125440*x^7 + 250880*x^9 - 250880*x^11 + 125440*x^13 - 25088*x^15)*#1^5 + (17
920*x^6 - 107520*x^8 + 268800*x^10 - 358400*x^12 + 268800*x^14 - 107520*x^16 + 1
7920*x^18)*#1^6 + (-40960*x^7 + 286720*x^9 - 860160*x^11 + 1433600*x^13 - 143360
0*x^15 + 860160*x^17 - 286720*x^19 + 40960*x^21)*#1^7 + (-81920*x^8 + 655360*x^1
0 - 2293760*x^12 + 4587520*x^14 - 5734400*x^16 + 4587520*x^18 - 2293760*x^20 + 6
55360*x^22 - 81920*x^24)*#1^8 + (65536*E^((40*C[1])/9) + 65536*x^10 - 655360*x^1
2 + 2949120*x^14 - 7864320*x^16 + 13762560*x^18 - 16515072*x^20 + 13762560*x^22
- 7864320*x^24 + 2949120*x^26 - 655360*x^28 + 65536*x^30)*#1^10 & , 8]^(-1))/5},
 {y[x] -> (-x - 4*x^3 + Root[1 + (30*x - 30*x^3)*#1 + (385*x^2 - 770*x^4 + 385*x
^6)*#1^2 + (2720*x^3 - 8160*x^5 + 8160*x^7 - 2720*x^9)*#1^3 + (11200*x^4 - 44800
*x^6 + 67200*x^8 - 44800*x^10 + 11200*x^12)*#1^4 + (25088*x^5 - 125440*x^7 + 250
880*x^9 - 250880*x^11 + 125440*x^13 - 25088*x^15)*#1^5 + (17920*x^6 - 107520*x^8
 + 268800*x^10 - 358400*x^12 + 268800*x^14 - 107520*x^16 + 17920*x^18)*#1^6 + (-
40960*x^7 + 286720*x^9 - 860160*x^11 + 1433600*x^13 - 1433600*x^15 + 860160*x^17
 - 286720*x^19 + 40960*x^21)*#1^7 + (-81920*x^8 + 655360*x^10 - 2293760*x^12 + 4
587520*x^14 - 5734400*x^16 + 4587520*x^18 - 2293760*x^20 + 655360*x^22 - 81920*x
^24)*#1^8 + (65536*E^((40*C[1])/9) + 65536*x^10 - 655360*x^12 + 2949120*x^14 - 7
864320*x^16 + 13762560*x^18 - 16515072*x^20 + 13762560*x^22 - 7864320*x^24 + 294
9120*x^26 - 655360*x^28 + 65536*x^30)*#1^10 & , 9]^(-1))/5}, {y[x] -> (-x - 4*x^
3 + Root[1 + (30*x - 30*x^3)*#1 + (385*x^2 - 770*x^4 + 385*x^6)*#1^2 + (2720*x^3
 - 8160*x^5 + 8160*x^7 - 2720*x^9)*#1^3 + (11200*x^4 - 44800*x^6 + 67200*x^8 - 4
4800*x^10 + 11200*x^12)*#1^4 + (25088*x^5 - 125440*x^7 + 250880*x^9 - 250880*x^1
1 + 125440*x^13 - 25088*x^15)*#1^5 + (17920*x^6 - 107520*x^8 + 268800*x^10 - 358
400*x^12 + 268800*x^14 - 107520*x^16 + 17920*x^18)*#1^6 + (-40960*x^7 + 286720*x
^9 - 860160*x^11 + 1433600*x^13 - 1433600*x^15 + 860160*x^17 - 286720*x^19 + 409
60*x^21)*#1^7 + (-81920*x^8 + 655360*x^10 - 2293760*x^12 + 4587520*x^14 - 573440
0*x^16 + 4587520*x^18 - 2293760*x^20 + 655360*x^22 - 81920*x^24)*#1^8 + (65536*E
^((40*C[1])/9) + 65536*x^10 - 655360*x^12 + 2949120*x^14 - 7864320*x^16 + 137625
60*x^18 - 16515072*x^20 + 13762560*x^22 - 7864320*x^24 + 2949120*x^26 - 655360*x
^28 + 65536*x^30)*#1^10 & , 10]^(-1))/5}}

Maple raw input

dsolve((x+4*x^3+5*y(x))*diff(y(x),x)+7*x^3+3*x^2*y(x)+4*y(x) = 0, y(x))

Maple raw output

[y(x) = 1/12005*(48020*x^7+115248*_C1-12005*x^5-72030*x^9-12005*x^13+48020*x^11-
16*x^15*RootOf((-2*x^15+10*x^13-20*x^11+20*x^9-10*x^7+2*x^5+96*_C1)*_Z^25+(-35*x
^15+175*x^13-350*x^11+350*x^9-175*x^7+35*x^5+1680*_C1)*_Z^20+11760*_C1*_Z^15+411
60*_C1*_Z^10+72030*_C1*_Z^5+50421*_C1)^20+80*x^13*RootOf((-2*x^15+10*x^13-20*x^1
1+20*x^9-10*x^7+2*x^5+96*_C1)*_Z^25+(-35*x^15+175*x^13-350*x^11+350*x^9-175*x^7+
35*x^5+1680*_C1)*_Z^20+11760*_C1*_Z^15+41160*_C1*_Z^10+72030*_C1*_Z^5+50421*_C1)
^20-160*x^11*RootOf((-2*x^15+10*x^13-20*x^11+20*x^9-10*x^7+2*x^5+96*_C1)*_Z^25+(
-35*x^15+175*x^13-350*x^11+350*x^9-175*x^7+35*x^5+1680*_C1)*_Z^20+11760*_C1*_Z^1
5+41160*_C1*_Z^10+72030*_C1*_Z^5+50421*_C1)^20-224*x^15*RootOf((-2*x^15+10*x^13-
20*x^11+20*x^9-10*x^7+2*x^5+96*_C1)*_Z^25+(-35*x^15+175*x^13-350*x^11+350*x^9-17
5*x^7+35*x^5+1680*_C1)*_Z^20+11760*_C1*_Z^15+41160*_C1*_Z^10+72030*_C1*_Z^5+5042
1*_C1)^15+160*x^9*RootOf((-2*x^15+10*x^13-20*x^11+20*x^9-10*x^7+2*x^5+96*_C1)*_Z
^25+(-35*x^15+175*x^13-350*x^11+350*x^9-175*x^7+35*x^5+1680*_C1)*_Z^20+11760*_C1
*_Z^15+41160*_C1*_Z^10+72030*_C1*_Z^5+50421*_C1)^20+1120*x^13*RootOf((-2*x^15+10
*x^13-20*x^11+20*x^9-10*x^7+2*x^5+96*_C1)*_Z^25+(-35*x^15+175*x^13-350*x^11+350*
x^9-175*x^7+35*x^5+1680*_C1)*_Z^20+11760*_C1*_Z^15+41160*_C1*_Z^10+72030*_C1*_Z^
5+50421*_C1)^15-80*x^7*RootOf((-2*x^15+10*x^13-20*x^11+20*x^9-10*x^7+2*x^5+96*_C
1)*_Z^25+(-35*x^15+175*x^13-350*x^11+350*x^9-175*x^7+35*x^5+1680*_C1)*_Z^20+1176
0*_C1*_Z^15+41160*_C1*_Z^10+72030*_C1*_Z^5+50421*_C1)^20-2240*x^11*RootOf((-2*x^
15+10*x^13-20*x^11+20*x^9-10*x^7+2*x^5+96*_C1)*_Z^25+(-35*x^15+175*x^13-350*x^11
+350*x^9-175*x^7+35*x^5+1680*_C1)*_Z^20+11760*_C1*_Z^15+41160*_C1*_Z^10+72030*_C
1*_Z^5+50421*_C1)^15+16*RootOf((-2*x^15+10*x^13-20*x^11+20*x^9-10*x^7+2*x^5+96*_
C1)*_Z^25+(-35*x^15+175*x^13-350*x^11+350*x^9-175*x^7+35*x^5+1680*_C1)*_Z^20+117
60*_C1*_Z^15+41160*_C1*_Z^10+72030*_C1*_Z^5+50421*_C1)^20*x^5+768*_C1*RootOf((-2
*x^15+10*x^13-20*x^11+20*x^9-10*x^7+2*x^5+96*_C1)*_Z^25+(-35*x^15+175*x^13-350*x
^11+350*x^9-175*x^7+35*x^5+1680*_C1)*_Z^20+11760*_C1*_Z^15+41160*_C1*_Z^10+72030
*_C1*_Z^5+50421*_C1)^20+784*x^15*RootOf((-2*x^15+10*x^13-20*x^11+20*x^9-10*x^7+2
*x^5+96*_C1)*_Z^25+(-35*x^15+175*x^13-350*x^11+350*x^9-175*x^7+35*x^5+1680*_C1)*
_Z^20+11760*_C1*_Z^15+41160*_C1*_Z^10+72030*_C1*_Z^5+50421*_C1)^10+2240*x^9*Root
Of((-2*x^15+10*x^13-20*x^11+20*x^9-10*x^7+2*x^5+96*_C1)*_Z^25+(-35*x^15+175*x^13
-350*x^11+350*x^9-175*x^7+35*x^5+1680*_C1)*_Z^20+11760*_C1*_Z^15+41160*_C1*_Z^10
+72030*_C1*_Z^5+50421*_C1)^15-3920*x^13*RootOf((-2*x^15+10*x^13-20*x^11+20*x^9-1
0*x^7+2*x^5+96*_C1)*_Z^25+(-35*x^15+175*x^13-350*x^11+350*x^9-175*x^7+35*x^5+168
0*_C1)*_Z^20+11760*_C1*_Z^15+41160*_C1*_Z^10+72030*_C1*_Z^5+50421*_C1)^10-1120*x
^7*RootOf((-2*x^15+10*x^13-20*x^11+20*x^9-10*x^7+2*x^5+96*_C1)*_Z^25+(-35*x^15+1
75*x^13-350*x^11+350*x^9-175*x^7+35*x^5+1680*_C1)*_Z^20+11760*_C1*_Z^15+41160*_C
1*_Z^10+72030*_C1*_Z^5+50421*_C1)^15+7840*x^11*RootOf((-2*x^15+10*x^13-20*x^11+2
0*x^9-10*x^7+2*x^5+96*_C1)*_Z^25+(-35*x^15+175*x^13-350*x^11+350*x^9-175*x^7+35*
x^5+1680*_C1)*_Z^20+11760*_C1*_Z^15+41160*_C1*_Z^10+72030*_C1*_Z^5+50421*_C1)^10
+224*RootOf((-2*x^15+10*x^13-20*x^11+20*x^9-10*x^7+2*x^5+96*_C1)*_Z^25+(-35*x^15
+175*x^13-350*x^11+350*x^9-175*x^7+35*x^5+1680*_C1)*_Z^20+11760*_C1*_Z^15+41160*
_C1*_Z^10+72030*_C1*_Z^5+50421*_C1)^15*x^5+10752*_C1*RootOf((-2*x^15+10*x^13-20*
x^11+20*x^9-10*x^7+2*x^5+96*_C1)*_Z^25+(-35*x^15+175*x^13-350*x^11+350*x^9-175*x
^7+35*x^5+1680*_C1)*_Z^20+11760*_C1*_Z^15+41160*_C1*_Z^10+72030*_C1*_Z^5+50421*_
C1)^15-2744*x^15*RootOf((-2*x^15+10*x^13-20*x^11+20*x^9-10*x^7+2*x^5+96*_C1)*_Z^
25+(-35*x^15+175*x^13-350*x^11+350*x^9-175*x^7+35*x^5+1680*_C1)*_Z^20+11760*_C1*
_Z^15+41160*_C1*_Z^10+72030*_C1*_Z^5+50421*_C1)^5-7840*x^9*RootOf((-2*x^15+10*x^
13-20*x^11+20*x^9-10*x^7+2*x^5+96*_C1)*_Z^25+(-35*x^15+175*x^13-350*x^11+350*x^9
-175*x^7+35*x^5+1680*_C1)*_Z^20+11760*_C1*_Z^15+41160*_C1*_Z^10+72030*_C1*_Z^5+5
0421*_C1)^10+13720*x^13*RootOf((-2*x^15+10*x^13-20*x^11+20*x^9-10*x^7+2*x^5+96*_
C1)*_Z^25+(-35*x^15+175*x^13-350*x^11+350*x^9-175*x^7+35*x^5+1680*_C1)*_Z^20+117
60*_C1*_Z^15+41160*_C1*_Z^10+72030*_C1*_Z^5+50421*_C1)^5+3920*x^7*RootOf((-2*x^1
5+10*x^13-20*x^11+20*x^9-10*x^7+2*x^5+96*_C1)*_Z^25+(-35*x^15+175*x^13-350*x^11+
350*x^9-175*x^7+35*x^5+1680*_C1)*_Z^20+11760*_C1*_Z^15+41160*_C1*_Z^10+72030*_C1
*_Z^5+50421*_C1)^10-27440*x^11*RootOf((-2*x^15+10*x^13-20*x^11+20*x^9-10*x^7+2*x
^5+96*_C1)*_Z^25+(-35*x^15+175*x^13-350*x^11+350*x^9-175*x^7+35*x^5+1680*_C1)*_Z
^20+11760*_C1*_Z^15+41160*_C1*_Z^10+72030*_C1*_Z^5+50421*_C1)^5-784*RootOf((-2*x
^15+10*x^13-20*x^11+20*x^9-10*x^7+2*x^5+96*_C1)*_Z^25+(-35*x^15+175*x^13-350*x^1
1+350*x^9-175*x^7+35*x^5+1680*_C1)*_Z^20+11760*_C1*_Z^15+41160*_C1*_Z^10+72030*_
C1*_Z^5+50421*_C1)^10*x^5+56448*_C1*RootOf((-2*x^15+10*x^13-20*x^11+20*x^9-10*x^
7+2*x^5+96*_C1)*_Z^25+(-35*x^15+175*x^13-350*x^11+350*x^9-175*x^7+35*x^5+1680*_C
1)*_Z^20+11760*_C1*_Z^15+41160*_C1*_Z^10+72030*_C1*_Z^5+50421*_C1)^10+27440*x^9*
RootOf((-2*x^15+10*x^13-20*x^11+20*x^9-10*x^7+2*x^5+96*_C1)*_Z^25+(-35*x^15+175*
x^13-350*x^11+350*x^9-175*x^7+35*x^5+1680*_C1)*_Z^20+11760*_C1*_Z^15+41160*_C1*_
Z^10+72030*_C1*_Z^5+50421*_C1)^5-13720*x^7*RootOf((-2*x^15+10*x^13-20*x^11+20*x^
9-10*x^7+2*x^5+96*_C1)*_Z^25+(-35*x^15+175*x^13-350*x^11+350*x^9-175*x^7+35*x^5+
1680*_C1)*_Z^20+11760*_C1*_Z^15+41160*_C1*_Z^10+72030*_C1*_Z^5+50421*_C1)^5+2744
*RootOf((-2*x^15+10*x^13-20*x^11+20*x^9-10*x^7+2*x^5+96*_C1)*_Z^25+(-35*x^15+175
*x^13-350*x^11+350*x^9-175*x^7+35*x^5+1680*_C1)*_Z^20+11760*_C1*_Z^15+41160*_C1*
_Z^10+72030*_C1*_Z^5+50421*_C1)^5*x^5+131712*_C1*RootOf((-2*x^15+10*x^13-20*x^11
+20*x^9-10*x^7+2*x^5+96*_C1)*_Z^25+(-35*x^15+175*x^13-350*x^11+350*x^9-175*x^7+3
5*x^5+1680*_C1)*_Z^20+11760*_C1*_Z^15+41160*_C1*_Z^10+72030*_C1*_Z^5+50421*_C1)^
5)/x^4/(x^8-4*x^6+6*x^4-4*x^2+1)]