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 = 1.0001 (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 = 0.049 (sec), leaf count = 99

\[ \left \{ {\frac {7}{5}\ln \left ({\frac {-35\,x-35\,y \relax (x ) }{8\,{x}^{3}+2\,x+10\,y \relax (x ) }} \right ) }+{\frac {7}{20}\ln \left ({\frac {140\,{x}^{3}+140\,y \relax (x ) }{12\,{x}^{3}+3\,x+15\,y \relax (x ) }} \right ) }-{\frac {7}{4}\ln \left ({\frac {28\,{x}^{3}-28\,x}{x+4\,{x}^{3}+5\,y \relax (x ) }} \right ) }+{\frac {7\,\ln \left ({x}^{3}-x \right ) }{4}}-{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

7/5*ln((-35*x-35*y(x))/(8*x^3+2*x+10*y(x)))+7/20*ln((140*x^3+140*y(x))/(12*x^3+3
*x+15*y(x)))-7/4*ln((28*x^3-28*x)/(x+4*x^3+5*y(x)))+7/4*ln(x^3-x)-_C1 = 0