##### 4.10.43 $$(5 y(x)+7 x) y'(x)+8 y(x)+10 x=0$$

ODE
$(5 y(x)+7 x) y'(x)+8 y(x)+10 x=0$ ODE Classiﬁcation

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

Book solution method
Homogeneous equation

Mathematica
cpu = 0.178264 (sec), leaf count = 276

$\left \{\left \{y(x)\to \text {Root}\left [\text {\#1}^5+8 \text {\#1}^4 x+25 \text {\#1}^3 x^2+38 \text {\#1}^2 x^3+28 \text {\#1} x^4+8 x^5-e^{c_1}\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [\text {\#1}^5+8 \text {\#1}^4 x+25 \text {\#1}^3 x^2+38 \text {\#1}^2 x^3+28 \text {\#1} x^4+8 x^5-e^{c_1}\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [\text {\#1}^5+8 \text {\#1}^4 x+25 \text {\#1}^3 x^2+38 \text {\#1}^2 x^3+28 \text {\#1} x^4+8 x^5-e^{c_1}\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [\text {\#1}^5+8 \text {\#1}^4 x+25 \text {\#1}^3 x^2+38 \text {\#1}^2 x^3+28 \text {\#1} x^4+8 x^5-e^{c_1}\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [\text {\#1}^5+8 \text {\#1}^4 x+25 \text {\#1}^3 x^2+38 \text {\#1}^2 x^3+28 \text {\#1} x^4+8 x^5-e^{c_1}\& ,5\right ]\right \}\right \}$

Maple
cpu = 0.237 (sec), leaf count = 40

$[y \left (x \right ) = x \RootOf \left (x^{5} \textit {\_C1} \,\textit {\_Z}^{25}-2 x^{5} \textit {\_C1} \,\textit {\_Z}^{20}+x^{5} \textit {\_C1} \,\textit {\_Z}^{15}-1\right )^{5}-2 x]$ Mathematica raw input

DSolve[10*x + 8*y[x] + (7*x + 5*y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> Root[-E^C[1] + 8*x^5 + 28*x^4*#1 + 38*x^3*#1^2 + 25*x^2*#1^3 + 8*x*#1^
4 + #1^5 & , 1]}, {y[x] -> Root[-E^C[1] + 8*x^5 + 28*x^4*#1 + 38*x^3*#1^2 + 25*x
^2*#1^3 + 8*x*#1^4 + #1^5 & , 2]}, {y[x] -> Root[-E^C[1] + 8*x^5 + 28*x^4*#1 + 3
8*x^3*#1^2 + 25*x^2*#1^3 + 8*x*#1^4 + #1^5 & , 3]}, {y[x] -> Root[-E^C[1] + 8*x^
5 + 28*x^4*#1 + 38*x^3*#1^2 + 25*x^2*#1^3 + 8*x*#1^4 + #1^5 & , 4]}, {y[x] -> Ro
ot[-E^C[1] + 8*x^5 + 28*x^4*#1 + 38*x^3*#1^2 + 25*x^2*#1^3 + 8*x*#1^4 + #1^5 & ,
 5]}}

Maple raw input

dsolve((7*x+5*y(x))*diff(y(x),x)+10*x+8*y(x) = 0, y(x))

Maple raw output

[y(x) = x*RootOf(_C1*_Z^25*x^5-2*_C1*_Z^20*x^5+_C1*_Z^15*x^5-1)^5-2*x]