##### 4.2.28 $$y(x)^2 (a x+y(x))+y'(x)$$

ODE
$y(x)^2 (a x+y(x))+y'(x)$ ODE Classiﬁcation

[_Abel]

Book solution method
Abel ODE, First kind

Mathematica
cpu = 0.184316 (sec), leaf count = 0 , could not solve

DSolve[y[x]^2*(a*x + y[x]) + Derivative[1][y][x], y[x], x]

Maple
cpu = 0.084 (sec), leaf count = 62

$\left [y \left (x \right ) = \frac {2 a}{a^{2} x^{2}+2 \RootOf \left (\AiryBi \left (\textit {\_Z} \right ) \left (-2 a^{2}\right )^{\frac {1}{3}} \textit {\_C1} x +\left (-2 a^{2}\right )^{\frac {1}{3}} x \AiryAi \left (\textit {\_Z} \right )+2 \AiryBi \left (1, \textit {\_Z}\right ) \textit {\_C1} +2 \AiryAi \left (1, \textit {\_Z}\right )\right ) \left (-2 a^{2}\right )^{\frac {1}{3}}}\right ]$ Mathematica raw input

DSolve[y[x]^2*(a*x + y[x]) + y'[x],y[x],x]

Mathematica raw output

DSolve[y[x]^2*(a*x + y[x]) + Derivative[1][y][x], y[x], x]

Maple raw input

dsolve(diff(y(x),x)+(a*x+y(x))*y(x)^2, y(x))

Maple raw output

[y(x) = 2*a/(a^2*x^2+2*RootOf(AiryBi(_Z)*(-2*a^2)^(1/3)*_C1*x+(-2*a^2)^(1/3)*x*A
iryAi(_Z)+2*AiryBi(1,_Z)*_C1+2*AiryAi(1,_Z))*(-2*a^2)^(1/3))]