4.2.28 $y(x{)}^2(ax+y(x))+y^{\prime }(x)$

ODE
$$y(x{)}^2(ax+y(x))+y^{\prime }(x)$$ ODE Classification

[_Abel]

Book solution method
Abel ODE, First kind

Mathematica ✗
cpu = 0.00569826 (sec), leaf count = 0 , could not solve

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

Maple ✓
cpu = 0.071 (sec), leaf count = 142

$$\{\mathit{\_}\mathit{C}\mathit{1}+1(\sqrt[3]{-2a^2}x\mathrm{A}\mathrm{i}(\frac{x^2}{4}{(-2a^2)}^{\frac{2}{3}}+\frac{a}{y\left(x\right)}\frac{1}{\sqrt[3]{-2a^2}})+2{\mathrm{A}\mathrm{i}}^{(1)}(1/4{(-2a^2)}^{2/3}{x}^2+\frac{a}{\sqrt[3]{-2a^2}y\left(x\right)})){(\sqrt[3]{-2a^2}x\mathrm{B}\mathrm{i}(\frac{x^2}{4}{(-2a^2)}^{\frac{2}{3}}+\frac{a}{y\left(x\right)}\frac{1}{\sqrt[3]{-2a^2}})+2{\mathrm{B}\mathrm{i}}^{(1)}(1/4{(-2a^2)}^{2/3}{x}^2+\frac{a}{\sqrt[3]{-2a^2}y\left(x\right)}))}^{-1}=0\}$$ 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),'implicit')

Maple raw output

_C1+((-2*a^2)^(1/3)*x*AiryAi(1/4*(-2*a^2)^(2/3)*x^2+1/(-2*a^2)^(1/3)*a/y(x))+2*A
iryAi(1,1/4*(-2*a^2)^(2/3)*x^2+1/(-2*a^2)^(1/3)*a/y(x)))/((-2*a^2)^(1/3)*x*AiryB
i(1/4*(-2*a^2)^(2/3)*x^2+1/(-2*a^2)^(1/3)*a/y(x))+2*AiryBi(1,1/4*(-2*a^2)^(2/3)*
x^2+1/(-2*a^2)^(1/3)*a/y(x))) = 0