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 = 0.00569826 (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

\[ \left \{ {\it \_C1}+{1 \left ( \sqrt [3]{-2\,{a}^{2}}x{{\rm Ai}\left ({\frac {{x}^{2}}{4} \left ( -2\,{a}^{2} \right ) ^{{\frac {2}{3}}}}+{\frac {a}{y \left ( x \right ) }{\frac {1}{\sqrt [3]{-2\,{a}^{2}}}}}\right )}+2\,{{\rm Ai}^{(1)}\left (1/4\, \left ( -2\,{a}^{2} \right ) ^{2/3}{x}^{2}+{\frac {a}{\sqrt [3]{-2\,{a}^{2}}y \left ( x \right ) }}\right )} \right ) \left ( \sqrt [3]{-2\,{a}^{2}}x{{\rm Bi}\left ({\frac {{x}^{2}}{4} \left ( -2\,{a}^{2} \right ) ^{{\frac {2}{3}}}}+{\frac {a}{y \left ( x \right ) }{\frac {1}{\sqrt [3]{-2\,{a}^{2}}}}}\right )}+2\,{{\rm Bi}^{(1)}\left (1/4\, \left ( -2\,{a}^{2} \right ) ^{2/3}{x}^{2}+{\frac {a}{\sqrt [3]{-2\,{a}^{2}}y \left ( x \right ) }}\right )} \right ) ^{-1}}=0 \right \} \] 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),'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