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))]