ODE
\[ a y(x)^2+x^3 y'(x) y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 90.6311 (sec), leaf count = 0 , could not solve
DSolve[a*y[x]^2 + x^3*Derivative[1][y][x]*Derivative[2][y][x] == 0, y[x], x]
Maple ✓
cpu = 0.173 (sec), leaf count = 38
\[ \left \{ y \left ( x \right ) ={{\rm e}^{\int ^{\ln \left ( x \right ) }\!{\it RootOf} \left ( -\int ^{{\it \_Z}}\!{\frac {{\it \_a}}{{{\it \_a}}^{3}-{{\it \_a}}^{2}+a}}{d{\it \_a}}-{\it \_b}+{\it \_C1} \right ) {d{\it \_b}}+{\it \_C2}}} \right \} \] Mathematica raw input
DSolve[a*y[x]^2 + x^3*y'[x]*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[a*y[x]^2 + x^3*Derivative[1][y][x]*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(x^3*diff(y(x),x)*diff(diff(y(x),x),x)+a*y(x)^2 = 0, y(x),'implicit')
Maple raw output
y(x) = exp(Intat(RootOf(-Intat(_a/(_a^3-_a^2+a),_a = _Z)-_b+_C1),_b = ln(x))+_C2)