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 = 1.2305 (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 = 0.482 (sec), leaf count = 38
\[\left [y \left (x \right ) = {\mathrm e}^{\int _{}^{\ln \left (x \right )}\RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a}}{\textit {\_a}^{3}-\textit {\_a}^{2}+a}d \textit {\_a} \right )-\textit {\_b} +\textit {\_C1} \right )d \textit {\_b} +\textit {\_C2}}\right ]\] 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))
Maple raw output
[y(x) = exp(Intat(RootOf(-Intat(_a/(_a^3-_a^2+a),_a = _Z)-_b+_C1),_b = ln(x))+_C2)]