ODE
\[ a y(x) y'(x)^2+b x+x^2 y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 208.267 (sec), leaf count = 0 , could not solve
DSolve[b*x + a*y[x]*Derivative[1][y][x]^2 + x^2*Derivative[2][y][x] == 0, y[x], x]
Maple ✓
cpu = 2.577 (sec), leaf count = 101
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) = \left ( {{\it \_a}}^{3}a+b \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}+ \left ( 2\,{{\it \_a}}^{2}a+1 \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+{\it \_b} \left ( {\it \_a} \right ) a{\it \_a} \right \} , \left \{ {\it \_a}={\frac {y \left ( x \right ) }{x}},{\it \_b} \left ( {\it \_a} \right ) ={\frac {x}{x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) }} \right \} , \left \{ x={{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},y \left ( x \right ) ={\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[b*x + a*y[x]*y'[x]^2 + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[b*x + a*y[x]*Derivative[1][y][x]^2 + x^2*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+a*y(x)*diff(y(x),x)^2+b*x = 0, y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(_a*exp(Int(_b(_a),_a)+_C1),[{diff(_b(_a),_a) = (_a^3*a+b)*_b(_a)^3+(2*_a^2*a+1)*_b(_a)^2+_b(_a)*a*_a}, {_a = y(x)/x, _b(_a) = x/(x*diff(y(x),x)-y(x))}, {x = exp(Int(_b(_a),_a)+_C1), y(x) = _a*exp(Int(_b(_a),_a)+_C1)}])