ODE
\[ a y'(x)+b x e^{y(x)}+x y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.603581 (sec), leaf count = 0 , could not solve
DSolve[b*E^y[x]*x + a*Derivative[1][y][x] + x*Derivative[2][y][x] == 0, y[x], x]
Maple ✓
cpu = 0.916 (sec), leaf count = 93
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}-2\,\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}-2\,{\it \_C1},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) = \left ( b{{\rm e}^{{\it \_a}}}-2\,a+2 \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}+ \left ( a-1 \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2} \right \} , \left \{ {\it \_a}=y \left ( x \right ) +2\,\ln \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) = \left ( x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2 \right ) ^{-1} \right \} , \left \{ x={{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},y \left ( x \right ) ={\it \_a}-2\,\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}-2\,{\it \_C1} \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[b*E^y[x]*x + a*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[b*E^y[x]*x + a*Derivative[1][y][x] + x*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+a*diff(y(x),x)+b*x*exp(y(x)) = 0, y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(_a-2*Int(_b(_a),_a)-2*_C1,[{diff(_b(_a),_a) = (b*exp(_a)-2*a+2)*_b(_a)^3+(a-1)*_b(_a)^2}, {_a = y(x)+2*ln(x), _b(_a) = 1/(x*diff(y(x),x)+2)}, {x = exp(Int(_b(_a),_a)+_C1), y(x) = _a-2*Int(_b(_a),_a)-2*_C1}])