ODE
\[ a y(x) y'(x)^2+b y(x)+y''(x)=0 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
Book solution method
TO DO
Mathematica ✗
cpu = 200.27 (sec), leaf count = 0 , could not solve
DSolve[b*y[x] + a*y[x]*Derivative[1][y][x]^2 + Derivative[2][y][x] == 0, y[x], x]
Maple ✓
cpu = 0.167 (sec), leaf count = 70
\[ \left \{ \int ^{y \left ( x \right ) }\!{a{\frac {1}{\sqrt {a \left ( {{\rm e}^{-{{\it \_a}}^{2}a}}{\it \_C1}\,a-b \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{a{\frac {1}{\sqrt {a \left ( {{\rm e}^{-{{\it \_a}}^{2}a}}{\it \_C1}\,a-b \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[b*y[x] + a*y[x]*y'[x]^2 + y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[b*y[x] + a*y[x]*Derivative[1][y][x]^2 + Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(diff(diff(y(x),x),x)+a*y(x)*diff(y(x),x)^2+b*y(x) = 0, y(x),'implicit')
Maple raw output
Intat(a/(a*(exp(-_a^2*a)*_C1*a-b))^(1/2),_a = y(x))-x-_C2 = 0, Intat(-a/(a*(exp(-_a^2*a)*_C1*a-b))^(1/2),_a = y(x))-x-_C2 = 0