ODE
\[ a \left (y(x)^2-1\right ) y'(x)+b y(x)+y''(x)=0 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✗
cpu = 32.9431 (sec), leaf count = 0 , could not solve
DSolve[b*y[x] + a*(-1 + y[x]^2)*Derivative[1][y][x] + Derivative[2][y][x] == 0, y[x], x]
Maple ✓
cpu = 1.026 (sec), leaf count = 60
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) + \left ( {{\it \_a}}^{2}a-a \right ) {\it \_b} \left ( {\it \_a} \right ) +b{\it \_a}=0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[b*y[x] + a*(-1 + y[x]^2)*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[b*y[x] + a*(-1 + y[x]^2)*Derivative[1][y][x] + Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(diff(diff(y(x),x),x)+a*(y(x)^2-1)*diff(y(x),x)+b*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(_a,[{diff(_b(_a),_a)*_b(_a)+(_a^2*a-a)*_b(_a)+b*_a = 0}, {_a = y(x), _b(_a) = diff(y(x),x)}, {x = Int(1/_b(_a),_a)+_C1, y(x) = _a}])