ODE
\[ y'(x)^3 (a x+b y(x))+y''(x)=0 \] ODE Classification
[[_2nd_order, _with_exponential_symmetries], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]
Book solution method
TO DO
Mathematica ✓
cpu = 2.11554 (sec), leaf count = 154
\[\left \{\text {Solve}\left [\frac {b \log \left (a^2 x+\sqrt {a} \sqrt {a^3 x^2+2 a^2 b x y(x)+b^2 \left (a y(x)^2-2 a c_1+1\right )}+a b y(x)\right )}{\sqrt {a}}+a c_2+b y(x)=0,y(x)\right ],\text {Solve}\left [b y(x)+a c_2=\frac {b \log \left (a^2 x+\sqrt {a} \sqrt {a^3 x^2+2 a^2 b x y(x)+b^2 \left (a y(x)^2-2 a c_1+1\right )}+a b y(x)\right )}{\sqrt {a}},y(x)\right ]\right \}\]
Maple ✓
cpu = 1.837 (sec), leaf count = 35
\[\left [y \left (x \right ) = \frac {\RootOf \left (-{\mathrm e}^{2 \textit {\_Z}} a \textit {\_C2} -2 \,{\mathrm e}^{\textit {\_Z}} a^{\frac {3}{2}} x -2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} b +\textit {\_C1} a \right )}{\sqrt {a}}\right ]\] Mathematica raw input
DSolve[(a*x + b*y[x])*y'[x]^3 + y''[x] == 0,y[x],x]
Mathematica raw output
{Solve[a*C[2] + (b*Log[a^2*x + a*b*y[x] + Sqrt[a]*Sqrt[a^3*x^2 + 2*a^2*b*x*y[x] + b^2*(1 - 2*a*C[1] + a*y[x]^2)]])/Sqrt[a] + b*y[x] == 0, y[x]], Solve[a*C[2] + b*y[x] == (b*Log[a^2*x + a*b*y[x] + Sqrt[a]*Sqrt[a^3*x^2 + 2*a^2*b*x*y[x] + b^2*(1 - 2*a*C[1] + a*y[x]^2)]])/Sqrt[a], y[x]]}
Maple raw input
dsolve(diff(diff(y(x),x),x)+(a*x+b*y(x))*diff(y(x),x)^3 = 0, y(x))
Maple raw output
[y(x) = RootOf(-exp(_Z)^2*a*_C2-2*exp(_Z)*a^(3/2)*x-2*_Z*exp(_Z)*b+_C1*a)/a^(1/2)]