ODE
\[ (a+y(x)) y''(x)+b y'(x)^2=0 \] ODE Classification
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.478874 (sec), leaf count = 25
\[\left \{\left \{y(x)\to -a+((b+1) c_1 (x+c_2)){}^{\frac {1}{b+1}}\right \}\right \}\]
Maple ✓
cpu = 0.426 (sec), leaf count = 29
\[\left [y \left (x \right ) = \left (\frac {1}{\left (b +1\right ) \left (\textit {\_C1} x +\textit {\_C2} \right )}\right )^{-\frac {1}{b +1}}-a\right ]\] Mathematica raw input
DSolve[b*y'[x]^2 + (a + y[x])*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -a + ((1 + b)*C[1]*(x + C[2]))^(1 + b)^(-1)}}
Maple raw input
dsolve((a+y(x))*diff(diff(y(x),x),x)+b*diff(y(x),x)^2 = 0, y(x))
Maple raw output
[y(x) = 1/((1/(b+1)/(_C1*x+_C2))^(1/(b+1)))-a]