ODE
\[ a y(x) y''(x)=(a-1) y'(x)^2 \] 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 = 0.291987 (sec), leaf count = 17
\[\left \{\left \{y(x)\to c_2 (x-a c_1){}^a\right \}\right \}\]
Maple ✓
cpu = 0.251 (sec), leaf count = 15
\[\left [y \left (x \right ) = \left (\frac {\textit {\_C1} x +\textit {\_C2}}{a}\right )^{a}\right ]\] Mathematica raw input
DSolve[a*y[x]*y''[x] == (-1 + a)*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (x - a*C[1])^a*C[2]}}
Maple raw input
dsolve(a*y(x)*diff(diff(y(x),x),x) = (a-1)*diff(y(x),x)^2, y(x))
Maple raw output
[y(x) = ((_C1*x+_C2)/a)^a]