ODE
\[ y(x) y''(x)=a y'(x)^2 \] 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 = 0.29333 (sec), leaf count = 26
\[\left \{\left \{y(x)\to c_2 (-a x+x-c_1){}^{\frac {1}{1-a}}\right \}\right \}\]
Maple ✓
cpu = 0.446 (sec), leaf count = 25
\[\left [y \left (x \right ) = \left (\frac {1}{\left (1-a \right ) \left (\textit {\_C1} x +\textit {\_C2} \right )}\right )^{\frac {1}{a -1}}\right ]\] Mathematica raw input
DSolve[y[x]*y''[x] == a*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (x - a*x - C[1])^(1 - a)^(-1)*C[2]}}
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x) = a*diff(y(x),x)^2, y(x))
Maple raw output
[y(x) = (1/(1-a)/(_C1*x+_C2))^(1/(a-1))]