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 = 0.0354637 (sec), leaf count = 26
\[\left \{\left \{y(x)\to c_2 \left (-a x-c_1+x\right ){}^{\frac {1}{1-a}}\right \}\right \}\]
Maple ✓
cpu = 0.017 (sec), leaf count = 26
\[ \left \{ -{\frac {y \left ( x \right ) }{ \left ( a-1 \right ) \left ( y \left ( x \right ) \right ) ^{a}}}-{\it \_C1}\,x-{\it \_C2}=0 \right \} \] 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),'implicit')
Maple raw output
-y(x)/(a-1)/(y(x)^a)-_C1*x-_C2 = 0