ODE
\[ y''(x)=a y'(x)^2 \] ODE Classification
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0284116 (sec), leaf count = 20
\[\left \{\left \{y(x)\to c_2-\frac {\log \left (a x+c_1\right )}{a}\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 22
\[ \left \{ -{\frac {{{\rm e}^{-ay \left ( x \right ) }}}{a}}-{\it \_C1}\,x-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[y''[x] == a*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> C[2] - Log[a*x + C[1]]/a}}
Maple raw input
dsolve(diff(diff(y(x),x),x) = a*diff(y(x),x)^2, y(x),'implicit')
Maple raw output
-1/a*exp(-a*y(x))-_C1*x-_C2 = 0