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 = 0.255006 (sec), leaf count = 20
\[\left \{\left \{y(x)\to c_2-\frac {\log (a x+c_1)}{a}\right \}\right \}\]
Maple ✓
cpu = 0.097 (sec), leaf count = 20
\[\left [y \left (x \right ) = -\frac {\ln \left (-\textit {\_C1} a x -\textit {\_C2} a \right )}{a}\right ]\] 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))
Maple raw output
[y(x) = -ln(-_C1*a*x-_C2*a)/a]