ODE
\[ a y'(x)^3+y''(x)=0 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0223869 (sec), leaf count = 50
\[\left \{\left \{y(x)\to c_2-\frac {\sqrt {2 a x-2 c_1}}{a}\right \},\left \{y(x)\to \frac {\sqrt {2 a x-2 c_1}}{a}+c_2\right \}\right \}\]
Maple ✓
cpu = 0.078 (sec), leaf count = 40
\[ \left \{ y \left ( x \right ) =-{ \left ( {\it \_C1}+x \right ) \sqrt {2}{\frac {1}{\sqrt {a \left ( {\it \_C1}+x \right ) }}}}+{\it \_C2},y \left ( x \right ) ={ \left ( {\it \_C1}+x \right ) \sqrt {2}{\frac {1}{\sqrt {a \left ( {\it \_C1}+x \right ) }}}}+{\it \_C2} \right \} \] Mathematica raw input
DSolve[a*y'[x]^3 + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(Sqrt[2*a*x - 2*C[1]]/a) + C[2]}, {y[x] -> Sqrt[2*a*x - 2*C[1]]/a + C[2]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+a*diff(y(x),x)^3 = 0, y(x),'implicit')
Maple raw output
y(x) = (_C1+x)*2^(1/2)/(a*(_C1+x))^(1/2)+_C2, y(x) = -(_C1+x)*2^(1/2)/(a*(_C1+x))^(1/2)+_C2