ODE
\[ a \sqrt [3]{y'(x)^3+1}+x y'(x)-y(x)=0 \] ODE Classification
[_Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.00438413 (sec), leaf count = 22
\[\left \{\left \{y(x)\to a \sqrt [3]{c_1^3+1}+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.028 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) =a\sqrt [3]{{{\it \_C1}}^{3}+1}+{\it \_C1}\,x \right \} \] Mathematica raw input
DSolve[-y[x] + x*y'[x] + a*(1 + y'[x]^3)^(1/3) == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] + a*(1 + C[1]^3)^(1/3)}}
Maple raw input
dsolve(a*(1+diff(y(x),x)^3)^(1/3)+x*diff(y(x),x)-y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = a*(_C1^3+1)^(1/3)+_C1*x