ODE
\[ a+x y'(x)^3-y(x) y'(x)^2=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.145663 (sec), leaf count = 16
\[\left \{\left \{y(x)\to \frac {a}{c_1{}^2}+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.083 (sec), leaf count = 92
\[\left [y \left (x \right ) = \frac {3 \,2^{\frac {1}{3}} \left (a \,x^{2}\right )^{\frac {1}{3}}}{2}, y \left (x \right ) = -\frac {3 \,2^{\frac {1}{3}} \left (a \,x^{2}\right )^{\frac {1}{3}}}{4}-\frac {3 i \sqrt {3}\, 2^{\frac {1}{3}} \left (a \,x^{2}\right )^{\frac {1}{3}}}{4}, y \left (x \right ) = -\frac {3 \,2^{\frac {1}{3}} \left (a \,x^{2}\right )^{\frac {1}{3}}}{4}+\frac {3 i \sqrt {3}\, 2^{\frac {1}{3}} \left (a \,x^{2}\right )^{\frac {1}{3}}}{4}, y \left (x \right ) = x \textit {\_C1} +\frac {a}{\textit {\_C1}^{2}}\right ]\] Mathematica raw input
DSolve[a - y[x]*y'[x]^2 + x*y'[x]^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> a/C[1]^2 + x*C[1]}}
Maple raw input
dsolve(x*diff(y(x),x)^3-y(x)*diff(y(x),x)^2+a = 0, y(x))
Maple raw output
[y(x) = 3/2*2^(1/3)*(a*x^2)^(1/3), y(x) = -3/4*2^(1/3)*(a*x^2)^(1/3)-3/4*I*3^(1/2)*2^(1/3)*(a*x^2)^(1/3), y(x) = -3/4*2^(1/3)*(a*x^2)^(1/3)+3/4*I*3^(1/2)*2^(1/3)*(a*x^2)^(1/3), y(x) = x*_C1+a/_C1^2]