ODE
\[ y(x)^2 y'(x)^3+2 x y'(x)-y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries]]
Book solution method
Change of variable
Mathematica ✓
cpu = 0.199832 (sec), leaf count = 39
\[\left \{\left \{y(x)\to -\sqrt {2 c_1 x+c_1{}^3}\right \},\left \{y(x)\to \sqrt {2 c_1 x+c_1{}^3}\right \}\right \}\]
Maple ✓
cpu = 0.829 (sec), leaf count = 103
\[\left [y \left (x \right ) = -\frac {2 \,2^{\frac {1}{4}} 3^{\frac {1}{4}} \left (-x^{3}\right )^{\frac {1}{4}}}{3}, y \left (x \right ) = \frac {2 \,2^{\frac {1}{4}} 3^{\frac {1}{4}} \left (-x^{3}\right )^{\frac {1}{4}}}{3}, y \left (x \right ) = -\frac {2 i 2^{\frac {1}{4}} 3^{\frac {1}{4}} \left (-x^{3}\right )^{\frac {1}{4}}}{3}, y \left (x \right ) = \frac {2 i 2^{\frac {1}{4}} 3^{\frac {1}{4}} \left (-x^{3}\right )^{\frac {1}{4}}}{3}, y \left (x \right ) = \sqrt {\textit {\_C1}^{3}+2 x \textit {\_C1}}, y \left (x \right ) = -\sqrt {\textit {\_C1}^{3}+2 x \textit {\_C1}}\right ]\] Mathematica raw input
DSolve[-y[x] + 2*x*y'[x] + y[x]^2*y'[x]^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[2*x*C[1] + C[1]^3]}, {y[x] -> Sqrt[2*x*C[1] + C[1]^3]}}
Maple raw input
dsolve(y(x)^2*diff(y(x),x)^3+2*x*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = -2/3*2^(1/4)*3^(1/4)*(-x^3)^(1/4), y(x) = 2/3*2^(1/4)*3^(1/4)*(-x^3)^(1/4), y(x) = -2/3*I*2^(1/4)*3^(1/4)*(-x^3)^(1/4), y(x) = 2/3*I*2^(1/4)*3^(1/4)*(-x^3)^(1/4), y(x) = (_C1^3+2*_C1*x)^(1/2), y(x) = -(_C1^3+2*_C1*x)^(1/2)]