ODE
\[ y(x)^2 y'(x)^3-x y'(x)+y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries]]
Book solution method
No Missing Variables ODE, Solve for \(x\)
Mathematica ✗
cpu = 600.021 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.928 (sec), leaf count = 185
\[\left [y \left (x \right ) = -\frac {2 \sqrt {-24 \textit {\_C1}^{3}+27 x \textit {\_C1} -3 \sqrt {64 \textit {\_C1}^{6}-144 \textit {\_C1}^{4} x +108 \textit {\_C1}^{2} x^{2}-27 x^{3}}}}{9}, y \left (x \right ) = \frac {2 \sqrt {-24 \textit {\_C1}^{3}+27 x \textit {\_C1} -3 \sqrt {64 \textit {\_C1}^{6}-144 \textit {\_C1}^{4} x +108 \textit {\_C1}^{2} x^{2}-27 x^{3}}}}{9}, y \left (x \right ) = -\frac {2 \sqrt {-24 \textit {\_C1}^{3}+27 x \textit {\_C1} +3 \sqrt {64 \textit {\_C1}^{6}-144 \textit {\_C1}^{4} x +108 \textit {\_C1}^{2} x^{2}-27 x^{3}}}}{9}, y \left (x \right ) = \frac {2 \sqrt {-24 \textit {\_C1}^{3}+27 x \textit {\_C1} +3 \sqrt {64 \textit {\_C1}^{6}-144 \textit {\_C1}^{4} x +108 \textit {\_C1}^{2} x^{2}-27 x^{3}}}}{9}\right ]\] Mathematica raw input
DSolve[y[x] - x*y'[x] + y[x]^2*y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(y(x)^2*diff(y(x),x)^3-x*diff(y(x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = -2/9*(-24*_C1^3+27*x*_C1-3*(64*_C1^6-144*_C1^4*x+108*_C1^2*x^2-27*x^3)^(1/2))^(1/2), y(x) = 2/9*(-24*_C1^3+27*x*_C1-3*(64*_C1^6-144*_C1^4*x+108*_C1^2*x^2-27*x^3)^(1/2))^(1/2), y(x) = -2/9*(-24*_C1^3+27*x*_C1+3*(64*_C1^6-144*_C1^4*x+108*_C1^2*x^2-27*x^3)^(1/2))^(1/2), y(x) = 2/9*(-24*_C1^3+27*x*_C1+3*(64*_C1^6-144*_C1^4*x+108*_C1^2*x^2-27*x^3)^(1/2))^(1/2)]