ODE
\[ 4 x y'(x)^3-6 y(x) y'(x)^2+3 y(x)-x=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _dAlembert]
Book solution method
No Missing Variables ODE, Solve for \(y\)
Mathematica ✓
cpu = 0.222654 (sec), leaf count = 74
\[\left \{\left \{y(x)\to -\frac {\sqrt {2} \sqrt {c_1 (x+c_1){}^3}+c_1{}^2}{3 c_1}\right \},\left \{y(x)\to -\frac {c_1{}^2-\sqrt {2} \sqrt {c_1 (x+c_1){}^3}}{3 c_1}\right \}\right \}\]
Maple ✓
cpu = 0.119 (sec), leaf count = 102
\[\left [y \left (x \right ) = x, y \left (x \right ) = \left (-\frac {1}{2}-\frac {\sqrt {3}}{2}\right ) x, y \left (x \right ) = \left (\frac {\sqrt {3}}{2}-\frac {1}{2}\right ) x, y \left (x \right ) = \frac {\left (\frac {\left (x +\textit {\_C1} \right ) \sqrt {2}\, \sqrt {\textit {\_C1} \left (x +\textit {\_C1} \right )}}{\textit {\_C1}^{2}}+1\right ) x}{-\frac {3 \left (x +\textit {\_C1} \right )}{\textit {\_C1}}+3}, y \left (x \right ) = \frac {\left (-\frac {\left (x +\textit {\_C1} \right ) \sqrt {2}\, \sqrt {\textit {\_C1} \left (x +\textit {\_C1} \right )}}{\textit {\_C1}^{2}}+1\right ) x}{-\frac {3 \left (x +\textit {\_C1} \right )}{\textit {\_C1}}+3}\right ]\] Mathematica raw input
DSolve[-x + 3*y[x] - 6*y[x]*y'[x]^2 + 4*x*y'[x]^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -1/3*(C[1]^2 + Sqrt[2]*Sqrt[C[1]*(x + C[1])^3])/C[1]}, {y[x] -> -1/3*(C[1]^2 - Sqrt[2]*Sqrt[C[1]*(x + C[1])^3])/C[1]}}
Maple raw input
dsolve(4*x*diff(y(x),x)^3-6*y(x)*diff(y(x),x)^2-x+3*y(x) = 0, y(x))
Maple raw output
[y(x) = x, y(x) = (-1/2-1/2*3^(1/2))*x, y(x) = (1/2*3^(1/2)-1/2)*x, y(x) = (1/_C1^2*(x+_C1)*2^(1/2)*(_C1*(x+_C1))^(1/2)+1)/(-3/_C1*(x+_C1)+3)*x, y(x) = (-1/_C1^2*(x+_C1)*2^(1/2)*(_C1*(x+_C1))^(1/2)+1)/(-3/_C1*(x+_C1)+3)*x]