ODE
\[ y'(x)^3-(y(x)+3) y'(x)+x=0 \] ODE Classification
[_dAlembert]
Book solution method
No Missing Variables ODE, Solve for \(x\)
Mathematica ✓
cpu = 152.507 (sec), leaf count = 1
\[\text {$\$$Aborted}\]
Maple ✓
cpu = 0.024 (sec), leaf count = 63
\[ \left \{ [x \left ( {\it \_T} \right ) ={{\it \_T} \left ( 2\,\sqrt {{\it \_T}-1}\sqrt {{\it \_T}+1}+{\it \_C1} \right ) {\frac {1}{\sqrt {{\it \_T}-1}}}{\frac {1}{\sqrt {{\it \_T}+1}}}},y \left ( {\it \_T} \right ) ={1 \left ( \sqrt {{\it \_T}+1} \left ( {{\it \_T}}^{2}-1 \right ) \sqrt {{\it \_T}-1}+{\it \_C1} \right ) {\frac {1}{\sqrt {{\it \_T}-1}}}{\frac {1}{\sqrt {{\it \_T}+1}}}}] \right \} \] Mathematica raw input
DSolve[x - (3 + y[x])*y'[x] + y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(diff(y(x),x)^3-(3+y(x))*diff(y(x),x)+x = 0, y(x),'implicit')
Maple raw output
[x(_T) = 1/(_T-1)^(1/2)/(_T+1)^(1/2)*_T*(2*(_T-1)^(1/2)*(_T+1)^(1/2)+_C1), y(_T) = ((_T+1)^(1/2)*(_T^2-1)*(_T-1)^(1/2)+_C1)/(_T+1)^(1/2)/(_T-1)^(1/2)]