ODE
\[ y'(x)^3-y(x)+x=0 \] ODE Classification
[[_homogeneous, `class C`], _dAlembert]
Book solution method
No Missing Variables ODE, Solve for \(x\)
Mathematica ✓
cpu = 1.49439 (sec), leaf count = 336
\[\left \{\text {Solve}\left [x=c_1+\frac {3}{2} (y(x)-x)^{2/3}+3 \sqrt [3]{y(x)-x}+3 \log \left (1-\sqrt [3]{y(x)-x}\right ),y(x)\right ],\text {Solve}\left [3 \sqrt [3]{-1} \sqrt [3]{y(x)-x}+\log \left (1-\sqrt [3]{y(x)-x}\right )-3 i \tan ^{-1}\left (\frac {2 \sqrt [3]{y(x)-x}+1}{\sqrt {3}}\right )+x=c_1+\frac {3}{2} (-1)^{2/3} (y(x)-x)^{2/3}+\log (-y(x)+x+1)+\frac {1}{2} \log \left ((y(x)-x)^{2/3}+\sqrt [3]{y(x)-x}+1\right ),y(x)\right ],\text {Solve}\left [(-1)^{2/3} (y(x)-x)+\frac {3}{2} (y(x)-x)^{2/3}+(-1)^{2/3} \log (-y(x)+x+1)+\frac {1}{2} \left (\sqrt [3]{-1}-1\right ) \log \left ((y(x)-x)^{2/3}+\sqrt [3]{y(x)-x}+1\right )+\sqrt {3} \left (1+\sqrt [3]{-1}\right ) \tan ^{-1}\left (\frac {2 \sqrt [3]{y(x)-x}+1}{\sqrt {3}}\right )=c_1+(-1)^{2/3} y(x)+3 \sqrt [3]{-1} \sqrt [3]{y(x)-x}+\left (\sqrt [3]{-1}-1\right ) \log \left (1-\sqrt [3]{y(x)-x}\right ),y(x)\right ]\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 43
\[ \left \{ [x \left ( {\it \_T} \right ) ={\frac {3\,{{\it \_T}}^{2}}{2}}+3\,{\it \_T}+3\,\ln \left ( {\it \_T}-1 \right ) +{\it \_C1},y \left ( {\it \_T} \right ) ={{\it \_T}}^{3}+{\frac {3\,{{\it \_T}}^{2}}{2}}+3\,{\it \_T}+3\,\ln \left ( {\it \_T}-1 \right ) +{\it \_C1}] \right \} \] Mathematica raw input
DSolve[x - y[x] + y'[x]^3 == 0,y[x],x]
Mathematica raw output
{Solve[x == C[1] + 3*Log[1 - (-x + y[x])^(1/3)] + 3*(-x + y[x])^(1/3) + (3*(-x + y[x])^(2/3))/2, y[x]], Solve[x - (3*I)*ArcTan[(1 + 2*(-x + y[x])^(1/3))/Sqrt[3]] + Log[1 - (-x + y[x])^(1/3)] + 3*(-1)^(1/3)*(-x + y[x])^(1/3) == C[1] + Log[1 + x - y[x]] + Log[1 + (-x + y[x])^(1/3) + (-x + y[x])^(2/3)]/2 + (3*(-1)^(2/3)*(-x + y[x])^(2/3))/2, y[x]], Solve[Sqrt[3]*(1 + (-1)^(1/3))*ArcTan[(1 + 2*(-x + y[x])^(1/3))/Sqrt[3]] + (-1)^(2/3)*Log[1 + x - y[x]] + ((-1 + (-1)^(1/3))*Log[1 + (-x + y[x])^(1/3) + (-x + y[x])^(2/3)])/2 + (3*(-x + y[x])^(2/3))/2 + (-1)^(2/3)*(-x + y[x]) == C[1] + (-1 + (-1)^(1/3))*Log[1 - (-x + y[x])^(1/3)] + (-1)^(2/3)*y[x] + 3*(-1)^(1/3)*(-x + y[x])^(1/3), y[x]]}
Maple raw input
dsolve(diff(y(x),x)^3+x-y(x) = 0, y(x),'implicit')
Maple raw output
[x(_T) = 3/2*_T^2+3*_T+3*ln(_T-1)+_C1, y(_T) = _T^3+3/2*_T^2+3*_T+3*ln(_T-1)+_C1]