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 = 1.63348 (sec), leaf count = 315
\[\left \{\text {Solve}\left [x=\frac {3}{2} (y(x)-x)^{2/3}+3 \sqrt [3]{y(x)-x}+3 \log \left (1-\sqrt [3]{y(x)-x}\right )+c_1,y(x)\right ],\text {Solve}\left [\frac {1}{2} \left (3 \sqrt [3]{y(x)-x} \left (\sqrt [3]{y(x)-x}+i \sqrt {3}-1\right )+\left (-3-3 i \sqrt {3}\right ) \log \left (2 \sqrt [3]{y(x)-x}-i \sqrt {3}+1\right )+i \sqrt {3} x+x\right )=c_1,y(x)\right ],\text {Solve}\left [\left (1-2 (-1)^{2/3}\right ) \log (-y(x)+x+1)+2 \left (3 \sqrt [3]{-1} \sqrt [3]{y(x)-x}+\sqrt [3]{-1} \log \left (1-\sqrt [3]{y(x)-x}\right )+(-1)^{2/3} x+(-1)^{2/3}+c_1\right )=3 (y(x)-x)^{2/3}+3 \log \left (1-\sqrt [3]{y(x)-x}\right )+\sqrt [3]{-1} \log \left ((y(x)-x)^{2/3}+\sqrt [3]{y(x)-x}+1\right )+2 \sqrt {3} \left (1+\sqrt [3]{-1}\right ) \tan ^{-1}\left (\frac {2 \sqrt [3]{y(x)-x}+1}{\sqrt {3}}\right ),y(x)\right ]\right \}\]
Maple ✓
cpu = 0.153 (sec), leaf count = 209
\[\left [x -\frac {3 \left (-x +y \left (x \right )\right )^{\frac {2}{3}}}{2}-3 \left (-x +y \left (x \right )\right )^{\frac {1}{3}}-3 \ln \left (\left (-x +y \left (x \right )\right )^{\frac {1}{3}}-1\right )-\textit {\_C1} = 0, x +\frac {3 \left (-x +y \left (x \right )\right )^{\frac {2}{3}}}{4}-\frac {3 i \sqrt {3}\, \left (-x +y \left (x \right )\right )^{\frac {2}{3}}}{4}+\frac {3 \left (-x +y \left (x \right )\right )^{\frac {1}{3}}}{2}+\frac {3 i \sqrt {3}\, \left (-x +y \left (x \right )\right )^{\frac {1}{3}}}{2}-3 \ln \left (-\frac {\left (-x +y \left (x \right )\right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (-x +y \left (x \right )\right )^{\frac {1}{3}}}{2}-1\right )-\textit {\_C1} = 0, x +\frac {3 \left (-x +y \left (x \right )\right )^{\frac {2}{3}}}{4}+\frac {3 i \sqrt {3}\, \left (-x +y \left (x \right )\right )^{\frac {2}{3}}}{4}+\frac {3 \left (-x +y \left (x \right )\right )^{\frac {1}{3}}}{2}-\frac {3 i \sqrt {3}\, \left (-x +y \left (x \right )\right )^{\frac {1}{3}}}{2}-3 \ln \left (-\frac {\left (-x +y \left (x \right )\right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (-x +y \left (x \right )\right )^{\frac {1}{3}}}{2}-1\right )-\textit {\_C1} = 0\right ]\] 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 + I*Sqrt[3]*x + (-3 - (3*I)*Sqrt[3])*Log[1 - I*Sqrt[3] + 2*(-x + y[x])^(1/3)] + 3*(-x + y[x])^(1/3)*(-1 + I*Sqrt[3] + (-x + y[x])^(1/3)))/2 == C[1], y[x]], Solve[(1 - 2*(-1)^(2/3))*Log[1 + x - y[x]] + 2*((-1)^(2/3) + (-1)^(2/3)*x + C[1] + (-1)^(1/3)*Log[1 - (-x + y[x])^(1/3)] + 3*(-1)^(1/3)*(-x + y[x])^(1/3)) == 2*Sqrt[3]*(1 + (-1)^(1/3))*ArcTan[(1 + 2*(-x + y[x])^(1/3))/Sqrt[3]] + 3*Log[1 - (-x + y[x])^(1/3)] + (-1)^(1/3)*Log[1 + (-x + y[x])^(1/3) + (-x + y[x])^(2/3)] + 3*(-x + y[x])^(2/3), y[x]]}
Maple raw input
dsolve(diff(y(x),x)^3+x-y(x) = 0, y(x))
Maple raw output
[x-3/2*(-x+y(x))^(2/3)-3*(-x+y(x))^(1/3)-3*ln((-x+y(x))^(1/3)-1)-_C1 = 0, x+3/4*(-x+y(x))^(2/3)-3/4*I*3^(1/2)*(-x+y(x))^(2/3)+3/2*(-x+y(x))^(1/3)+3/2*I*3^(1/2)*(-x+y(x))^(1/3)-3*ln(-1/2*(-x+y(x))^(1/3)-1/2*I*3^(1/2)*(-x+y(x))^(1/3)-1)-_C1 = 0, x+3/4*(-x+y(x))^(2/3)+3/4*I*3^(1/2)*(-x+y(x))^(2/3)+3/2*(-x+y(x))^(1/3)-3/2*I*3^(1/2)*(-x+y(x))^(1/3)-3*ln(-1/2*(-x+y(x))^(1/3)+1/2*I*3^(1/2)*(-x+y(x))^(1/3)-1)-_C1 = 0]