Internal problem ID [2339]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 38, page 173
Problem number: 2.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {-y+{y^{\prime }}^{3}=-x} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 217
dsolve(x=y(x)-diff(y(x),x)^3,y(x), singsol=all)
\begin{align*} 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 )-c_{1} &= 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}+6 \ln \left (2\right )-3 \ln \left (-4-2 i \sqrt {3}\, \left (-x +y \left (x \right )\right )^{\frac {1}{3}}-2 \left (-x +y \left (x \right )\right )^{\frac {1}{3}}\right )-c_{1} &= 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}+6 \ln \left (2\right )-3 \ln \left (2 i \sqrt {3}\, \left (-x +y \left (x \right )\right )^{\frac {1}{3}}-2 \left (-x +y \left (x \right )\right )^{\frac {1}{3}}-4\right )-c_{1} &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 11.095 (sec). Leaf size: 298
DSolve[x==y[x]-y'[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [\frac {3}{2} (y(x)-x)^{2/3}+3 \sqrt [3]{y(x)-x}+3 \log \left (\sqrt [3]{y(x)-x}-1\right )-x&=c_1,y(x)\right ] \\ \text {Solve}\left [\frac {1}{2} \left (\frac {1}{2} \sqrt [3]{y(x)-x} \left (4 i (y(x)-x)^{2/3}+3 \sqrt {3} \sqrt [3]{y(x)-x}-3 i \sqrt [3]{y(x)-x}-6 \sqrt {3}-6 i\right )+6 i \log \left (\sqrt {2-2 i \sqrt {3}}-2 i \sqrt [3]{y(x)-x}\right )\right )-i (y(x)-x)&=c_1,y(x)\right ] \\ \text {Solve}\left [\frac {y(x)}{2}+\frac {1}{4} \left (-\frac {1}{2} \sqrt [3]{y(x)-x} \left (4 (y(x)-x)^{2/3}+3 i \sqrt {3} \sqrt [3]{y(x)-x}-3 \sqrt [3]{y(x)-x}-6 i \sqrt {3}-6\right )-6 \log \left (2 i \sqrt [3]{y(x)-x}+\sqrt {2+2 i \sqrt {3}}\right )\right )&=c_1,y(x)\right ] \\ \end{align*}