Internal problem ID [15129]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 11. Singular solutions of differential equations. Exercises page 92
Problem number: 267.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2}-27 y=-27 x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 37
dsolve(8*diff(y(x),x)^3-12*diff(y(x),x)^2=27*(y(x)-x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= x -\frac {4}{27} \\ y \left (x \right ) &= \left (-x +c_{1} \right ) \sqrt {x -c_{1}}+c_{1} \\ y \left (x \right ) &= \left (x -c_{1} \right )^{\frac {3}{2}}+c_{1} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[8*y'[x]^3-12*y'[x]^2==27*(y[x]-x),y[x],x,IncludeSingularSolutions -> True]
Timed out